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			{{Short description|Arab physicist, mathematician and astronomer (c. 965 – c. 1040)}}
	:''This article is about the scientist. For the crater on the Moon named after him, see ].''
			{{redirect2|Alhazen|Alhaitham|other uses|Alhazen (disambiguation)|the fictional character|List of Genshin Impact characters#Alhaitham}}
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	{{Infobox_Muslim scholars |
			{{Use dmy dates|date=March 2022}}
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			{{Infobox scientist
	<!-- Philosopher Category -->
			| name = Alhazen<br />{{transliteration|ar|Ḥasan Ibn al-Haytham}}
	region = ]|
			| native_name = {{lang|ar|ابن الهيثم}}
	era = ]|
	color = #cef2e0 |		| image = Hazan.png
			| birth_date = {{nowrap |{{birth-date|0965|{{circa}} 965}} ({{c.|354 ]}})<ref name=Lorch>{{cite encyclopedia |last=Lorch |first=Richard |title=Ibn al-Haytham: Arab astronomer and mathematician |publisher=Encyclopedia Britannica |date=1 February 2017 |url=https://www.britannica.com/biography/Ibn-al-Haytham |access-date=14 January 2022 |archive-date=12 August 2018 |archive-url=https://web.archive.org/web/20180812045403/https://www.britannica.com/biography/Ibn-al-Haytham |url-status=live }}</ref>}}
			| birth_place = ], ]
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			| death_date = {{nowrap |{{death-date|1040|{{circa}} 1040}} ({{c.|430 AH}})<ref name=Lorch />}} (aged around 75)
	image_name = Ibn_haithem_portrait.jpg|
			| death_place = ], ]
	image_caption = Ibn al-Haytham depicted in an Iraqi 10,000-dinar note. |
			| workplaces =
	signature = |
			| field = ], ], ]
	<!-- Information -->		| alma_mater =
			| notable_students =
	name = '''Abū ‘Alī al-{{Unicode|Ḥ}}asan ibn al-{{Unicode|Ḥ}}asan ibn al-Haytham'''|
			| known_for = '']'', '']'', ], ],<ref>{{Harvnb|O'Connor|Robertson|1999}}.</ref> ],<ref>{{Harvnb|El-Bizri|2010|p=11}}: "Ibn al-Haytham's groundbreaking studies in optics, including his research in catoptrics and dioptrics (respectively the sciences investigating the principles and instruments pertaining to the reflection and refraction of light), were principally gathered in his monumental opus: Kitåb al-manåóir (The Optics; De Aspectibus or Perspectivae; composed between 1028 CE and 1038 CE)."</ref> ], ], ] of ], ], ], ]ology,<ref>{{Harvnb|Rooney|2012|p=39}}: "As a rigorous experimental physicist, he is sometimes credited with inventing the scientific method."</ref> ]<ref>{{Harvnb|Baker|2012|p=449}}: "As shown earlier, Ibn al-Haytham was among the first scholars to experiment with animal psychology.</ref>
	title= '''Ibn al-Haytham''' and '''Alhacen'''|
	birth = 965|		| footnotes =
	death = 1039|		| Religion =
	Maddhab = |
	main_interests = ], ], ], ], ], ], ], ], ], ], ], ] |
	influences = ], ], ], ], ], ], ], ] |
	influenced = ], ], ], ], ], ], ], ], ], ], ], ], etc. |
	works = '']'', ''Analysis and Synthesis'', ''Balance of Wisdom'', ''Discourse on Place'', ''Doubts concerning Ptolemy'', ''Maqala fi'l-qarastun'', ''On the Configuration of the World'', ''Opuscula'', ''The Model of the Motions'', ''The Resolution of Doubts'', ''Treatise on Light'', ''Treatise on Place'' |
	}}		}}
			'''Ḥasan Ibn al-Haytham''' (] as '''Alhazen'''; {{IPAc-en|æ|l|ˈ|h|æ|z|ən}}; full name {{transliteration|ar|ALA|Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham}} {{lang|ar|أبو علي، الحسن بن الحسن بن الهيثم}}; {{c.|lk=no|965|1040}}) was a medieval ], ], and ] of the ] from present-day Iraq.<ref>Also ''Alhacen'', ''Avennathan'', ''Avenetan'', etc.; the identity of "Alhazen" with Ibn al-Haytham al-Basri "was identified towards the end of the 19th century". ({{harvnb|Vernet|1996|p=788}})</ref><ref>{{Cite American Heritage Dictionary|Ibn al-Haytham|access-date=23 June 2019}}</ref><ref>{{cite book|last1=Esposito|first1=John L.|title=The Oxford History of Islam|date=2000|publisher=Oxford University Press|page=192}}: "Ibn al-Haytham (d. 1039), known in the West as Alhazan, was a leading Arab mathematician, astronomer, and physicist. His optical compendium, Kitab al-Manazir, is the greatest medieval work on optics."</ref><ref name="Vernet 1996 788">For the description of his main fields, see e.g. {{harvnb|Vernet|1996|p=788}} ("He is one of the principal Arab mathematicians and, without any doubt, the best physicist.") {{Harvnb|Sabra|2008}}, {{Harvnb|Kalin|Ayduz|Dagli|2009|p=}} ("Ibn al-Ḥaytam was an eminent eleventh-century Arab optician, geometer, arithmetician, algebraist, astronomer, and engineer."), {{Harvnb|Dallal|1999|p=}} ("Ibn al-Haytham (d.&nbsp;1039), known in the West as Alhazan, was a leading Arab mathematician, astronomer, and physicist. His optical compendium, Kitab al-Manazir, is the greatest medieval work on optics.")</ref> Referred to as "the father of modern optics",<ref>{{Cite journal |last=Masic |first=Izet |date=2008 |title=Ibn al-Haitham--father of optics and describer of vision theory. |journal=Medicinski Arhiv |volume=62 |issue=3 |pages=183–188 |pmid=18822953 |url=https://www.researchgate.net/publication/23286650}}</ref><ref>{{Cite web|url=https://en.unesco.org/news/international-year-light-ibn-al-haytham-pioneer-modern-optics-celebrated-unesco|title=International Year of Light: Ibn al Haytham, pioneer of modern optics celebrated at UNESCO|website=UNESCO|language=en|access-date=2 June 2018|archive-date=18 September 2015|archive-url=https://web.archive.org/web/20150918044445/https://en.unesco.org/news/international-year-light-ibn-al-haytham-pioneer-modern-optics-celebrated-unesco|url-status=live}}</ref><ref name="Khalili">{{Cite news|url=http://news.bbc.co.uk/2/hi/science/nature/7810846.stm|work=BBC News|title=The 'first true scientist'|author=Al-Khalili, Jim|date=4 January 2009|access-date=2 June 2018|archive-date=26 April 2015|archive-url=https://web.archive.org/web/20150426041228/http://news.bbc.co.uk/2/hi/science/nature/7810846.stm|url-status=live}}</ref> he made significant contributions to the principles of ] and ] in particular. His most influential work is titled '']'' (]: {{lang|ar|كتاب المناظر}}, "Book of Optics"), written during 1011–1021, which survived in a Latin edition.<ref>{{Harvnb|Selin|2008|p=}}: "The three most recognizable Islamic contributors to meteorology were: the Alexandrian mathematician/ astronomer Ibn al-Haytham (Alhazen 965–1039), the Arab-speaking Persian physician Ibn Sina (Avicenna 980–1037), and the Spanish Moorish physician/jurist Ibn Rushd (Averroes; 1126–1198)." He has been dubbed the "father of modern optics" by the ]. {{Cite journal|date=1976|title=Impact of Science on Society|url=https://books.google.com/books?id=4YE3AAAAMAAJ|journal=UNESCO|volume=26–27|page=140|access-date=12 September 2019|archive-date=5 February 2023|archive-url=https://web.archive.org/web/20230205005719/https://books.google.com/books?id=4YE3AAAAMAAJ|url-status=live}}.
	'''{{transl|ar|ALA|Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham}}''' (]: أبو علي الحسن بن الحسن بن الهيثم, ]ized: '''Alhacen''' or (deprecated) '''Alhazen''') (965 – 1039), was an ]<ref name=Smith>Smith (1992).</ref> or ]<ref name=MacTutor>{{MacTutor Biography|id=Al-Haytham}}</ref> ] ]<ref>Hamarneh:
			{{Cite web|url=http://www.light2015.org/Home/ScienceStories/1000-Years-of-Arabic-Optics.html|title=International Year of Light – Ibn Al-Haytham and the Legacy of Arabic Optics|website=www.light2015.org|language=en|access-date=9 October 2017|archive-date=1 October 2014|archive-url=https://web.archive.org/web/20141001171116/http://www.light2015.org/Home/ScienceStories/1000-Years-of-Arabic-Optics.html|url-status=dead}}.
	{{quote|"A great man and a universal genius, long neglected even by his own people."}}</ref><ref>Bettany:
			{{Cite web|url=https://en.unesco.org/news/international-year-light-ibn-al-haytham-pioneer-modern-optics-celebrated-unesco|title=International Year of Light: Ibn al Haytham, pioneer of modern optics celebrated at UNESCO|website=UNESCO|language=en|access-date=9 October 2017|archive-date=18 September 2015|archive-url=https://web.archive.org/web/20150918044445/https://en.unesco.org/news/international-year-light-ibn-al-haytham-pioneer-modern-optics-celebrated-unesco|url-status=live}}. Specifically, he was the first to explain that vision occurs when light bounces on an object and then enters an eye. {{cite book|last=Adamson|first=Peter|title=Philosophy in the Islamic World: A History of Philosophy Without Any Gaps|url=https://books.google.com/books?id=KEpRDAAAQBAJ|date=2016|publisher=Oxford University Press|isbn=978-0-19-957749-1|page=77|access-date=3 October 2016|archive-date=5 February 2023|archive-url=https://web.archive.org/web/20230205005719/https://books.google.com/books?id=KEpRDAAAQBAJ|url-status=live}}</ref> The works of Alhazen were frequently cited during the scientific revolution by ], ], ], and ].
	{{quote|"Ibn ai-Haytham provides us with the historical personage of a versatile universal genius."}}</ref>
	who made significant contributions to the principles of ], as well as to ], ], ], ], ], ], ], ], ], ], and to ] in general with his introduction of the ]. He is sometimes called '''al-Basri''' (Arabic: البصري), after his birthplace in the city of ] in ] (]), then ruled by the ] of ].<ref name=Persia></ref>
			Ibn al-Haytham was the first to correctly explain the theory of vision,<ref name="Adamson 2016 77">{{cite book|last=Adamson|first=Peter|title=Philosophy in the Islamic World: A History of Philosophy Without Any Gaps|url=https://books.google.com/books?id=KEpRDAAAQBAJ|year=2016|publisher=Oxford University Press|isbn=978-0-19-957749-1|page=77|access-date=3 October 2016|archive-date=5 February 2023|archive-url=https://web.archive.org/web/20230205005719/https://books.google.com/books?id=KEpRDAAAQBAJ|url-status=live}}</ref> and to argue that vision occurs in the brain, pointing to observations that it is subjective and affected by personal experience.{{sfn|Baker|2012|p=445}} He also stated the principle of least time for refraction which would later become ].<ref>{{Cite journal |last=Rashed |first=Roshdi |date=2019-04-01 |title=Fermat et le principe du moindre temps |journal= Comptes Rendus Mécanique |volume=347 |issue=4 |pages=357–364 |doi=10.1016/j.crme.2019.03.010 |bibcode=2019CRMec.347..357R |s2cid=145904123 |issn=1631-0721|doi-access=free }}</ref> He made major contributions to catoptrics and dioptrics by studying reflection, refraction and nature of images formed by light rays.{{sfn|Selin|2008|p=1817}}<ref>{{Cite book |last1=Boudrioua |first1=Azzedine |url=https://books.google.com/books?id=6_0wDwAAQBAJ&dq=Law+of+reflection+ibn+al+haitham&pg=PT29 |title=Light-Based Science: Technology and Sustainable Development, The Legacy of Ibn al-Haytham |last2=Rashed |first2=Roshdi |last3=Lakshminarayanan |first3=Vasudevan |year=2017 |publisher=CRC Press |isbn=978-1-351-65112-7 |language=en |access-date=22 February 2023 |archive-date=6 March 2023 |archive-url=https://web.archive.org/web/20230306044312/https://books.google.com/books?id=6_0wDwAAQBAJ&dq=Law+of+reflection+ibn+al+haitham&pg=PT29 |url-status=live }}</ref> Ibn al-Haytham was an early proponent of the concept that a hypothesis must be supported by experiments based on confirmable procedures or mathematical reasoning{{snd}}an early pioneer in the ] five centuries before ],<ref>] (2009). "Science in Islam". Oxford Dictionary of the Middle Ages. {{ISSN|1703-7603}}. Retrieved 22 October 2014.</ref><ref>]. {{jstor|1=228328?pg=464}}, Toomer's 1964 review of Matthias Schramm (1963) ''Ibn Al-Haythams Weg Zur Physik''] {{Webarchive|url=https://web.archive.org/web/20170326070235/http://www.jstor.org/stable/228328?pg=464 |date=26 March 2017 }} Toomer p. 464: "Schramm sums up achievement in the development of scientific method."</ref><ref>{{cite web|url=http://www.light2015.org/Home/ScienceStories/1000-Years-of-Arabic-Optics.html|title=International Year of Light – Ibn Al-Haytham and the Legacy of Arabic Optics|access-date=4 January 2015|archive-date=1 October 2014|archive-url=https://web.archive.org/web/20141001171116/http://www.light2015.org/Home/ScienceStories/1000-Years-of-Arabic-Optics.html|url-status=dead}}</ref><ref>{{Cite journal|last=Gorini|first=Rosanna|title=Al-Haytham the man of experience. First steps in the science of vision|url=http://www.ishim.net/ishimj/4/10.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.ishim.net/ishimj/4/10.pdf |archive-date=2022-10-09 |url-status=live|journal=Journal of the International Society for the History of Islamic Medicine|volume=2|issue=4|pages=53–55|date=October 2003|access-date=25 September 2008}}</ref> he is sometimes described as the world's "first true scientist".<ref name=Khalili /> He was also a ], writing on ], ] and ].<ref>], ''Ibn al-Haytham's Geometrical Methods and the Philosophy of Mathematics: A History of Arabic Sciences and Mathematics, Volume 5'', Routledge (2017), p. 635</ref>
	Ibn al-Haytham is regarded as the father of ] for his influential '']'', which correctly explained and proved the modern intromission theory of ], and for his ]s on optics, including experiments on ], ]s, ], ], and the dispersion of ] into its constituent ].<ref name=Deek/>
	He studied ] and the ], speculated on the ], ] and ] aspects of light,<ref>Hamarneh, p. 119.</ref> and argued that ] of light are streams of ]<ref>Rashed (2007), p. 19.</ref> travelling in straight lines.<ref>J. J. O'Connor and E. F. Robertson (2002). , '']''.</ref>
	Due to his ], ] and ]al approach to ] and ], he is considered the pioneer of the modern ]<ref name=Agar>David Agar (2001). . ].</ref><ref name=Gorini/> and of ],<ref>Rüdiger Thiele (2005). "In Memoriam: Matthias Schramm", ''Arabic Sciences and Philosophy'' '''15''', p. 329–331. ].</ref> and some have described him as the "first ]" for this reason.<ref>Steffens.</ref>
	He is also considered by some to be the founder of ] and ]<ref name=Khaleefa>Khaleefa.</ref> for his experimental approach to the ] of ],<ref name=Steffens>Steffens, Chapter 5.</ref> and a pioneer of the philosophical field of ].
	His ''Book of Optics'' has been ranked alongside ]'s '']'' as one of the most influential books ever written in the ].<ref name=Salih>Salih, Al-Amri, El Gomati.</ref>
			Born in ], he spent most of his productive period in the ] capital of ] and earned his living authoring various treatises and tutoring members of the nobilities.<ref>According to ]. {{Harvnb|O'Connor|Robertson|1999}}.</ref> Ibn al-Haytham is sometimes given the ] ''al-Baṣrī'' after his birthplace,<ref>{{harvnb|O'Connor|Robertson|1999}}</ref> or ''al-Miṣrī'' ("the Egyptian").<ref>{{harvnb|O'Connor|Robertson|1999|p=}}</ref><ref>Disputed: {{harvnb|Corbin|1993|p=149}}.</ref> Al-Haytham was dubbed the "Second ]" by ]<ref name=bayhaqi>Noted by ] (c. 1097–1169), and by
	Among his other achievements, Ibn al-Haytham described the ] and invented the ] (a precursor to the modern ]),<ref name=Wade/> discovered ] of least time and the law of ] (known as ]),<ref name=Salam/> discovered the concept of ] (part of ]),<ref name=Nasr/> described the ] between ]es and was aware of the ] of ] due to ] at a distance,<ref name=Bizri>El-Bizri (2006).</ref> discovered that the ] were accountable to the ], presented the earliest critique and reform of the ], first stated ] in ], pioneered ], formulated and solved ] geometrically, developed and proved the earliest general formula for ] and ] ] using ],<ref name=Katz/> and in his optical research laid the foundations for the later development of ] astronomy,<ref name=Marshall>Marshall.</ref> as well as for the ] and the use of optical aids in ] ].<ref name=Power/>
			* {{Webarchive|url=https://web.archive.org/web/20230205005728/https://books.google.com/books?id=AsnaAAAAMAAJ |date=5 February 2023 }} p. 197
			* </ref> and "The Physicist" by ].<ref>{{harvnb|Lindberg|1967|p=331}}:"Peckham continually bows to the authority of Alhazen, whom he cites as "the Author" or "the Physicist"."</ref> Ibn al-Haytham paved the way for the modern science of physical optics.<ref>{{Cite book|url=https://books.google.com/books?id=mhLVHR5QAQkC|title=Ptolemy's Theory of Visual Perception: An English Translation of the Optics|last=A. Mark Smith|publisher=American Philosophical Society|year=1996|isbn=978-0-87169-862-9|page=57|access-date=16 August 2019|archive-date=5 February 2023|archive-url=https://web.archive.org/web/20230205005720/https://books.google.com/books?id=mhLVHR5QAQkC|url-status=live}}</ref>
			== Biography ==
	--] 01:41, 12 October 2007 (UTC)<nowiki>hey</nowiki>==Overview==
	<nowiki> text here</nowiki>===Biography===
	Abū ‘Alī al-Hasan ibn al-Hasan ibn al-Haytham was born in the ] city of ], ] (]), then part of the ] of ],<ref name=Persia/> and he probably died in ], ].<ref name=MacTutor>{{MacTutor Biography|id=Al-Haytham|title=Abu Ali al-Hasan ibn al-Haytham}}</ref> Known in the West as Alhacen or Alhazen, Ibn al-Haytham was born in 965 in ], and was educated there and in ].
			Ibn al-Haytham (Alhazen) was born c. 965 to a family of ]<ref name="Vernet 1996 788" /><ref name="Simon 2006">{{harvnb|Simon|2006}}</ref><ref>{{Cite book |last=Gregory |first=Richard Langton |url=https://books.google.com/books?id=FpMYAAAAIAAJ |title=The Oxford Companion to the Mind |date=2004 |publisher=Oxford University Press |isbn=978-0-19-866224-2 |page=24 |language=en |access-date=28 June 2023 |archive-date=4 December 2023 |archive-url=https://web.archive.org/web/20231204161231/https://books.google.com/books?id=FpMYAAAAIAAJ |url-status=live }}</ref><ref>
	One account of his career has him summoned to Egypt by the mercurial ] ] to regulate the ] of the ]. After his field work made him aware of the impracticality of this scheme, and fearing the caliph's anger, he ]. He was kept under ] until Hakim's death in 1021. During this time, he wrote his influential '']'' and scores of other important treatises on ] and ]. He later traveled to ] and, during this period, he had ample time for his scientific pursuits, which included ], mathematics, physics, ], and the development of scientific methods — on all of which he has left several outstanding books.
			"Alhazen Arab mathematician and physicist who was born around 965 in what is now Iraq." Critical Companion to Chaucer: A Literary Reference to His Life and Work
			</ref><ref>Esposito (2000)، The Oxford History of Islam، Oxford University Press، p. 192. : "Ibn al-Haytham (d. 1039), known in the West as Alhazan, was a leading Arab mathematician, astronomer, and physicist. His optical compendium, Kitab al-Manazir, is the greatest medieval work on optics"</ref> or ]<ref>{{Cite book |url=https://books.google.com/books?id=mk_CBAAAQBAJ&dq=alhazen+History+and+Evolution+of+Concepts+in+Physics&pg=PA23 |title=History and Evolution of Concepts in Physics |page =24 |isbn=978-3-319-04292-3 |access-date=13 March 2023 |archive-date=20 June 2023 |archive-url=https://web.archive.org/web/20230620164804/https://books.google.com/books?id=mk_CBAAAQBAJ&dq=alhazen+History+and+Evolution+of+Concepts+in+Physics&pg=PA23 |url-status=live |last1=Varvoglis |first1=Harry |date=29 January 2014 |publisher=Springer }}</ref><ref>{{Cite web |url=https://books.google.com/books?id=3nBJAAAAYAAJ&dq=alhazen&pg=PA59 |title=Chemical News and Journal of Industrial Science|volume =34 |page =59 |date=6 January 1876 |access-date=13 March 2023 |archive-date=26 March 2023 |archive-url=https://web.archive.org/web/20230326164818/https://books.google.com/books?id=3nBJAAAAYAAJ&dq=alhazen&pg=PA59 |url-status=live }}</ref><ref>{{Cite book |url=https://books.google.com/books?id=_NDOCwAAQBAJ&dq=Renaissance++John+Shannon+Hendrix,+Charles+eleventh+century&pg=PA77 |title=Renaissance Theories of Vision edited by John Shannon Hendrix, Charles |page =77 |isbn=978-1-317-06640-8 |access-date=13 March 2023 |archive-date=20 June 2023 |archive-url=https://web.archive.org/web/20230620164804/https://books.google.com/books?id=_NDOCwAAQBAJ&dq=Renaissance++John+Shannon+Hendrix,+Charles+eleventh+century&pg=PA77 |url-status=live |last1=Hendrix |first1=John Shannon |last2=Carman |first2=Charles H. |date=5 December 2016 |publisher=Routledge }}</ref><ref>{{Cite book |url=https://books.google.com/books?id=ZQfcDwAAQBAJ&dq=Quantum+Mechanics+for+Beginners+alhazen&pg=PA81 |title=Quantum Mechanics for Beginners: With Applications to Quantum Communication By M. Suhail Zubairy |page =81 |isbn=978-0-19-885422-7 |access-date=13 March 2023 |archive-date=20 June 2023 |archive-url=https://web.archive.org/web/20230620164806/https://books.google.com/books?id=ZQfcDwAAQBAJ&dq=Quantum+Mechanics+for+Beginners+alhazen&pg=PA81 |url-status=live |last1=Suhail Zubairy |first1=M. |date=6 January 2024 |publisher=Oxford University Press }}</ref><ref>{{Harvard citation|Child|Shuter|Taylor|1992|p=70}}, {{Harvard citation|Dessel|Nehrich|Voran|1973|p=164}}, ''Understanding History'' by John Child, Paul Shuter, David Taylor, p. 70. "Alhazen, a Persian scientist, showed that the eye saw light from other objects. This started optics, the science of light. The Arabs also studied astronomy, the study of the stars. "</ref> origin in ], ], which was at the time part of the ]. His initial influences were in the study of religion and service to the community. At the time, society had a number of conflicting views of religion that he ultimately sought to step aside from religion. This led to him delving into the study of mathematics and science.<ref name=Tbakhi>{{Cite journal|last1=Tbakhi|first1=Abdelghani|last2=Amr|first2=Samir S.|date=2007|title=Ibn Al-Haytham: Father of Modern Optics|journal=Annals of Saudi Medicine|volume=27|issue=6|pages=464–467|doi=10.5144/0256-4947.2007.464|issn=0256-4947|pmc=6074172|pmid=18059131}}</ref> He held a position with the title of ] in his native Basra, and became famous for his knowledge of applied mathematics, as evidenced by his attempt to regulate the ].<ref name="Corbin 1993 149">{{Harvnb|Corbin|1993|p=149}}.</ref>
			Upon his return to Cairo, he was given an administrative post. After he proved unable to fulfill this task as well, he contracted the ire of the caliph ],<ref>The Prisoner of Al-Hakim. Clifton, NJ: Blue Dome Press, 2017. {{ISBN|1682060160}}</ref> and is said to have been forced into hiding until the caliph's death in 1021, after which his confiscated possessions were returned to him.<ref>], ''Geschichte der arabischen Litteratur'', vol. 1 (1898), .</ref>
	===Works===
			Legend has it that Alhazen ] and was kept under house arrest during this period.<ref>{{cite web|url=http://www.cgie.org.ir/shavad.asp?id=123&avaid=1917 |title=the Great Islamic Encyclopedia |publisher=Cgie.org.ir |access-date=27 May 2012 |url-status=dead |archive-url=https://web.archive.org/web/20110930153427/http://www.cgie.org.ir/shavad.asp?id=123&avaid=1917 |archive-date=30 September 2011 }}{{verify source|date=February 2016}}</ref> During this time, he wrote his influential '']''. Alhazen continued to live in Cairo, in the neighborhood of the famous ], and lived from the proceeds of his literary production<ref>For Ibn al-Haytham's life and works, {{harvnb|Smith|2001|p=cxix}} recommends {{harvnb|Sabra|1989|pp=vol. 2, xix–lxxiii}}</ref> until his death in c. 1040.<ref name="Corbin 1993 149" /> (A copy of ]' ''Conics'', written in Ibn al-Haytham's own handwriting exists in ]: (MS Aya Sofya 2762, 307 fob., dated Safar 415 A.H. ).)<ref>{{cite web| url = https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/ibn-al-haytham-abu| title = A. I. Sabra encyclopedia.com Ibn Al-Haytham, Abū| access-date = 4 November 2018| archive-date = 26 March 2023| archive-url = https://web.archive.org/web/20230326025108/https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/ibn-al-haytham-abu| url-status = live}}</ref>{{rp|Note 2}}
	Ibn al-Haytham was a pioneer in ], ], ], ], ], and ]. His optical writings influenced many Western intellectuals such as ], ], ], and ].<ref>Lindberg (1967).</ref>
			Among his students were Sorkhab (Sohrab), a Persian from ], and ], an Egyptian prince.<ref>Sajjadi, Sadegh, "Alhazen", ''Great Islamic Encyclopedia'', Volume 1, Article No. 1917</ref>{{verify source|date=February 2016}}
	Yasmeen M. Faruqi writes:
	{{quote|"In seventeenth century Europe the problems formulated by Ibn al-Haytham (965-1041) became known as “Alhazen’s problem”. Al-Haytham’s contributions to ] and ] went well beyond the ] tradition. Al-Haytham also worked on ] and the beginnings of the link between ] and geometry. Subsequently, this work led in ] to the harmonious fusion of algebra and geometry that was epitomised by ] in ] and by ] in the ]. Al-Haytham was a scientist who made major contributions to the fields of ], ] and ] during the latter half of the tenth century."<ref>Faruqi, p. 395-396.</ref>}}
			== ''Book of Optics'' ==
	According to medieval biographers, Ibn al-Haytham wrote more than 200 works on a wide range of subjects,<ref name=Ezine>Steffens (] Bradley Steffens, "Who Was the First Scientist?", ''Ezine Articles'').</ref> of which at least 96 of his scientific works are known. Most of his works are now lost, but more than 50 of them have survived to some extent. Nearly half of his surviving works are on mathematics, 23 of them are on astronomy, and 14 of them are on optics, with a few on other areas of science.<ref name=Rashed>Rashed (2002), p. 773.</ref> Not all of his surviving works have yet been studied, but some of his most important ones are described below. These include:
			{{Main|Book of Optics}}
			Alhazen's most famous work is his seven-volume treatise on ] ''Kitab al-Manazir'' (''Book of Optics''), written from 1011 to 1021.<ref>{{Harvnb|Al-Khalili|2015}}.</ref> In it, Ibn al-Haytham was the first to explain that vision occurs when light reflects from an object and then passes to one's eyes,<ref name="Adamson 2016 77"/> and to argue that vision occurs in the brain, pointing to observations that it is subjective and affected by personal experience.{{sfn|Baker|2012|p=445}}
	*'']'' (1021)
	*''Analysis and Synthesis''
	*''Balance of Wisdom''
	*''Discourse on Place''
	*''Maqala fi'l-qarastun''
	*''Doubts concerning Ptolemy'' (1028)
	*''On the Configuration of the World''
	*''Opuscula''
	*''The Model of the Motions of Each of the Seven Planets'' (1038)
	*''The Resolution of Doubts''
	*''Treatise on Light''
	*''Treatise on Place''
			''Optics'' was ] by an unknown scholar at the end of the 12th century or the beginning of the 13th century.<ref>{{harvnb|Crombie|1971|p=147, n. 2}}.</ref>{{ efn| A. Mark Smith has determined that there were at least two translators, based on their facility with Arabic; the first, more experienced scholar began the translation at the beginning of Book One, and handed it off in the middle of Chapter Three of Book Three. {{harvnb|Smith|2001}} '''91''' Volume 1: Commentary and Latin text pp.xx–xxi. See also his 2006, 2008, 2010 translations.}}
	===Scientific method===
	Rosanna Gorini wrote the following on Ibn al-Haytham's introduction of the ]:
	{{quote|"According to the majority of the historians al-Haytham was the pioneer of the modern scientific method. With his book he changed the meaning of the term optics and established experiments as the norm of proof in the field. His investigations are based not on abstract theories, but on experimental evidences and his experiments were systematic and repeatable."<ref name=Gorini>Gorini.</ref>}}
			This work enjoyed a great reputation during the ]. The Latin version of ''De aspectibus'' was translated at the end of the 14th century into Italian vernacular, under the title ''De li aspecti''.<ref>{{Cite journal |author=] | title=Nota intorno ad una traduzione italiana fatta nel secolo decimoquarto del trattato d'ottica d'Alhazen |journal=Bollettino di Bibliografia e di Storia delle Scienze Matematiche e Fisiche | year=1871 | volume=4 |pages=1–40}}. On this version, see {{harvnb|Raynaud|2020|pp=139–153}}.</ref>
	Roshdi Rashed wrote the following on Ibn al-Haytham:
	{{quote|"His work on optics, which includes a theory of vision and a theory of light, is considered by many to be his most important contribution, setting the scene for developments well into the 17th century. His contributions to geometry and number theory go well beyond the archimedean tradition. And by promoting the use of experiments in scientific research, al-Haytham played an important part in setting the scene for modern science."<ref name=Rashed/>}}
			It was printed by ] in 1572, with the title ''Opticae thesaurus: Alhazeni Arabis libri septem, nuncprimum editi; Eiusdem liber De Crepusculis et nubium ascensionibus'' (English: Treasury of Optics: seven books by the Arab Alhazen, first edition; by the same, on twilight and the height of clouds).<ref>{{Citation|url=http://www.mala.bc.ca/~mcneil/cit/citlcalhazen1.htm |title=Alhazen (965–1040): Library of Congress Citations | publisher=Malaspina Great Books |access-date=23 January 2008 |url-status=dead |archive-url=https://web.archive.org/web/20070927190009/http://www.mala.bc.ca/~mcneil/cit/citlcalhazen1.htm |archive-date=27 September 2007 }}{{verify source|date=February 2016}}</ref>
	Ibn al-Haytham developed rigorous ]al methods of controlled ] in order to verify theoretical ] and substantiate ] ]s.<ref name=Bizri/> Ibn al-Haytham's scientific method was very similar to the modern scientific method and consisted of the following procedures:<ref name=Ezine/>
			Risner is also the author of the name variant "Alhazen"; before Risner he was known in the west as Alhacen.<ref>{{harvnb|Smith|2001|p=xxi}}.</ref>
			Works by Alhazen on geometric subjects were discovered in the ] in ] in 1834 by E. A. Sedillot. In all, A. Mark Smith has accounted for 18 full or near-complete manuscripts, and five fragments, which are preserved in 14 locations, including one in the ] at ], and one in the library of ].<ref>{{harvnb|Smith|2001|p=xxii}}.</ref>
			=== Theory of optics ===
	#]
			{{See also|Horopter}}
	#Statement of ]
			]
	#Formulation of ]
			Two major theories on vision prevailed in ]. The first theory, the ], was supported by such thinkers as ] and ], who believed that sight worked by the ] emitting ] of ]. The second theory, the ] supported by ] and his followers, had physical forms entering the eye from an object. Previous Islamic writers (such as ]) had argued essentially on Euclidean, Galenist, or Aristotelian lines. The strongest influence on the ''Book of Optics'' was from Ptolemy's ], while the description of the anatomy and physiology of the eye was based on Galen's account.<ref>{{harvnb|Smith|2001|p=lxxix}}.</ref> Alhazen's achievement was to come up with a theory that successfully combined parts of the mathematical ray arguments of Euclid, the medical tradition of ], and the intromission theories of Aristotle. Alhazen's intromission theory followed al-Kindi (and broke with Aristotle) in asserting that "from each point of every colored body, illuminated by any light, issue light and color along every straight line that can be drawn from that point".<ref name="{{harvnb|lindberg|1976|p=73}}.">{{harvnb|Lindberg|1976|p=73}}.</ref> This left him with the problem of explaining how a coherent image was formed from many independent sources of radiation; in particular, every point of an object would send rays to every point on the eye.
	#Testing of hypothesis using ]ation
	#Analysis of experimental ]s
	#Interpretation of ] and formulation of ]
	#] of findings
			What Alhazen needed was for each point on an object to correspond to one point only on the eye.<ref name="{{harvnb|lindberg|1976|p=73}}." /> He attempted to resolve this by asserting that the eye would only perceive perpendicular rays from the object{{snd}}for any one point on the eye, only the ray that reached it directly, without being refracted by any other part of the eye, would be perceived. He argued, using a physical analogy, that perpendicular rays were stronger than oblique rays: in the same way that a ball thrown directly at a board might break the board, whereas a ball thrown obliquely at the board would glance off, perpendicular rays were stronger than refracted rays, and it was only perpendicular rays which were perceived by the eye. As there was only one perpendicular ray that would enter the eye at any one point, and all these rays would converge on the centre of the eye in a cone, this allowed him to resolve the problem of each point on an object sending many rays to the eye; if only the perpendicular ray mattered, then he had a one-to-one correspondence and the confusion could be resolved.<ref>{{harvnb|Lindberg|1976|p=74}}</ref> He later asserted (in book seven of the ''Optics'') that other rays would be refracted through the eye and perceived ''as if'' perpendicular.<ref>{{harvnb|Lindberg|1976|p=76}}</ref> His arguments regarding perpendicular rays do not clearly explain why ''only'' perpendicular rays were perceived; why would the weaker oblique rays not be perceived more weakly?<ref>{{harvnb|Lindberg|1976|p=75}}</ref> His later argument that refracted rays would be perceived as if perpendicular does not seem persuasive.<ref>{{harvnb|Lindberg|1976|pages=76–78}}</ref> However, despite its weaknesses, no other theory of the time was so comprehensive, and it was enormously influential, particularly in Western Europe. Directly or indirectly, his ''De Aspectibus'' (]) inspired much activity in optics between the 13th and 17th centuries. ]'s later theory of the ]l image (which resolved the problem of the correspondence of points on an object and points in the eye) built directly on the conceptual framework of Alhazen.<ref>{{harvnb|Lindberg|1976|p=86}}.</ref>
	In ''The Model of the Motions'', Ibn al-Haytham also describes an early version of ], where he employs only minimal hypotheses regarding the properties that characterize astronomical motions, as he attempts to eliminate from his planetary model the ] hypotheses that cannot be observed from ].<ref name=Rashed-35-36>Rashed (2007), p. 35-36.</ref>
			Alhazen showed through experiment that light travels in straight lines, and carried out various experiments with ], ]s, ], and ].<ref name="auto">{{harvnb|Al Deek|2004}}.</ref> His analyses of reflection and refraction considered the vertical and horizontal components of light rays separately.<ref>{{harvnb|Heeffer|2003}}.</ref>
	===Legacy===
	Ibn al-Haytham was one of the most eminent ]s, whose developments in ] and the ] were particularly outstanding. Ibn al-Haytham's work on optics is credited with contributing a new emphasis on ]. His influence on ]s in general, and on optics in particular, has been held in high esteem and, in fact, ushered in a new era in optical research, both in theory and practice.<ref name=Deek/> The scientific method is considered to be so fundamental to ] that some — especially ] and practicing scientists — consider earlier inquiries into nature to be ''pre-scientific''.<ref>], p. 190-202:
	{{quote|"What we call science arose as a result of new methods of experiment, observation, and measurement, which were introduced into Europe by the ]s. Science is the most momentous contribution of ] to the ], but its fruits were slow in ripening. Not until long after ] culture had sunk back into darkness did the giant to which it had given birth, rise in his might. It was not science only which brought Europe back to life. Other and manifold influences from the civilization of Islam communicated its first glow to European life. The debt of our science to that of the Arabs does not consist in startling discoveries or revolutionary theories; science owes a great deal more to Arab culture, it owes its existence....The ancient world was, as we saw, pre-scientific. The astronomy and mathematics of Greeks were a foreign importation never thoroughly acclimatized in Greek culture. The Greeks systematized, generalized and theorized, but the patient ways of investigations, the accumulation of positive knowledge, the minute methods of science, detailed and prolonged observation and experimental inquiry were altogether alien to the Greek temperament. What we call science arose in Europe as a result of new spirit of enquiry, of new methods of experiment, observation, measurement, of the development of mathematics, in a form unknown to the Greeks. That spirit and those methods were introduced into the European world by the Arabs."}}
	</ref>
	Due to its importance in the ], some have considered his development of the scientific method to be the most important scientific development of the ].<ref name=Power>Richard Power (]), , '']'', April 18, 1999.</ref>
			Alhazen studied the process of sight, the structure of the eye, image formation in the eye, and the ]. Ian P. Howard argued in a 1996 '']'' article that Alhazen should be credited with many discoveries and theories previously attributed to Western Europeans writing centuries later. For example, he described what became in the 19th century ]. He wrote a description of vertical ]s 600 years before ] that is actually closer to the modern definition than Aguilonius's{{snd}}and his work on ] was repeated by Panum in 1858.<ref>{{harvnb|Howard|1996}}.</ref> Craig Aaen-Stockdale, while agreeing that Alhazen should be credited with many advances, has expressed some caution, especially when considering Alhazen in isolation from ], with whom Alhazen was extremely familiar. Alhazen corrected a significant error of Ptolemy regarding binocular vision, but otherwise his account is very similar; Ptolemy also attempted to explain what is now called Hering's law.<ref>{{harvnb|Aaen-Stockdale|2008}}</ref> In general, Alhazen built on and expanded the optics of Ptolemy.<ref>{{harvnb|Wade|1998|pages=240, 316, 334, 367}}; {{harvnb|Howard|Wade|1996|pages=1195, 1197, 1200}}.</ref>
	] winning physicist ] wrote:
	{{quote|"Ibn-al-Haitham (Alhazen, 965-1039 CE) was one of the greatest physicists of all time. He made experimental contributions of the highest order in optics. He enunciated that a ray of light, in passing through a medium, takes the path which is the easier and 'quicker'. In this he was anticipating ] by many centuries. He enunciated the law of ], later to become ]. Part V of ]'s "''Opus Majus''" is practically an annotation to Ibn al Haitham's ''Optics''."<ref name=Salam>], in Lai.</ref>}}
			In a more detailed account of Ibn al-Haytham's contribution to the study of binocular vision based on Lejeune<ref>{{harvnb|Lejeune|1958}}.</ref> and Sabra,<ref name="{{harvnb|sabra|1989}}.">{{harvnb|Sabra|1989}}.</ref> Raynaud<ref>{{harvnb|Raynaud|2003}}.</ref> showed that the concepts of correspondence, homonymous and crossed diplopia were in place in Ibn al-Haytham's optics. But contrary to Howard, he explained why Ibn al-Haytham did not give the circular figure of the horopter and why, by reasoning experimentally, he was in fact closer to the discovery of Panum's fusional area than that of the Vieth-Müller circle. In this regard, Ibn al-Haytham's theory of binocular vision faced two main limits: the lack of recognition of the role of the retina, and obviously the lack of an experimental investigation of ocular tracts.
	], the "father of the history of science", wrote in the ''Introduction to the History of Science'':
	{{quote|" was not only the greatest Muslim physicist, but by all means the greatest of ]."<ref>], ''Introduction to the History of Science'', "The Time of Al-Biruni".</ref>}}
	{{quote|"Ibn Haytham's writings reveal his fine development of the experimental faculty. His tables of corresponding ] and refraction of light passing from one medium to another show how closely he had approached discovering the ], later attributed to ]. He accounted correctly for twilight as due to ], estimating the sun's depression to be 19 degrees below the horizon, at the commencement of the phenomenon in the mornings or at its termination in the evenings."<ref>Dr. A. Zahoor and Dr. Z. Haq (1997). , Cyberistan.</ref>}}
			] according to Ibn al-Haytham. Note the depiction of the ]. —Manuscript copy of his ] (MS Fatih 3212, vol. 1, fol. 81b, ] Library, Istanbul)]]
	Robert S. Elliot wrote the following on the '']'':
			Alhazen's most original contribution was that, after describing how he thought the eye was anatomically constructed, he went on to consider how this anatomy would behave functionally as an optical system.<ref>{{harvnb|Russell|1996|p=691}}.</ref> His understanding of ] from his experiments appears to have influenced his consideration of image inversion in the eye,<ref>{{harvnb|Russell|1996|p=689}}.</ref> which he sought to avoid.<ref>{{harvnb|Lindberg|1976|pages= 80–85}}</ref> He maintained that the rays that fell perpendicularly on the lens (or glacial humor as he called it) were further refracted outward as they left the glacial humor and the resulting image thus passed upright into the optic nerve at the back of the eye.<ref>{{harvnb|Smith|2004|pages=186, 192}}.</ref> He followed ] in believing that the ] was the receptive organ of sight, although some of his work hints that he thought the ] was also involved.<ref>{{harvnb|Wade|1998|p=14}}</ref>
	{{quote|"Alhazen was one of the ablest students of optics of all times and published a seven-volume treatise on this subject which had great celebrity throughout the medieval period and strongly influenced Western thought, notably that of Roger Bacon and Kepler. This treatise discussed ] and ] ]s in both ] and ] geometries, anticipated ], and considered refraction and the magnifying power of lenses. It contained a remarkably lucid description of the optical system of the eye, which study led Alhazen to the belief that light consists of rays which originate in the object seen, and not in the eye, a view contrary to that of Euclid and Ptolemy."<ref>Elliott, Chapter 1.</ref>}}
			Alhazen's synthesis of light and vision adhered to the Aristotelian scheme, exhaustively describing the process of vision in a logical, complete fashion.<ref>{{Cite journal|url=http://www.jstor.org/stable/3657357|title=Alhacen's Theory of Visual Perception: A Critical Edition, with English Translation and Commentary, of the First Three Books of Alhacen's "De aspectibus", the Medieval Latin Version of Ibn al-Haytham's "Kitāb al-Manāẓir": Volume Two|author=Smith, A. Mark|year=2001|journal=Transactions of the American Philosophical Society|volume=91|issue=5|pages=339–819|doi=10.2307/3657357|jstor=3657357|access-date=12 January 2015|archive-date=30 June 2015|archive-url=https://web.archive.org/web/20150630235046/http://www.jstor.org/stable/3657357?|url-status=live}}</ref>
	The ''Biographical Dictionary of Scientists'' wrote the following on Ibn al-Haytham::
	{{quote|"He was probably the greatest scientist of the Middle Ages and his work remained unsurpassed for nearly 600 years until the time of Johannes Kepler."<ref>"Alhazen", in Abbott, p. 75.</ref>}}
	The Latin translation of his main work, ''Kitab al-Manazir'', exerted a great influence upon Western science: for example, on the work of ], who cites him by name,<ref>Lindberg (1996), p. 11, passim.</ref> and on ]. It brought about a great progress in ]al methods. His research in ] centered on spherical and ] mirrors and ]. He made the important observation that the ratio between the ] and ] does not remain constant, and investigated the ] power of a ]. His work on catoptrics also contains the important problem known as ].		His research in ] (the study of optical systems using mirrors) was centred on spherical and ] mirrors and ]. He made the observation that the ratio between the ] and ] does not remain constant, and investigated the ] power of a ].<ref name="auto" />
			=== Law of reflection ===
	The list of his books runs to 200 or so, yet very few of the books have survived. Even his monumental treatise on optics survived only through its Latin translation. During the Middle Ages his books on ] were translated into Latin, ] and other languages.
			{{Main|Specular reflection}}
			Alhazen was the first physicist to give complete statement of the law of reflection.<ref>{{Cite book |last=Stamnes |first=J. J. |url=https://books.google.com/books?id=dGQ-DwAAQBAJ&dq=alhazen+law+of+reflection&pg=PT15 |title=Waves in Focal Regions: Propagation, Diffraction and Focusing of Light, Sound and Water Waves |date=2017 |publisher=Routledge |isbn=978-1-351-40468-6 |language=en |access-date=22 February 2023 |archive-date=31 March 2023 |archive-url=https://web.archive.org/web/20230331171120/https://books.google.com/books?id=dGQ-DwAAQBAJ&dq=alhazen+law+of+reflection&pg=PT15 |url-status=live }}</ref><ref>{{Cite book |last=Mach |first=Ernst |url=https://books.google.com/books?id=7dPCAgAAQBAJ&dq=alhazen+incident+ray+reflected+ray+lie+on+same+plane&pg=PA29 |title=The Principles of Physical Optics: An Historical and Philosophical Treatment |date=2013 |publisher=Courier Corporation |isbn=978-0-486-17347-4 |language=en |access-date=22 February 2023 |archive-date=31 March 2023 |archive-url=https://web.archive.org/web/20230331172406/https://books.google.com/books?id=7dPCAgAAQBAJ&dq=alhazen+incident+ray+reflected+ray+lie+on+same+plane&pg=PA29 |url-status=live }}</ref><ref>{{Cite book |last=Iizuka |first=Keigo |url=https://books.google.com/books?id=h9n6CAAAQBAJ&dq=alhazen+law+of+reflection&pg=PA7 |title=Engineering Optics |date=2013 |publisher=Springer Science & Business Media |isbn=978-3-662-07032-1 |language=en |access-date=22 February 2023 |archive-date=31 March 2023 |archive-url=https://web.archive.org/web/20230331171118/https://books.google.com/books?id=h9n6CAAAQBAJ&dq=alhazen+law+of+reflection&pg=PA7 |url-status=live }}</ref> He was first to state that the incident ray, the reflected ray, and the normal to the surface all lie in a same plane perpendicular to reflecting plane.{{sfn|Selin|2008|p=1817}}<ref>{{Cite book |last=Mach |first=Ernst |url=https://books.google.com/books?id=7dPCAgAAQBAJ&dq=alhazen+first+incident+ray+reflected+ray+lie+on+same+plane&pg=PA29 |title=The Principles of Physical Optics: An Historical and Philosophical Treatment |date=2013 |publisher=Courier Corporation |isbn=978-0-486-17347-4 |language=en |access-date=22 February 2023 |archive-date=31 March 2023 |archive-url=https://web.archive.org/web/20230331171118/https://books.google.com/books?id=7dPCAgAAQBAJ&dq=alhazen+first+incident+ray+reflected+ray+lie+on+same+plane&pg=PA29 |url-status=live }}</ref>
			=== Alhazen's problem ===
	The ] on the ] was named in his honour. Ibn al-Haytham is also featured on the obverse of the Iraqi 10,000 dinars banknote issued in 2003. The ] "59239 Alhazen" was also named in his honour, while ]'s largest laser research facility, located in the ] headquarters in ], is named after him as well.
			{{Main|Alhazen's problem}}
			]]]
			His work on ] in Book V of the Book of Optics contains a discussion of what is now known as Alhazen's problem, first formulated by ] in 150 AD. It comprises drawing lines from two points in the ] of a circle meeting at a point on the ] and making equal angles with the ] at that point. This is equivalent to finding the point on the edge of a circular ] at which a player must aim a cue ball at a given point to make it bounce off the table edge and hit another ball at a second given point. Thus, its main application in optics is to solve the problem, "Given a light source and a spherical mirror, find the point on the mirror where the light will be reflected to the eye of an observer." This leads to an ].<ref>{{harvnb|O'Connor|Robertson|1999}}, {{harvnb|Weisstein|2008}}.</ref> This eventually led Alhazen to derive a formula for the sum of ]s, where previously only the formulas for the sums of squares and cubes had been stated. His method can be readily generalized to find the formula for the sum of any integral powers, although he did not himself do this (perhaps because he only needed the fourth power to calculate the volume of the paraboloid he was interested in). He used his result on sums of integral powers to perform what would now be called an ], where the formulas for the sums of integral squares and fourth powers allowed him to calculate the volume of a ].<ref>{{harvnb|Katz|1995|pp=165–169, 173–174}}.</ref> Alhazen eventually solved the problem using ]s and a geometric proof. His solution was extremely long and complicated and may not have been understood by mathematicians reading him in Latin translation.
			Later mathematicians used ]' analytical methods to analyse the problem.<ref>{{harvnb|Smith|1992}}.</ref> An algebraic solution to the problem was finally found in 1965 by Jack M. Elkin, an actuarian.<ref>{{Citation|last=Elkin|first=Jack M.|title=A deceptively easy problem|journal=Mathematics Teacher|volume=58|issue=3|pages=194–199|year=1965|doi=10.5951/MT.58.3.0194|jstor=27968003}}</ref> Other solutions were discovered in 1989, by Harald Riede<ref>{{Citation|last=Riede|first=Harald|title=Reflexion am Kugelspiegel. Oder: das Problem des Alhazen|journal=Praxis der Mathematik|volume=31|issue=2|pages=65–70|year=1989|language=de}}</ref> and in 1997 by the ] mathematician ].<ref>{{Citation|last=Neumann|first=Peter M.|author-link=Peter M. Neumann|title=Reflections on Reflection in a Spherical Mirror|journal=]|volume=105|issue=6|pages=523–528|year=1998|jstor=2589403|mr=1626185|doi=10.1080/00029890.1998.12004920}}</ref><ref>{{Citation|last=Highfield |first=Roger |author-link=Roger Highfield |date=1 April 1997 |title=Don solves the last puzzle left by ancient Greeks |journal=] |volume=676 |url=https://www.telegraph.co.uk/htmlContent.jhtml?html=/archive/1997/04/01/ngre01.html|url-status=dead |archive-url=https://web.archive.org/web/20041123051228/http://www.telegraph.co.uk/htmlContent.jhtml?html=%2Farchive%2F1997%2F04%2F01%2Fngre01.html |archive-date=23 November 2004 }}</ref>
			Recently, ] (MERL) researchers solved the extension of Alhazen's problem to general rotationally symmetric quadric mirrors including hyperbolic, parabolic and elliptical mirrors.<ref>{{harvnb|Agrawal|Taguchi|Ramalingam|2011}}.</ref>
			=== Camera Obscura ===
	==Physics==
			The ] was known to the ], and was described by the ] ] ] in his scientific book '']'', published in the year 1088 C.E. ] had discussed the basic principle behind it in his ''Problems'', but Alhazen's work contained the first clear description of ].<ref>{{harvnb|Kelley|Milone|Aveni|2005|p=83}}: "The first clear description of the device appears in the ''Book of Optics'' of Alhazen."</ref> and early analysis<ref>{{harvnb|Wade|Finger|2001}}: "The principles of the camera obscura first began to be correctly analysed in the eleventh century, when they were outlined by Ibn al-Haytham."</ref> of the device.
	===''Book of Optics''===
	{{main|Book of Optics}}
			Ibn al-Haytham used a ] mainly to observe a partial solar eclipse.<ref>German physicist Eilhard Wiedemann first provided an abridged German translation of ''On the shape of the eclipse'': {{Cite journal |author=Eilhard Wiedemann |title=Über der Camera obscura bei Ibn al Haiṭam |journal=Sitzungsberichte phys.-med. Sozietät in Erlangen |year=1914 |volume=46 | pages=155–169}} The work is now available in full: {{harvnb|Raynaud|2016}}.</ref>
	His seven volume treatise on ], ''Kitab al-Manazir'' (''Book of Optics'') (written from 1011 to 1021),<ref>Steffens (] , ''The Critics'', ].)</ref> which has been ranked alongside ]'s '']'' as one of the most influential books ever written in ],<ref name=Salih/> drastically transformed the understanding of ] and ]. In ], there were two major theories on vision. The first theory, the ], was supported by such thinkers as ] and ], who believed that sight worked by the eye emitting ] of ]. The second theory, the intromission theory, supported by ] and his followers, had physical forms entering the eye from an object. Ibn al-Haytham argued on the basis of common observations (such as the eye being dazzled or even injured if we look at a very bright light) and logical arguments (such as how a ray could proceeding from the eyes reach the distant stars the instant after we open our eye) to maintain that we cannot see by rays being emitted from the eye, nor through physical forms entering the eye. He instead developed a highly successful theory which explained the process of vision as rays of light proceeding to the eye from each point on an object, which he proved through the use of ]ation.<ref>Lindberg (1976), p. 60-67.</ref>
			In his essay, Ibn al-Haytham writes that he observed the sickle-like shape of the sun at the time of an eclipse. The introduction reads as follows: "The image of the sun at the time of the eclipse, unless it is total, demonstrates that when its light passes through a narrow, round hole and is cast on a plane opposite to the hole it takes on the form of a moonsickle."
			It is admitted that his findings solidified the importance in the history of the ]<ref>{{Cite book|title=History of Photography|last=Eder|first=Josef|publisher=Columbia University Press|year=1945|location=New York|page=37}}</ref> but this treatise is important in many other respects.
	Ibn al-Haytham proved that rays of light travel in straight lines, and carried out a number of experiments with ], ]s, ], and ].<ref name=Deek/> He was also the first to reduce reflected and refracted light rays into vertical and horizontal components, which was a fundamental development in geometric optics.<ref>Albrecht Heeffer. , ], ].</ref> He also discovered a result similar to ], but did not quantify it and derive the law mathematically.<ref>] (1981). (] Pavlos Mihas, , p. 5, Demokritus University, ], ].)</ref> Ibn al-Haytham is also credited with the invention of the ] and ].<ref name=Wade>Wade, Finger.</ref>
			Ancient optics and medieval optics were divided into optics and burning mirrors. Optics proper mainly focused on the study of vision, while burning mirrors focused on the properties of light and luminous rays. ''On the shape of the eclipse'' is probably one of the first attempts made by Ibn al-Haytham to articulate these two sciences.
	''Optics'' was ] by an unknown scholar at the end of the 12th century or the beginning of the 13th century.<ref>Crombie, p. 147, n. 2.</ref> It was printed by ] in 1572, with the title ''Opticae thesaurus: Alhazeni Arabis libri septem, nuncprimum editi; Eiusdem liber De Crepusculis et nubium ascensionibus'' . Risner is also the author of the name variant "Alhazen"; before Risner he was known in the west as Alhacen, which is the correct transcription of the Arabic name.<ref>Smith (2001).</ref> This work enjoyed a great reputation during the ]. Works by Alhacen on geometrical subjects were discovered in the ] in ] in 1834 by E. A. Sedillot. Other manuscripts are preserved in the ] at ] and in the library of ]. Ibn al-Haytham's optical studies were influential in a number of later developments, including the ], which laid the foundations of telescopic astronomy,<ref name=Marshall/> as well as of the modern ], the ], and the use of optical aids in ] ].<ref name=Power/>
			Very often Ibn al-Haytham's discoveries benefited from the intersection of mathematical and experimental contributions. This is the case with ''On the shape of the eclipse''. Besides the fact that this treatise allowed more people to study partial eclipses of the sun, it especially allowed to better understand how the camera obscura works. This treatise is a physico-mathematical study of image formation inside the camera obscura. Ibn al-Haytham takes an experimental approach, and determines the result by varying the size and the shape of the aperture, the focal length of the camera, the shape and intensity of the light source.<ref>{{harvnb|Raynaud|2016|pp=130–160}}</ref>
	===Other treatises on optics===
	Besides the '']'', Ibn al-Haytham wrote a number of other treatises on ]. His ''Risala fi l-Daw’'' (''Treatise on Light'') is a supplement to his ''Kitab al-Manazir'' (''Book of Optics''). The text contained further investigations on the properties of ] and its ] dispersion through various ] media. He also carried out further observations, investigations and examinations on the ] of the ], the ] and ], ] in ], the ] of the ] and the ] of the ], various ] phenomena (including the ], ], and ]), ], ], ], ] and ] mirrors, and ].<ref name=Bizri/>
			In his work he explains the inversion of the image in the camera obscura,<ref>{{harvnb|Raynaud|2016|pp=114–116}}</ref> the fact that the image is similar to the source when the hole is small, but also the fact that the image can differ from the source when the hole is large. All these results are produced by using a point analysis of the image.<ref>{{harvnb|Raynaud|2016|pp=91–94}}</ref>
	In his treatise, ''Mizan al-Hikmah'' (''Balance of Wisdom''), Ibn al-Haytham discussed the ] of the ] and related it to ]. He also studied ]. He discovered that the ] only ceases or begins when the Sun is 19° below the horizon and attempted to measure the height of the atmosphere on that basis.<ref name=Deek>Dr. Mahmoud Al Deek. "Ibn Al-Haitham: Master of Optics, Mathematics, Physics and Medicine", ''Al Shindagah'', November-December 2004.</ref>
			=== Refractometer ===
	===Astrophysics, celestial mechanics, and statics===
			{{Main|Refractometer}}
	In ] and the ] field of ], Ibn al-Haytham, in his ''Epitome of Astronomy'', discovered that the ] "were accountable to the ]".<ref>Duhem, p. 28.</ref>
			In the seventh tract of his book of optics, Alhazen described an apparatus for experimenting with various cases of refraction, in order to investigate the relations between the angle of incidence, the angle of refraction and the angle of deflection. This apparatus was a modified version of an apparatus used by Ptolemy for similar purpose.<ref>{{Cite book |url=http://archive.org/details/history-of-science-and-technology-in-islam-fuat-sezgin |title=History Of Science And Technology In Islam Fuat Sezgin |date=2011}}</ref><ref>{{Cite book |last=Gaukroger |first=Stephen |url=https://books.google.com/books?id=QVwDs_Ikad0C&dq=ptolemy+alhazen+refractometer&pg=PA142 |title=Descartes: An Intellectual Biography |date=1995 |publisher=Clarendon Press |isbn=978-0-19-151954-3 |language=en}}</ref><ref>{{Cite book |last=Newton |first=Isaac |url=https://books.google.com/books?id=gNrLQN0VbAoC&dq=ptolemy+alhazen+refractometer&pg=PA175 |title=The Optical Papers of Isaac Newton|volume =1: The Optical Lectures 1670–1672 |date=1984|publisher=Cambridge University Press |isbn=978-0-521-25248-5 |language=en}}</ref>
			=== Unconscious inference ===
	Ibn al-Haytham's ''Mizan al-Hikmah'' (''Balance of Wisdom'') dealt with ], astrophysics, and celestial mechanics. He discussed the theory of ] between ]es, and it seems that he was also aware of the ] of ] due to ] at a distance.<ref name=Bizri/>
			{{Main|Unconscious inference}}
			Alhazen basically states the concept of unconscious inference in his discussion of colour before adding that the inferential step between sensing colour and differentiating it is shorter than the time taken between sensing and any other visible characteristic (aside from light), and that "time is so short as not to be clearly apparent to the beholder." Naturally, this suggests that the colour and form are perceived elsewhere. Alhazen goes on to say that information must travel to the central nerve cavity for processing and:<blockquote>the sentient organ does not sense the forms that reach it from the visible objects until
			after it has been affected by these forms; thus it does not sense color as color or light as light until after it has been affected by the form of color or light. Now the affectation received by the sentient organ from the form of color or of light is a certain change; and change must take place in time; .....and it is in the time during which the form extends from the sentient organ's surface to the cavity of the common nerve, and in (the time) following that, that the sensitive faculty, which exists in the whole of the sentient body will perceive color as color...Thus the last sentient's perception of color as such and of light as such takes place at a time following that in which the form arrives from the surface of the sentient organ to the cavity of the common nerve.<ref>{{Cite book |last1=Boudrioua |first1=Azzedine |url=https://books.google.com/books?id=WD0PEAAAQBAJ&dq=the+sentient+organ+does+not+sense+the+forms+that+reach+it+from+the+visible+objects+until+after+it+has+been+a&pg=PA76 |title=Light-Based Science: Technology and Sustainable Development, The Legacy of Ibn al-Haytham |last2=Rashed |first2=Roshdi |last3=Lakshminarayanan |first3=Vasudevan |date=2017 |publisher=CRC Press |isbn=978-1-4987-7940-1 |language=en}}</ref></blockquote>
			=== Color constancy ===
	His ''Maqala fi'l-qarastun'' is a treatise on ]. Little is currently known about the work, except for what is known through the later works of ] in the 12th century. In this treatise, Ibn al-Haytham formulated the theory that the ] of bodies varies with their distance from the center of the ].<ref>Professor Mohammed Abattouy (2002). "The Arabic Science of weights: A Report on an Ongoing Research Project", ''The Bulletin of the Royal Institute for Inter-Faith Studies'' '''4''', p. 109-130.</ref>
			{{Main|Color constancy}}
			Alhazen explained ] by observing that the light reflected from an object is modified by the object's color. He explained that the quality of the light and the color of the object are mixed, and the visual system separates light and color. In Book II, Chapter 3 he writes:<blockquote>Again the light does not travel from the colored object to the eye unaccompanied by the color, nor does the form of the color pass from the colored object to the eye unaccompanied by the light. Neither the form of the light nor that of the color existing in the colored object can pass except as mingled together and the last sentient can only
			perceive them as mingled together. Nevertheless, the sentient perceives that the visible object is luminous and that the light seen in the object is other than the color and that these are two properties.<ref>{{Cite book |last1=Boudrioua |first1=Azzedine |url=https://books.google.com/books?id=WD0PEAAAQBAJ&dq=Al-Haytham+described+color+constancy+by+observing+that+light+reflected+by+an+object+is+modified+by+the+color+of+the+object&pg=PA78 |title=Light-Based Science: Technology and Sustainable Development, The Legacy of Ibn al-Haytham |last2=Rashed |first2=Roshdi |last3=Lakshminarayanan |first3=Vasudevan |date=2017|publisher=CRC Press |isbn=978-1-4987-7940-1 |language=en}}</ref></blockquote>
			=== Other contributions ===
	===Dynamics and kinematics===
			The ''Kitab al-Manazir'' (Book of Optics) describes several experimental observations that Alhazen made and how he used his results to explain certain optical phenomena using mechanical analogies. He conducted experiments with ]s and concluded that only the impact of ] projectiles on surfaces was forceful enough to make them penetrate, whereas surfaces tended to deflect ] projectile strikes. For example, to explain refraction from a rare to a dense medium, he used the mechanical analogy of an iron ball thrown at a thin slate covering a wide hole in a metal sheet. A perpendicular throw breaks the slate and passes through, whereas an oblique one with equal force and from an equal distance does not.<ref>{{harvnb|Russell|1996|p=695}}.</ref> He also used this result to explain how intense, direct light hurts the eye, using a mechanical analogy: Alhazen associated 'strong' lights with perpendicular rays and 'weak' lights with oblique ones. The obvious answer to the problem of multiple rays and the eye was in the choice of the perpendicular ray, since only one such ray from each point on the surface of the object could penetrate the eye.<ref>{{harvnb|Russell|1996|p=}}.</ref>
	In the ] and ] fields of ], Ibn al-Haytham's ''Risala fi’l-makan'' (''Treatise on Place'') discussed theories on the ] of a body. He maintained that a body moves ] unless an external force stops it or changes its direction of motion.<ref name=Bizri/> This was a precursor to the law of ] later stated by ] in the 16th century and now known as ].<ref name=Salam/>
			Sudanese psychologist Omar Khaleefa has argued that Alhazen should be considered the founder of ], for his pioneering work on the psychology of visual perception and ]s.<ref name="auto2">{{harvnb|Khaleefa|1999}}</ref> Khaleefa has also argued that Alhazen should also be considered the "founder of ]", a sub-discipline and precursor to modern psychology.<ref name="auto2" /> Although Alhazen made many subjective reports regarding vision, there is no evidence that he used quantitative psychophysical techniques and the claim has been rebuffed.<ref>{{harvnb|Aaen-Stockdale|2008}}.</ref>
	Ibn al-Haytham also discovered the concept of ], part of ], around the same time as his contemporary, ] (Avicenna).<ref name=Nasr>Seyyed ], "The achievements of Ibn Sina in the field of science and his contributions to its philosophy", ''Islam & Science'', December 2003.</ref>
			Alhazen offered an explanation of the ], an illusion that played an important role in the scientific tradition of medieval Europe.<ref>{{harvnb|Ross|Plug|2002}}.</ref> Many authors repeated explanations that attempted to solve the problem of the Moon appearing larger near the horizon than it does when higher up in the sky. Alhazen argued against Ptolemy's refraction theory, and defined the problem in terms of perceived, rather than real, enlargement. He said that judging the distance of an object depends on there being an uninterrupted sequence of intervening bodies between the object and the observer. When the Moon is high in the sky there are no intervening objects, so the Moon appears close. The perceived size of an object of constant angular size varies with its perceived distance. Therefore, the Moon appears closer and smaller high in the sky, and further and larger on the horizon. Through works by ], ] and Witelo based on Alhazen's explanation, the Moon illusion gradually came to be accepted as a psychological phenomenon, with the refraction theory being rejected in the 17th century.<ref>{{harvnb|Hershenson|1989|pp=9–10}}.</ref> Although Alhazen is often credited with the perceived distance explanation, he was not the first author to offer it. ] ({{circa}} 2nd century) gave this account (in addition to refraction), and he credited it to ] ({{circa}} 135–50 BCE).<ref>{{harvnb|Ross|2000}}.</ref> Ptolemy may also have offered this explanation in his ''Optics'', but the text is obscure.<ref>{{harvnb|Ross|Ross|1976}}.</ref> Alhazen's writings were more widely available in the Middle Ages than those of these earlier authors, and that probably explains why Alhazen received the credit.
	==Astronomy==
	===''Doubts concerning Ptolemy''===
	In his ''Al-Shukūk ‛alā Batlamyūs'', variously translated as ''Doubts concerning Ptolemy'' or ''Aporias against Ptolemy'', written between 1025 and 1028, Ibn al-Haytham criticized many of ]'s works, including the '']'', ''Planetary Hypotheses'', and ''Optics'', pointing out various contradictions he found in these works. He considered that some of the mathematical devices Ptolemy introduced into astronomy, especially the ], failed to satisfy the physical requirement of uniform circular motion, and wrote a scathing critique of the physical reality of Ptolemy's astronomical system, noting the absurdity of relating actual physical motions to imaginary mathematical points, lines, and circles:<ref>Langerman, p. 8-10</ref>
	{{quote|"Ptolemy assumed an arrangement (''hay'a'') that cannot exist, and the fact that this arrangement produces in his imagination the motions that belong to the planets does not free him from the error he committed in his assumed arrangement, for the existing motions of the planets cannot be the result of an arrangement that is impossible to exist.... or a man to imagine a circle in the heavens, and to imagine the planet moving in it does not bring about the planet's motion."<ref>] (1978), p. 121, n. 13.</ref><ref>, ] (2004).</ref>}}
			== Scientific method ==
	In his ''Aporias against Ptolemy'', Ibn al-Haytham also commented on the difficulty of attaining scientific knowledge:
			{{further|Scientific method}}
	{{quote|"Truth is sought for itself the truths, are immersed in uncertainties not immune from error..."<ref name=Sabra>] (2003).</ref>}}
			{{blockquote|Therefore, the seeker after the truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them, but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration, and not to the sayings of a human being whose nature is fraught with all kinds of imperfection and deficiency. The duty of the man who investigates the writings of scientists, if learning the truth is his goal, is to make himself an enemy of all that he reads, and ... attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency.|Alhazen<ref name="{{harvnb|sabra|1989}}." />}}
			An aspect associated with Alhazen's optical research is related to systemic and methodological reliance on experimentation (''i'tibar'')(Arabic: اختبار) and ] in his scientific inquiries. Moreover, his experimental directives rested on combining classical physics (''ilm tabi'i'') with mathematics (''ta'alim''; geometry in particular). This mathematical-physical approach to experimental science supported most of his propositions in ''Kitab al-Manazir'' (''The Optics''; ''De aspectibus'' or ''Perspectivae'')<ref>See, for example, {{Webarchive|url=https://web.archive.org/web/20180818182120/http://perspectiva.biblhertz.it/doc01.VII.html |date=18 August 2018 }}, for his experiments in refraction</ref> and grounded his theories of vision, light and colour, as well as his research in catoptrics and ] (the study of the reflection and refraction of light, respectively).<ref name="{{harvs|nb|last=el-bizri|year=2005a|year2=2005b}}.">{{harvs|nb|last=El-Bizri|year=2005a|year2=2005b}}.</ref> <!-- ] in his book ''Ibn Al-Haytham: First Scientist'' has argued that Alhazen's approach to testing and experimentation made an important contribution to the scientific method. -->
			According to Matthias Schramm,<ref name=thiele2005>{{cite web| url = https://core.ac.uk/download/pdf/82356023.pdf| title = see Schramm's Habilitationsschrift, ''Ibn al-Haythams Weg zur Physik'' (Steiner, Wiesbaden, 1963) as cited by Rüdiger Thiele (2005) ''Historia Mathematica'' '''32''', 271–274. "In Memoriam: Matthias Schramm, 1928–2005"| access-date = 25 October 2017| archive-date = 25 October 2017| archive-url = https://web.archive.org/web/20171025192431/https://core.ac.uk/download/pdf/82356023.pdf| url-status = live}}</ref> Alhazen "was the first to make a systematic use of the method of varying the experimental conditions in a constant and uniform manner, in an experiment showing that the intensity of the light-spot formed by the projection of the ] through two small ] onto a screen diminishes constantly as one of the apertures is gradually blocked up."<ref>{{harvnb|Toomer|1964|pp=463–464}}</ref> G. J. Toomer expressed some skepticism regarding Schramm's view,<ref name="auto1">{{harvnb|Toomer|1964|p=465}}</ref> partly because at the time (1964) the ''Book of Optics'' had not yet been fully translated from Arabic, and Toomer was concerned that without context, specific passages might be read anachronistically. While acknowledging Alhazen's importance in developing experimental techniques, Toomer argued that Alhazen should not be considered in isolation from other Islamic and ancient thinkers.<ref name="auto1" /> Toomer concluded his review by saying that it would not be possible to assess Schramm's claim that Ibn al-Haytham was the true founder of modern physics without translating more of Alhazen's work and fully investigating his influence on later medieval writers.<ref name=toomer1964Review>]. {{Webarchive|url=https://web.archive.org/web/20170326070235/http://www.jstor.org/stable/228328?pg=464 |date=26 March 2017 }} Toomer p. 464: "Schramm sums up achievement in the development of scientific method.", p. 465: "Schramm has demonstrated .. beyond any dispute that Ibn al-Haytham is a major figure in the Islamic scientific tradition, particularly in the creation of experimental techniques." p. 465: "Only when the influence of ibn al-Haytam and others on the mainstream of later medieval physical writings has been seriously investigated can Schramm's claim that ibn al-Haytam was the true founder of modern physics be evaluated."</ref>
	He held that the criticism of existing theories — which dominated this book — holds a special place in the growth of scientific knowledge:
	{{quote|"Therefore, the seeker after the truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them, but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration, and not to the sayings of a human being whose nature is fraught with all kinds of imperfection and deficiency. Thus the duty of the man who investigates the writings of scientists, if learning the truth is his goal, is to make himself an enemy of all that he reads, and, applying his mind to the core and margins of its content, attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency."<ref name=Sabra/>}}
			== Other works on physics ==
	===''On the Configuration of the World''===
	In his ''On the Configuration of the World'', despite his criticisms directed towards Ptolemy, Ibn al-Haytham continued to accept the physical reality of the ] of the universe,<ref>Some writers, however, argue that Alhazen's critique constituted a form of ] (see Qadir, p. 5-6, 10).</ref> presenting a detailed description of the physical structure of the ] in his ''On the Configuration of the World'':
	{{quote|"The earth as a whole is a round sphere whose center is the center of the world. It is stationary in its middle, fixed in it and not moving in any direction nor moving with any of the varieties of motion, but always at rest."<ref>Langerman, chap. 2, sect. 22, p. 61.</ref>}}
			=== Optical treatises<!--Linked from ]--> ===
	While he attempted to discover the physical reality behind Ptolemy's mathematical model, he developed the concept of a single ] for each component of Ptolemy's planetary motions. This work was eventually translated into ] and ] in the 13th and 14th centuries and subsequently had an important influence during the European Middle Ages and ].<ref>Langerman, p. 34-41.</ref><ref>Gondhalekar (2001), p. 21.</ref>
			Besides the ''Book of Optics'', Alhazen wrote several other treatises on the same subject, including his ''Risala fi l-Daw''' (''Treatise on Light''). He investigated the properties of ], the ], ]s, ], and ]. Experiments with mirrors and the refractive interfaces between air, water, and glass cubes, hemispheres, and quarter-spheres provided the foundation for his theories on ].<ref name="{{harvnb|el-bizri|2006}}.">{{harvnb|El-Bizri|2006}}.</ref>
	===''The Model of the Motions''===
	Ibn al-Haytham's ''The Model of the Motions of Each of the Seven Planets'', written in 1038, was an important book on astronomy. The surviving manuscript of this work has only recently been discovered, with much of it still missing, hence the work has not yet been published in modern times. Following on from his ''Doubts on Ptolemy'' and ''The Resolution of Doubts'', Ibn al-Haytham described the first non-Ptolemaic model in ''The Model of the Motions''. His reform excluded ], as he developed a systematic study of ] ] that was completely ]. This in turn led to innovative developments in ] ].<ref>Rashed (2007).</ref>
			=== Celestial physics ===
	His reformed model was the first to reject the ]<ref>Rashed (2007), p. 20, 53.</ref> and ],<ref>Rashed (2007), p. 33-34.</ref> free celestial kinematics from cosmology, and reduce physical entities to geometrical entities. The model also propounded the ] about its axis,<ref>Rashed (2007), p. 20, 32-33.</ref> and the centres of motion were geometrical points without any physical significance, like ]'s model centuries later.<ref>Rashed (2007), p. 51-52.</ref>
			Alhazen discussed the ] of the celestial region in his ''Epitome of Astronomy'', arguing that Ptolemaic models must be understood in terms of physical objects rather than abstract hypotheses{{snd}}in other words that it should be possible to create physical models where (for example) none of the celestial bodies would collide with each other. The suggestion of mechanical models for the Earth centred ] "greatly contributed to the eventual triumph of the Ptolemaic system among the Christians of the West". Alhazen's determination to root astronomy in the realm of physical objects was important, however, because it meant astronomical hypotheses "were accountable to the ]", and could be criticised and improved upon in those terms.<ref>{{harvnb|Duhem|1969|p=28}}.</ref>
			He also wrote ''Maqala fi daw al-qamar'' (''On the Light of the Moon'').
	In the text, Ibn al-Haytham also describes an early version of ], where he employs only minimal hypotheses regarding the properties that characterize astronomical motions, as he attempts to eliminate from his planetary model the cosmological hypotheses that cannot be observed from ].<ref name=Rashed-35-36/>
	==Engineering==		=== Mechanics ===
	===Civil engineering===
	In ], one account of his career as a ] has him summoned to Egypt by the mercurial ] ] to regulate the ] of the ]. His field work, however, later made him aware of the impracticality of this scheme.
			In his work, Alhazen discussed theories on the ] of a body.<ref name="{{harvnb|el-bizri|2006}}."/>
	===Water clock===
	According to ], Ibn al-Haytham wrote a treatise providing a description on the ] of a ].<ref>], </ref>
			{{anchor|Astronomy}}<!-- -Anchor for a wikilink in Celestial Spheres article. Please do not remove or rename without making the appropriate amendments to that article.- -->
	==Mathematics==
	In ], Ibn al-Haytham builds on the mathematical works of ] and ], and goes on to systemize ] ], ]s, ], and ] after linking ] to ].
			== Astronomical works ==
	===Alhazen's problem===
	His work on ] in ''Book V'' of the ''Book of Optics'' contains the important problem known as ''Alhazen's problem''. It comprises drawing lines from two points in the plane of a circle meeting at a point on the ] and making equal angles with the normal at that point. This leads to an ]. This eventually led Ibn al-Haytham to derive the earliest formula for the sum of ]s; and by using an early ] by ], he developed a method for determining the general formula for the sum of any ] ]. This was fundamental to the development of ] and ] ].<ref name=Katz>Katz.</ref>
			=== ''On the Configuration of the World'' ===
	While Ibn al-Haytham solved the problem using ]s and a geometric proof, Alhazen's problem remained influential in Europe, as later mathematicians such as ], ], ], ] and many others attempted to find an algebraic solution to the problem, using various methods including ] and derivation by ]s.<ref name=Smith/> Mathematicians were not able to find an algebraic solution to the problem until the end of the 20th century.<ref name=Steffens/>
			In his ''On the Configuration of the World'' Alhazen presented a detailed description of the physical structure of the earth:{{blockquote|The earth as a whole is a round sphere whose center is the center of the world. It is stationary in its middle, fixed in it and not moving in any direction nor moving with any of the varieties of motion, but always at rest.<ref>{{harvnb|Langermann|1990}}, chap. 2, sect. 22, p. 61</ref>}}
	===Geometry===
	In ], Ibn al-Haytham developed ] by establishing the linkage between ] and ]. Ibn al-Haytham also discovered a formula for adding the first 100 natural numbers (which may later have been intuited by ] as a youth). Ibn al-Haytham used a geometric proof to prove the formula.<ref>J. Rottman. ''A first course in Abstract Algebra'', Chapter 1.</ref> His attempted proof of the ] was also similar to the ] and ] in the 18th century.<ref name=Smith/>
			The book is a non-technical explanation of Ptolemy's '']'', which was eventually translated into ] and ] in the 13th and 14th centuries and subsequently had an influence on astronomers such as ]<ref name="{{harvnb|lorch|2008}}.">{{harvnb|Lorch|2008}}.</ref> during the European ] and ].<ref>{{harvnb|Langermann|1990|pp=34–41}}; {{harvnb|Gondhalekar|2001|p=21}}.</ref>
	In ], Ibn al-Haytham attempted to solve the problem of ] using the area of ]s, but later gave up on the impossible task.<ref name=MacTutor/> Ibn al-Haytham also tackled other problems in elementary (]) and advanced (] and ]) geometry, some of which he was the first to solve.<ref name=Sabra/>
			=== ''Doubts Concerning Ptolemy'' ===
	===Number theory===
	His contributions to ] includes his work on ]s. In his ''Analysis and Synthesis'', Ibn al-Haytham was the first to realize that every even perfect number is of the form 2<sup>''n''&minus;1</sup>(2<sup>''n''</sup>&nbsp;&minus;&nbsp;1) where 2<sup>''n''</sup>&nbsp;&minus;&nbsp;1 is ], but he was not able to prove this result successfully (] later proved it in the 18th century).<ref name=MacTutor/>
			In his ''Al-Shukūk ‛alā Batlamyūs'', variously translated as ''Doubts Concerning Ptolemy'' or ''Aporias against Ptolemy'', published at some time between 1025 and 1028, Alhazen criticized ]'s ''Almagest'', ''Planetary Hypotheses'', and ''Optics'', pointing out various contradictions he found in these works, particularly in astronomy. Ptolemy's ''Almagest'' concerned mathematical theories regarding the motion of the planets, whereas the ''Hypotheses'' concerned what Ptolemy thought was the actual configuration of the planets. Ptolemy himself acknowledged that his theories and configurations did not always agree with each other, arguing that this was not a problem provided it did not result in noticeable error, but Alhazen was particularly scathing in his criticism of the inherent contradictions in Ptolemy's works.<ref name="{{harvnb|sabra|1998}}.">{{harvnb|Sabra|1998}}.</ref> He considered that some of the mathematical devices Ptolemy introduced into astronomy, especially the ], failed to satisfy the physical requirement of uniform circular motion, and noted the absurdity of relating actual physical motions to imaginary mathematical points, lines and circles:<ref>{{harvnb|Langermann|1990|pp=8–10}}</ref>
	Ibn al-Haytham solved problems involving ] using what is now called ]. In his ''Opuscula'', Ibn al-Haytham considers the solution of a system of congruences, and gives two general methods of solution. His first method, the canonical method, involved Wilson's theorem, while his second method involved a version of the ].<ref name=MacTutor/>
			{{blockquote|Ptolemy assumed an arrangement (''hay'a'') that cannot exist, and the fact that this arrangement produces in his imagination the motions that belong to the planets does not free him from the error he committed in his assumed arrangement, for the existing motions of the planets cannot be the result of an arrangement that is impossible to exist... or a man to imagine a circle in the heavens, and to imagine the planet moving in it does not bring about the planet's motion.<ref>{{harvnb|Sabra|1978b|p=121, n. 13}}</ref>}}
	==Medicine==
	===''Book of Optics''===
	{{main|Book of Optics}}
			Having pointed out the problems, Alhazen appears to have intended to resolve the contradictions he pointed out in Ptolemy in a later work. Alhazen believed there was a "true configuration" of the planets that Ptolemy had failed to grasp. He intended to complete and repair Ptolemy's system, not to replace it completely.<ref name="{{harvnb|sabra|1998}}." /> In the ''Doubts Concerning Ptolemy'' Alhazen set out his views on the difficulty of attaining scientific knowledge and the need to question existing authorities and theories:
	In ] and ], Ibn al-Haytham made important advances in ], and he studied and correctly explained the process of ] and ] for the first time.<ref>Bashar Saad, Hassan Azaizeh, Omar Said (October 2005). "Tradition and Perspectives of Arab Herbal Medicine: A Review", ''Evidence-based Complementary and Alternative Medicine'' '''2''' (4), p. 475-479 . ].</ref>
			{{blockquote|Truth is sought for itself the truths, are immersed in uncertainties not immune from error...<ref name="{{harvnb|sabra|1989}}." />}}
	==Philosophy==
	===Phenomenology===
	In ], Ibn al-Haytham is considered a pioneer of ]. He articulated a relationship between the physical and observable ] and that of ], ] and ]s. His theories regarding ] and ], linking the domains of science and religion, led to a philosophy of ] based on the direct observation of ] from the observer's point of view. Much of his thought on phenomenology was not further developed until the 20th century.<ref>Dr Valérie Gonzalez, "Universality and Modernity", ''The Ismaili United Kingdom'', December 2002, p. 50-53.</ref>
			He held that the criticism of existing theories{{snd}}which dominated this book{{snd}}holds a special place in the growth of scientific knowledge.
	===Place===
	Ibn al-Haytham's ''Risala fi’l-makan'' (''Treatise on Place'') presents a critique of ]'s concept of ] (]). Aristotle's '']'' stated that the place of something is the two-dimensional boundary of the containing body that is at rest and is in contact with what it contains. Ibn al-Haytham disagreed and demonstrated that place (al-makan) is the imagined three-dimensional void between the inner surfaces of the containing body. He showed that place was akin to ], foreshadowing ]'s concept of place in the ''Extensio'' in the 17th century.
			=== ''Model of the Motions of Each of the Seven Planets'' ===
	Following on from his ''Treatise on Place'', Ibn al-Haytham's ''Qawl fi al-Makan'' (''Discourse on Place'') was an important treatise which presents ] demonstrations for his geometrization of ], in opposition to ]'s philosophical concept of place, which Ibn al-Haytham rejected on mathematical grounds. ], a supporter of Aristotle's philosophical view of place, later criticized the work in ''Fi al-Radd ‘ala Ibn al-Haytham fi al-makan'' (''A refutation of Ibn al-Haytham’s place'') for its geometrization of place.<ref>El-Bizri (2007).</ref>
			Alhazen's ''The Model of the Motions of Each of the Seven Planets'' was written {{circa}} 1038. Only one damaged manuscript has been found, with only the introduction and the first section, on the theory of planetary motion, surviving. (There was also a second section on astronomical calculation, and a third section, on astronomical instruments.) Following on from his ''Doubts on Ptolemy'', Alhazen described a new, geometry-based planetary model, describing the motions of the planets in terms of spherical geometry, infinitesimal geometry and trigonometry. He kept a geocentric universe and assumed that celestial motions are uniformly circular, which required the inclusion of ] to explain observed motion, but he managed to eliminate Ptolemy's ]. In general, his model didn't try to provide a causal explanation of the motions, but concentrated on providing a complete, geometric description that could explain observed motions without the contradictions inherent in Ptolemy's model.<ref>{{harvnb|Rashed|2007}}.</ref>
	===Theology===
	Ibn al-Haytham is said to have been a supporter of the ] school of ],<ref>], </ref> and opposed to the views of the ] school,<ref>Bettany, p. 251.</ref> though he may have been a Mu'tazili supporter himself at some point in his life.<ref>Hodgson (2006), p. 53.</ref>
			=== Other astronomical works ===
	==Psychology==
	Ibn al-Haytham is considered by some to be the founder of ] and ],<ref name=Khaleefa/> for his pioneering work on the ] of ].<ref name=Steffens/>
			Alhazen wrote a total of twenty-five astronomical works, some concerning technical issues such as ''Exact Determination of the Meridian'', a second group concerning accurate astronomical observation, a third group concerning various astronomical problems and questions such as the location of the ]; Alhazen made the first systematic effort of evaluating the Milky Way's parallax, combining Ptolemy's data and his own. He concluded that the parallax is (probably very much) smaller than Lunar parallax, and the Milky way should be a celestial object. Though he was not the first who argued that the Milky Way does not belong to the atmosphere, he is the first who did quantitative analysis for the claim.<ref>{{harvnb|Eckart|2018}}</ref>
	===''Book of Optics''===
			The fourth group consists of ten works on astronomical theory, including the ''Doubts'' and ''Model of the Motions'' discussed above.<ref>{{harvnb|Rashed|2007|pp=8–9}}.</ref>
	{{main|Book of Optics}}
			== Mathematical works ==
	In the '']'', Ibn al-Haytham was the first scientist to argue that vision occurs in the brain, rather than the eyes. He pointed out that personal experience has an effect on what people see and how they see, and that vision and perception are subjective. He explained possible errors in vision in detail, and as an example described how a small child with less experience may have more difficulty interpreting what he or she sees. He also gave an example of how an adult can make mistakes in vision due to experience that suggests that one is seeing one thing, when one is really seeing something else.<ref name=Steffens/>
			]
			In ], Alhazen built on the mathematical works of ] and ] and worked on "the beginnings of the link between ] and ]". Alhazen made developments in ]s and number theory.<ref>{{harvnb|Faruqi|2006|pp=395–396}}:
			In seventeenth century Europe the problems formulated by Ibn al-Haytham (965–1041) became known as 'Alhazen's problem'. ... Al-Haytham's contributions to geometry and number theory went well beyond the Archimedean tradition. Al-Haytham also worked on analytical geometry and the beginnings of the link between algebra and geometry. Subsequently, this work led in pure mathematics to the harmonious fusion of algebra and geometry that was epitomised by Descartes in geometric analysis and by Newton in the calculus. Al-Haytham was a scientist who made major contributions to the fields of mathematics, physics and astronomy during the latter half of the tenth century.</ref>
			He developed a formula for summing the first 100 natural numbers, using a geometric proof to prove the formula.<ref>{{harvnb|Rottman|2000}}, Chapter 1.</ref>
	==Arts==
	===Hockney-Falco thesis===
	{{main|Hockney-Falco thesis}}
			=== Geometry ===
	At a scientific conference in February 2007, ] argued that Ibn al-Haytham's work on optics may have influenced the use of optical aids by ] ]ists. Falco said that his and ]'s examples of Renaissance art "demonstrate a continuum in the use of optics by artists from c. 1430, arguably initiated as a result of Ibn al-Haytham's influence, until today."<ref>] "Ibn al-Haytham and the Origins of Modern Image Analysis", presented at a plenary session at the International Conference on Information Sciences, Signal Processing and its Applications, 12–15 February 2007. Sharjah, United Arab Emirates (U.A.E.). </ref>
			]
			Alhazen explored what is now known as the ] ], the fifth ] in ], using a ],<ref>{{harvnb|Eder|2000}}.</ref> and in effect introducing the concept of motion into geometry.<ref>{{harvnb|Katz|1998|p=269}}: "In effect, this method characterised parallel lines as lines always equidistant from one another and also introduced the concept of motion into geometry."</ref> He formulated the ], which Boris Abramovich Rozenfeld names the "Ibn al-Haytham–Lambert quadrilateral".<ref>{{harvnb|Rozenfeld|1988|p=65}}.</ref> He was criticised by Omar Khayyam who pointed that Aristotle had condemned the use of ].<ref>{{Cite book |last1=Boyer |first1=Carl B. |url=https://books.google.com/books?id=bR9HAAAAQBAJ&dq=motion+geometry+alhazen&pg=PA220 |title=A History of Mathematics |last2=Merzbach |first2=Uta C. |date=2011 |publisher=John Wiley & Sons |isbn=978-0-470-63056-3 |language=en |access-date=19 March 2023 |archive-date=7 September 2023 |archive-url=https://web.archive.org/web/20230907232753/https://books.google.com/books?id=bR9HAAAAQBAJ&dq=motion+geometry+alhazen&pg=PA220 |url-status=live }}</ref>
			In elementary geometry, Alhazen attempted to solve the problem of ] using the area of ] (crescent shapes), but later gave up on the impossible task.<ref name="{{harvnb|o'connor|robertson|1999}}.">{{harvnb|O'Connor|Robertson|1999}}.</ref> The two lunes formed from a ] by erecting a semicircle on each of the triangle's sides, inward for the hypotenuse and outward for the other two sides, are known as the ]; they have the same total area as the triangle itself.<ref>{{Harvnb|Alsina|Nelsen|2010}}.</ref>
	==See also==
	*]
	*]
	*]
	*]
	*]
	*]
	*]
	*]
			=== Number theory ===
	==Notes==
	<!-- This article is very poorly referenced. Can we combine the 'references' and 'notes' sections, as having both is rather redundant...? -->
	{{reflist|2}}
			Alhazen's contributions to ] include his work on ]s. In his ''Analysis and Synthesis'', he may have been the first to state that every even perfect number is of the form 2<sup>''n''−1</sup>(2<sup>''n''</sup>&nbsp;−&nbsp;1) where 2<sup>''n''</sup>&nbsp;−&nbsp;1 is ], but he was not able to prove this result; ] later proved it in the 18th century, and it is now called the ].<ref name="{{harvnb|o'connor|robertson|1999}}." />
	==References==
	* Abbott, David, ed. (1983), ''Biographical Dictionary of Scientists'', Vol. I.
			Alhazen solved problems involving ] using what is now called ]. In his ''Opuscula'', Alhazen considers the solution of a system of congruences, and gives two general methods of solution. His first method, the canonical method, involved Wilson's theorem, while his second method involved a version of the ].<ref name="{{harvnb|o'connor|robertson|1999}}." />
	* Bettany, Laurence (1995). "Ibn al-Haytham: an answer to multicultural science teaching?", ''Physics Education'' '''30''', p. 247-252.
	* ] (1928). ''The Making of Humanity''. G. Allen & Unwin Ltd.
			=== Calculus ===
	* Crombie, A. C. (1971). ''Robert Grosseteste and the Origins of Experimental Science, 1100 - 1700''. Clarendon Press, Oxford.
			Alhazen discovered the sum formula for the fourth power, using a method that could be generally used to determine the sum for any integral power. He used this to find the volume of a ]. He could find the integral formula for any polynomial without having developed a general formula.<ref>{{cite journal |doi=10.2307/2691411 |author=Katz, Victor J. |author-link=Victor J. Katz |title=Ideas of Calculus in Islam and India |jstor=2691411 |journal=Mathematics Magazine |year=1995 |volume=68 |issue=3 |pages=163–174 year=1995}}</ref>
	* Duhem, Pierre (1908, 1969). ''To Save the Phenomena: An Essay on the Idea of Physical theory from Plato to Galileo''. University of Chicago Press, Chicago.
	* El-Bizri, Nader (2006), "Ibn al-Haytham or Alhazen", in Meri, Josef W. (2006), ''Medieval Islamic Civilization: An Encyclopaedia'', Vol. II, p. 343-345, ], New York, London.
			== Other works ==
	* El-Bizri, Nader (2007). "In Defence of the Sovereignty of Philosophy: Al-Baghdadi's Critique of Ibn al-Haytham's Geometrisation of Place", ''Arabic Sciences and Philosophy'' '''17''', p. 57-80. ].
	* Elliott, R. S. (1966). ''Electromagnetics''. ].
			=== ''Influence of Melodies on the Souls of Animals'' ===
	* Faruqi, Yasmeen M. (2006). "Contributions of Islamic scholars to the scientific enterprise", ''International Education Journal'' '''7''' (4), p. 391-396.
	* Gondhalekar, Prabhakar M. (2001). ''The Grip of Gravity: The Quest to Understand the Laws of Motion and Gravitation''. ]. ISBN 0521803160.
			Alhazen also wrote a ''Treatise on the Influence of Melodies on the Souls of Animals'', although no copies have survived. It appears to have been concerned with the question of whether animals could react to music, for example whether a camel would increase or decrease its pace.
	* Gorini, Rosanna (2003). "Al-Haytham the Man of Experience: First Steps in the Science of Vision", ''International Society for the History of Islamic Medicine''. Institute of Neurosciences, Laboratory of Psychobiology and Psychopharmacology, Rome, Italy.
	* Hamarneh, Sami (1972). Review of Hakim Mohammed Said, ''Ibn al-Haitham'', ''Isis'' '''63''' (1), p. 118-119.
			=== Engineering ===
			In ], one account of his career as a ] has him summoned to Egypt by the Fatimid ], ], to regulate the ] of the ] River. He carried out a detailed scientific study of the annual ] of the Nile River, and he drew plans for building a ], at the site of the modern-day ]. His field work, however, later made him aware of the impracticality of this scheme, and he soon ] so he could avoid punishment from the Caliph.<ref>{{harvnb|Plott|2000}}, Pt. II, p. 459.</ref>
			=== Philosophy ===
			In his ''Treatise on Place'', Alhazen disagreed with ]'s view that nature abhors a ], and he used ] in an attempt to demonstrate that place (''al-makan'') is the imagined three-dimensional void between the inner surfaces of a containing body.<ref name="{{harvnb|el-bizri|2007}}.">{{harvnb|El-Bizri|2007}}.</ref> ], a supporter of Aristotle's philosophical view of place, later criticized the work in ''Fi al-Radd 'ala Ibn al-Haytham fi al-makan'' (''A refutation of Ibn al-Haytham's place'') for its geometrization of place.<ref name="{{harvnb|el-bizri|2007}}." />
			Alhazen also discussed ] and its ] implications in his '']''. In "tying the visual perception of space to prior bodily experience, Alhazen unequivocally rejected the intuitiveness of spatial perception and, therefore, the autonomy of vision. Without tangible notions of distance and size for
			correlation, sight can tell us next to nothing about such things."<ref>{{harvnb|Smith|2005|pp=219–240}}.</ref>
			=== Theology ===
			Alhazen was a Muslim and most sources report that he was a Sunni and a follower of the ] school.<ref name="ishaq">Ishaq, Usep Mohamad, and Wan Mohd Nor Wan Daud. "Tinjauan biografi-bibliografi Ibn al-haytham." Historia : Jurnal Program Studi Pendidikan Sejarah 5.2 (2017): 107–124.</ref><ref name="george">Kaminski, Joseph J. "The Trajectory of the Development of Islamic Thought{{snd}}A Comparison Between Two Earlier and Two Later Scholars." ''The Contemporary Islamic Governed State.'' Palgrave Macmillan, Cham, 2017. 31–70. "For example, Ibn al-Haytham and Abū Rayhān al-Bīrūnī were among the most important medieval scholars who used the scientific method in their approach to natural science, and they were both Ash'arites"</ref><ref name="Sardar 1998">{{harvnb|Sardar|1998}}</ref><ref name="Bettany 1995 251">{{harvnb|Bettany|1995|p=251}}</ref> ] says that some of the greatest ], such as Ibn al-Haytham and ], who were pioneers of the ], were themselves followers of the Ashʿari school of Islamic theology.<ref name="Sardar 1998" /> Like other Ashʿarites who believed that faith or ''taqlid'' should apply only to Islam and not to any ancient ] authorities,<ref>Anwar, Sabieh (October 2008), "Is Ghazālī really the Halagu of Science in Islam?", '']'', '''18''' (10), retrieved 14 October 2008</ref> Ibn al-Haytham's view that ''taqlid'' should apply only to ] and not to any other authorities formed the basis for much of his ] and criticism against ] and other ancient authorities in his ''Doubts Concerning Ptolemy'' and '']''.<ref>Rashed, Roshdi (2007), "The Celestial Kinematics of Ibn al-Haytham", ''Arabic Sciences and Philosophy'', ], '''17''' (1): 7–55 , {{doi|10.1017/S0957423907000355}}</ref>
			Alhazen wrote a work on Islamic theology in which he discussed prophethood and developed a system of philosophical criteria to discern its false claimants in his time.<ref>{{harvnb|Plott|2000}}, Pt. II, p. 464</ref>
			He also wrote a treatise entitled ''Finding the Direction of Qibla by Calculation'' in which he discussed finding the ], where prayers (]) are directed towards, mathematically.<ref>{{harvnb|Topdemir|2007|pp=8–9}}.</ref>
			There are occasional references to theology or religious sentiment in his technical works, e.g.
			in ''Doubts Concerning Ptolemy'':
			{{blockquote|Truth is sought for its own sake ... Finding the truth is difficult, and the road to it is rough. For the truths are plunged in obscurity. ... God, however, has not preserved the scientist from error and has not safeguarded science from shortcomings and faults. If this had been the case, scientists would not have disagreed upon any point of science...<ref name=Sambursky1974>Translated by S. Pines, as quoted in {{harvnb|Sambursky|1974|p=139}}.</ref>}}
			In ''The Winding Motion'':
			{{blockquote|From the statements made by the noble Shaykh, it is clear that he believes in Ptolemy's words in everything he says, without relying on a demonstration or calling on a proof, but by pure imitation (''taqlid''); that is how experts in the prophetic tradition have faith in Prophets, may the blessing of God be upon them. But it is not the way that mathematicians have faith in specialists in the demonstrative sciences.<ref>{{harvnb|Rashed|2007|p=11}}.</ref>}}
			Regarding the relation of objective truth and God:
			{{blockquote|I constantly sought knowledge and truth, and it became my belief that for gaining access to the effulgence and closeness to God, there is no better way than that of searching for truth and knowledge.<ref>{{harvnb|Plott|2000}}, Pt. II, p. 465</ref>}}
			== Legacy ==
			]'']]
			Alhazen made significant contributions to optics, number theory, geometry, astronomy and natural philosophy. Alhazen's work on optics is credited with contributing a new emphasis on experiment.
			His main work, '']'' (''Book of Optics''), was known in the ] mainly, but not exclusively, through the thirteenth-century commentary by ], the ''Tanqīḥ ''al-Manāẓir'' li-dhawī l-abṣār wa l-baṣā'ir''.<ref>{{harvnb|Sabra|2007}}.</ref> In ], it was used by the eleventh-century prince of the ] of ] and author of an important mathematical text, ]. A Latin translation of the ''Kitab al-Manazir'' was made probably in the late twelfth or early thirteenth century.<ref>{{harvnb|Sabra|2007|pages=122, 128–129}}. {{harvnb||Grant|1974|p=}} notes the ''Book of Optics'' has also been denoted as ''Opticae Thesaurus Alhazen Arabis'', as ''De Aspectibus'', and also as ''Perspectiva''</ref> This translation was read by and greatly influenced a number of scholars in Christian Europe including: ],<ref>{{harvnb|Lindberg|1996|p=11}}, passim.</ref> ],<ref>{{Harvnb|Authier|2013|p=23}}: "Alhazen's works in turn inspired many scientists of the Middle Ages, such as the English bishop, Robert Grosseteste (c. 1175–1253), and the English Franciscan, Roger Bacon (c. 1214–1294), Erazmus Ciolek Witelo, or Witelon (c. 1230* 1280), a Silesian-born Polish friar, philosopher and scholar, published in c. 1270 a treatise on optics, Perspectiva, largely based on Alhazen's works."</ref> ], ],<ref>{{Harvnb|Magill|Aves|1998|p=66}}: "Roger Bacon, John Peckham, and Giambattista della Porta are only some of the many thinkers who were influenced by Alhazen's work."</ref> ],<ref>{{Harvnb|Zewail|Thomas|2010|p=5}}: "The Latin translation of Alhazen's work influenced scientists and philosophers such as (Roger) Bacon and da Vinci, and formed the foundation for the work by mathematicians like Kepler, Descartes and Huygens..."</ref> ],<ref>{{Harvnb|El-Bizri|2010|p=12}}: "This version of Ibn al-Haytham's Optics, which became available in print, was read and consulted by scientists and philosophers of the caliber of Kepler, Galileo, Descartes, and Huygens as discussed by ]."</ref> ],<ref>{{Harvnb|Magill|Aves|1998|p=66}}: "Sabra discusses in detail the impact of Alhazen's ideas on the optical discoveries of such men as Descartes and Christiaan Huygens; see also {{harvnb|El-Bizri|2005a}}."</ref> ],<ref>{{Harvnb|El-Bizri|2010|p=12}}.</ref> and ].<ref>{{Harvnb|Magill|Aves|1998|p=66}}: "Even Kepler, however, used some of Alhazen's ideas, for example, the one-to-one correspondence between points on the object and points in the eye. It would not be going too far to say that Alhazen's optical theories defined the scope and goals of the field from his day to ours."</ref> Meanwhile, in the Islamic world, Alhazen's work influenced ]' writings on optics,{{citation needed|date=June 2020}} and his legacy was further advanced through the 'reforming' of his ''Optics'' by Persian scientist ] (died c. 1320) in the latter's ''Kitab Tanqih al-Manazir'' (''The Revision of'' ''Optics'').<ref name="{{harvs|nb|last=el-bizri|year=2005a|year2=2005b}}." /> Alhazen wrote as many as 200 books, although only 55 have survived. Some of his treatises on optics survived only through Latin translation. During the Middle Ages his books on ] were translated into Latin, ] and other languages.
			H. J. J. Winter, a British historian of science, summing up the importance of Ibn al-Haytham in the history of ] wrote:
			<blockquote>After the death of Archimedes no really great physicist appeared until Ibn al-Haytham. If, therefore, we confine our interest only to the history of physics, there is a long period of over twelve hundred years during which the Golden Age of Greece gave way to the era of Muslim Scholasticism, and the experimental spirit of the noblest physicist of Antiquity lived again in the Arab Scholar from Basra.<ref>{{cite journal |last1=Winter |first1=H. J. J. |title=The Optical Researches of Ibn Al-Haitham |journal=Centaurus |date=September 1953 |volume=3 |issue=1 |pages=190–210 |doi=10.1111/j.1600-0498.1953.tb00529.x |pmid=13209613 |language=en |issn=0008-8994|bibcode=1953Cent....3..190W }}</ref></blockquote>
			Although only one commentary on Alhazen's optics has survived the Islamic Middle Ages, ] mentions the work in '']'':<ref>{{cite web |title=Ibn al-Haytham's scientific method |website=UNESCO |date=14 May 2018 |url=https://en.unesco.org/courier/news-views-online/ibn-al-haytham-s-scientific-method |access-date=25 October 2021 |archive-date=25 October 2021 |archive-url=https://web.archive.org/web/20211025160618/https://en.unesco.org/courier/news-views-online/ibn-al-haytham-s-scientific-method |url-status=live }}</ref>
			<blockquote><poem>"They spoke of Alhazen and Vitello,
			And Aristotle, who wrote, in their lives,
			On strange mirrors and optical instruments."</poem></blockquote>
			The ] ] on the Moon is named in his honour,<ref>{{Harvnb|Chong|Lim|Ang|2002}} Appendix 3, .</ref> as was the ] ].<ref>{{Harvnb|NASA|2006}}.</ref> In honour of Alhazen, the ] (Pakistan) named its Ophthalmology endowed chair as "The Ibn-e-Haitham Associate Professor and Chief of Ophthalmology".<ref>{{Cite web|url=http://www.aku.edu/res-office/pdfs/AKU_Research_Publications_1995–1998.pdf|archiveurl=https://web.archive.org/web/20150104215931/http://www.aku.edu/res-office/pdfs/AKU_Research_Publications_1995|url-status=dead|title=AKU Research Publications 1995–98|archivedate=4 January 2015}}</ref>
			The 2015 ] celebrated the 1000th anniversary of the works on optics by Ibn Al-Haytham.<ref>{{cite web|title=Ibn Al-Haytham and the Legacy of Arabic Optics|publisher=2015 International Year of Light|url=http://www.light2015.org/Home/ScienceStories/1000-Years-of-Arabic-Optics.html|date=2015|access-date=4 January 2015|archive-date=1 October 2014|archive-url=https://web.archive.org/web/20141001171116/http://www.light2015.org/Home/ScienceStories/1000-Years-of-Arabic-Optics.html|url-status=dead}}</ref>
			]'s '']'', showing Alhasen {{sic}} representing reason, and ] representing the senses]]
			In 2014, the "]" episode of '']'', presented by ], focused on the accomplishments of Ibn al-Haytham. He was voiced by ] in the episode.
			Over forty years previously, ] presented Alhazen's work in a similar television documentary (and the corresponding book), '']''. In episode 5 (''The Music of the Spheres''), Bronowski remarked that in his view, Alhazen was "the one really original scientific mind that Arab culture produced", whose theory of optics was not improved on till the time of Newton and Leibniz.
			] declared 2015 the ] and its Director-General Irina Bokova dubbed Ibn al-Haytham 'the father of optics'.<ref>{{cite web| url = http://www.unesco.org/fileadmin/MULTIMEDIA/HQ/SC/pdf/Programme-Opening_IYL2015.pdf| title = 2015, International Year of Light| access-date = 10 October 2017| archive-date = 15 April 2017| archive-url = https://web.archive.org/web/20170415175814/http://www.unesco.org/fileadmin/MULTIMEDIA/HQ/SC/pdf/Programme-Opening_IYL2015.pdf| url-status = live}}</ref> Amongst others, this was to celebrate Ibn Al-Haytham's achievements in optics, mathematics and astronomy. An international campaign, created by the ] organisation, titled ''1001 Inventions and the World of Ibn Al-Haytham'' featuring a series of interactive exhibits, workshops and live shows about his work, partnering with science centers, science festivals, museums, and educational institutions, as well as digital and social media platforms.<ref>{{cite web |url=http://www.unesco.org/new/en/media-services/single-view/news/1000_years_of_arabic_optics_to_be_a_focus_of_the_international_year_of_light_in_2015 |title=1000 Years of Arabic Optics to be a Focus of the International Year of Light in 2015 |publisher=United Nations |access-date=27 November 2014 |archive-date=21 November 2014 |archive-url=https://web.archive.org/web/20141121010107/http://www.unesco.org/new/en/media-services/single-view/news/1000_years_of_arabic_optics_to_be_a_focus_of_the_international_year_of_light_in_2015/ |url-status=live }}</ref> The campaign also produced and released the short educational film ].
			Ibn al-Haytham appears on the 10,000 dinar banknote of the ], series 2003.<ref>{{Cite web |title=10 Dinars, Iraq |url=https://en.numista.com/catalogue/note203100.html |access-date=2024-05-28 |website=en.numista.com |language=en}}</ref>
			== List of works ==
			According to medieval biographers, Alhazen wrote more than 200 works on a wide range of subjects, of which at least 96 of his scientific works are known. Most of his works are now lost, but more than 50 of them have survived to some extent. Nearly half of his surviving works are on mathematics, 23 of them are on astronomy, and 14 of them are on optics, with a few on other subjects.<ref>{{harvnb|Rashed|2002a|p=773}}.</ref> Not all his surviving works have yet been studied, but some of the ones that have are given below.<ref>{{harvnb|Rashed|2007|pp=8–9}}; {{harvnb|Topdemir|2007}}</ref>
			{{Div col|small=yes}}
			# '']'' (كتاب المناظر)
			# ''Analysis and Synthesis'' (مقالة في التحليل والتركيب)
			# ''Balance of Wisdom'' (ميزان الحكمة)
			# ''Corrections to the Almagest'' (تصويبات على المجسطي)
			# ''Discourse on Place'' (مقالة في المكان)
			# ''Exact Determination of the Pole'' (التحديد الدقيق للقطب)
			# ''Exact Determination of the Meridian'' (رسالة في الشفق)
			# ''Finding the Direction of Qibla by Calculation'' (كيفية حساب اتجاه القبلة)
			# ''Horizontal Sundials'' (المزولة الأفقية)
			# ''Hour Lines'' (خطوط الساعة)
			# ''Doubts Concerning Ptolemy'' (شكوك على بطليموس)
			# ''Maqala fi'l-Qarastun'' (مقالة في قرسطون)
			# ''On Completion of the Conics'' (إكمال المخاريط)
			# ''On Seeing the Stars'' (رؤية الكواكب)
			# ''On Squaring the Circle'' (مقالة فی تربیع الدائرة)
			# ''On the Burning Sphere'' (المرايا المحرقة بالدوائر)
			# ''On the Configuration of the World'' (تكوين العالم)
			# ''On the Form of Eclipse'' (مقالة فی صورة ‌الکسوف)
			# ''On the Light of Stars'' (مقالة في ضوء النجوم)<ref name= onTheLightOfTheStars >Ibn Al-Haytham, W. 'Arafat and H. J. J. Winter (1971) {{jstor|4025317}} (c. 1027–1038) The Light of the Stars: A Short Discourse by Ibn Al-Haytham {{Webarchive|url=https://web.archive.org/web/20220921160132/https://www.jstor.org/stable/4025317 |date=21 September 2022 }} ''The British Journal for the History of Science'' Vol. '''5''', No. 3 (Jun., 1971), pp. 282–288 </ref>
			# ''On the Light of the Moon'' (مقالة في ضوء القمر)
			# ''On the Milky Way'' (مقالة في درب التبانة)
			# ''On the Nature of Shadows'' (كيفيات الإظلال)
			# ''On the Rainbow and Halo'' (مقالة في قوس قزح)
			# ''Opuscula'' (Minor Works)
			# ''Resolution of Doubts Concerning the Almagest'' (تحليل شكوك حول الجست)
			# ''Resolution of Doubts Concerning the Winding Motion''
			# ''The Correction of the Operations in Astronomy'' (تصحيح العمليات في الفلك)
			# ''The Different Heights of the Planets'' (اختلاف ارتفاع الكواكب)
			# ''The Direction of Mecca'' (اتجاه القبلة)
			# ''The Model of the Motions of Each of the Seven Planets'' (نماذج حركات الكواكب السبعة)
			# ''The Model of the Universe'' (نموذج الكون)
			# ''The Motion of the Moon'' (حركة القمر)
			# ''The Ratios of Hourly Arcs to their Heights''
			# ''The Winding Motion'' (الحركة المتعرجة)
			# ''Treatise on Light'' (رسالة في الضوء)<ref name=treatiseOnLight2>Alhacen (c.1035) ''Treatise on Light'' (رسالة في الضوء) as cited in ], ed. (1975) , p.137</ref>
			# ''Treatise on Place'' (رسالة في المكان)
			# ''Treatise on the Influence of Melodies on the Souls of Animals'' (تأثير اللحون الموسيقية في النفوس الحيوانية)
			# كتاب في تحليل المسائل الهندسية (A book in engineering analysis)
			# الجامع في أصول الحساب (The whole in the assets of the account)
			# قول فی مساحة الکرة (Say in the sphere)
			# القول المعروف بالغریب فی حساب المعاملات (Saying the unknown in the calculation of transactions)
			# خواص المثلث من جهة العمود (Triangle properties from the side of the column)
			# رسالة فی مساحة المسجم المکافی (A message in the free space)
			# شرح أصول إقليدس (Explain the origins of Euclid)
			# المرايا المحرقة بالقطوع (The burning mirrors of the rainbow)
			# مقالة في القرصتن (Treatise on Centers of Gravity)
			{{Div col end}}
			=== Lost works ===
			# ''A Book in which I have Summarized the Science of Optics from the Two Books of Euclid and Ptolemy, to which I have added the Notions of the First Discourse which is Missing from Ptolemy's Book''<ref>From ]'s catalog, as cited in {{harvnb|Smith|2001}} '''91'''(vol. 1), p. xv.</ref>
			# ''Treatise on Burning Mirrors''
			# ''Treatise on the Nature of Sight and on How Vision is Achieved Through It''
			== See also ==
			{{Div col|small=yes}}
			* ]
			* "]"
			* ]
			* ]
			* ]
			* ]
			* ]
			* ]
			* ]
			* ]
			* ]
			* ]
			* ]
			* ]
			{{Div col end}}
			== Notes ==
			{{notelist}}
			== References ==
			{{Reflist}}
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			{{Refend}}
	==Further reading==		== Further reading ==
	===Primary sources===		=== Primary ===
			{{refbegin}}
	* Langermann, Y. Tzvi, ed. and trans. ''Ibn al-Haytham's'' On the Configuration of the World, Harvard Dissertations in the History of Science. New York: Garland, 1990. ISBN 0824000412
			* {{Citation
	* Sabra, A. I., ed. ''The Optics of Ibn al-Haytham, Books I-II-III: On Direct Vision. The Arabic text, edited and with Introduction, Arabic-Latin Glossaries and Concordance Tables.'' Kuwait: National Council for Culture, Arts and Letters, 1983.
			|editor-last=Sabra |editor-first=A. I
	* Sabra, A. I., ed. ''The Optics of Ibn al-Haytham. Edition of the Arabic Text of Books IV-V: On Reflection and Images Seen by Reflection.'' 2 vols., Kuwait: The National Council for Culture, Arts and Letters, 2002.
			|editor-link=A. I. Sabra
	* Sabra, A. I., trans. ''The Optics of Ibn al-Haytham. Books I-II-III: On Direct Vision. English Translation and Commentary.'' 2 vols. Studies of the Warburg Institute, vol. 40. London: The Warburg Institute, University of London, 1989. ISBN 0-85481-072-2
			|date=1983
	* Smith, A. Mark, ed. and trans. ''Alhacen's Theory of Visual Perception: A Critical Edition, with English Translation and Commentary, of the First Three Books of Alhacen's'' De aspectibus,'' the Medieval Latin Version of Ibn al-Haytham's'' Kitāb al-Manāzir, 2 vols. Transactions of the American Philosophical Society, 91.4-5, Philadelphia, 2001. ISBN 0-87169-914-1
			|title=The Optics of Ibn al-Haytham, Books I–II–III: On Direct Vision. The Arabic text, edited and with Introduction, Arabic-Latin Glossaries and Concordance Tables
	* Smith, A. Mark, ed. and trans. ''Alhacen on the Principles of Reflection: A Critical Edition, with English Translation and Commentary, of Books 4 and 5 of Alhacen's ''De Aspectibus,'' the Medieval Latin version of Ibn-al-Haytham's'' Kitāb al-Manāzir, 2 vols. Transactions of the American Philosophical Society, 96.2-3, Philadelphia, 2006. ISBN 0-87169-962-1
			|publisher= National Council for Culture, Arts and Letters
			|location= Kuwait
			}}
			* {{Citation
			|editor-last=Sabra |editor-first=A. I
			|editor-link=A. I. Sabra
			|date=2002
			|title=The Optics of Ibn al-Haytham. Edition of the Arabic Text of Books IV–V: On Reflection and Images Seen by Reflection. 2 vols
			|publisher= National Council for Culture, Arts and Letters
			|location= Kuwait
			}}
			* {{Citation
			|last= Smith |first= A. Mark, ed. and trans.
			|year= 2006
			|title= Alhacen on the principles of reflection: A Critical Edition, with English Translation and Commentary, of books 4 and 5 of Alhacen's ''De Aspectibus'', the Medieval Latin Version of Ibn al-Haytham's ''Kitāb al-Manāẓir'', 2 vols.
			|journal= Transactions of the American Philosophical Society
			|volume= 95
			|issue= 2–3
			|publisher= ]
			|location= Philadelphia
			}} 2 vols: . (]: ]), 2006 – {{Webarchive|url=https://web.archive.org/web/20180924155318/https://www.jstor.org/stable/20020399 |date=24 September 2018 }}; {{Webarchive|url=https://web.archive.org/web/20161006112053/http://www.jstor.org/stable/20020403?seq=1#page_thumbnails_tab_contents |date=6 October 2016 }}
			* Smith, A. Mark, ed. and trans. (2008) ''Alhacen on Image-formation and distortion in mirrors'' : a critical edition, with English translation and commentary, of Book 6 of Alhacen's ''De aspectibus'', , ''Transactions of the American Philosophical Society'', 2 vols: Vol 1 '''98'''(#1, section 1 – Vol 1 Commentary and Latin text); '''98'''(#1, section 2 – Vol 2 English translation). (]: ]), 2008. {{Webarchive|url=https://web.archive.org/web/20180924152501/https://www.jstor.org/stable/27757395 |date=24 September 2018 }}; {{Webarchive|url=https://web.archive.org/web/20161006050915/http://www.jstor.org/stable/27757399?seq=1#page_thumbnails_tab_contents |date=6 October 2016 }}
			* Smith, A. Mark, ed. and trans. (2010) ''Alhacen on Refraction'' : a critical edition, with English translation and commentary, of Book 7 of Alhacen's ''De aspectibus'', , ''Transactions of the American Philosophical Society'', 2 vols: '''100'''(#3, section 1 – Vol 1, Introduction and Latin text); '''100'''(#3, section 2 – Vol 2 English translation). (]: ]), 2010. {{Webarchive|url=https://web.archive.org/web/20180924152455/https://www.jstor.org/stable/20787647 |date=24 September 2018 }}; {{Webarchive|url=https://web.archive.org/web/20161006052700/http://www.jstor.org/stable/20787651?seq=1#page_thumbnails_tab_contents |date=6 October 2016 }}
			{{refend}}
	===Secondary literature===		=== Secondary ===
			{{refbegin}}
	* ] "Ibn al-Haytham and the Origins of Modern Image Analysis" presented at a plenary session at the International Conference on Information Sciences, Signal Processing and its Applications, 12–15 February 2007. Sharjah, United Arab Emirates (U.A.E.). In this lecture, Falco speculates that Ibn al-Haytham may have influenced the use of optical aids in Renaissance art. (See ].)
			* Belting, Hans, , in: Variantology 4. On Deep Time Relations of Arts, Sciences and Technologies in the Arabic-Islamic World and Beyond, ed. by Siegfried Zielinski and Eckhard Fürlus in cooperation with Daniel Irrgang and Franziska Latell (Cologne: Verlag der Buchhandlung Walther König, 2010), pp.&nbsp;19–42.
	* Omar, Saleh Beshara. ''Ibn al-Haytham and Greek optics: a comparative study in scientific methodology''. PhD Dissertation, Univ. of Chicago, Dept. of Near Eastern Languages and Civilizations, June 1975.
			* {{Citation
			|last=El-Bizri
			|first=Nader
			|author-link=Nader El-Bizri
			|date=2009b
			|title=Ibn al-Haytham et le problème de la couleur
			|journal=Oriens Occidens
			|volume=7
			|issue=1
			|pages=201–226
			|publisher=]
			|location= Paris
			}}
			* {{Citation
			|last=El-Bizri
			|first=Nader
			|author-link=Nader El-Bizri
			| editor-last = Cunningham
			| editor-first = Jack P.
			| editor2-last = Hocknull
			| editor2-first = Mark
			| date = 2016
			| title = Robert Grosseteste and the Pursuit of Religious and Scientific Knowledge in the Middle Ages
			| chapter = Grosseteste's Meteorological Optics: Explications of the Phenomenon of the Rainbow after Ibn al-Haytham
			| series = Studies in the History of Philosophy of Mind
			| volume = 18
			| publisher = Springer
			| place = Dordrecht
			| pages = 21–39
			| isbn = 978-3-319-33466-0 }}
			* {{Citation
			|last=Falco
			|first=Charles M.
			|title=Ibn al-Haytham and the Origins of Modern Image Analysis
			|date=12–15 February 2007
			|url=https://wp.optics.arizona.edu/falco/wp-content/uploads/sites/57/2016/08/FalcoPlenaryUAE.pdf
			|author-link=Charles M. Falco
			|publisher=presented at a plenary session at the International Conference on Information Sciences, Signal Processing and its Applications
			|access-date=23 January 2008
			|archive-date=4 December 2020
			|archive-url=https://web.archive.org/web/20201204162652/https://wp.optics.arizona.edu/falco/wp-content/uploads/sites/57/2016/08/FalcoPlenaryUAE.pdf
			|url-status=dead
			}}
			* {{cite book |last1=Gazı Topdemır |first1=Hüseyın |title=İBNÜ'l-HEYSEM – An article published in 21st volume of Turkish Encyclopedia of Islam |date=2000 |publisher=] |location=Istanbul |isbn=978-97-53-89448-7 |pages=82–87 |volume=21 |url=https://islamansiklopedisi.org.tr/ibnul-heysem |language=tr |access-date=14 January 2022 |archive-date=9 June 2021 |archive-url=https://web.archive.org/web/20210609071112/https://islamansiklopedisi.org.tr/ibnul-heysem |url-status=live }}
			* Graham, Mark. ''How Islam Created the Modern World''. Amana Publications, 2006.
			* {{Citation
			|last=Omar
			|first=Saleh Beshara
			|title=Ibn al-Haytham and Greek optics: a comparative study in scientific methodology
			|publisher=PhD Dissertation, ], Department of Near Eastern Languages and Civilizations
			|date=June 1975}}
			* ], Optics and Mathematics: Research on the history of scientific thought in Arabic, Variorum reprints, Aldershot, 1992.
			* Roshdi Rashed, Geometry and Dioptrics the tenth century: Ibn Sahl al-Quhi and Ibn al-Haytham (in French), Les Belles Lettres, Paris, 1993
			* Roshdi Rashed, Infinitesimal Mathematics, vols. 1–5, ], London, 1993–2006
			* {{Citation
			|last=Saliba
			|first=George
			|author-link=George Saliba
			|title=Islamic Science and the Making of the European Renaissance
			|date=2007
			|publisher=]
			|isbn=978-0-262-19557-7
			|url=https://doaj.org/article/c3c039c19a15439aa5a01afcc8393031
			|access-date=18 April 2017
			|archive-date=19 April 2017
			|archive-url=https://web.archive.org/web/20170419191742/https://doaj.org/article/c3c039c19a15439aa5a01afcc8393031
			|url-status=live
			}}
			* Siegfried Zielinski & Franziska Latell, ''How One Sees'', in: Variantology 4. On Deep Time Relations of Arts, Sciences and Technologies in the Arabic-Islamic World and Beyond, ed. by Siegfried Zielinski and Eckhard Fürlus in cooperation with Daniel Irrgang and Franziska Latell (Cologne: Verlag der Buchhandlung Walther König, 2010), pp.&nbsp;19–42.
			{{refend}}
	== External links ==		== External links ==
	* {{MacTutor Biography|id=Al-Haytham|title=Abu Ali al-Hasan ibn al-Haytham}}		{{Commons category|Ibn al-Haytham}}
			* {{OL author|883756A}}
	* {{ScienceWorldBiography | urlname=Alhazen | title=Alhazen (ca. 965-1039)}}
			* {{cite encyclopedia | editor = Thomas Hockey | last = Langermann | first = Y. Tzvi | title=Ibn al-Haytham: Abū ʿAlī al-Ḥasan ibn al-Ḥasan | encyclopedia = The Biographical Encyclopedia of Astronomers | publisher = Springer | date = 2007 | location = New York | pages = 556–5567 | url=http://islamsci.mcgill.ca/RASI/BEA/Ibn_al-Haytham_BEA.htm | isbn=978-0-387-31022-0|display-editors=etal}} ()
	*
			*
	* http://www.daviddarling.info/encyclopedia/A/Alhazen.html
			* {{Webarchive|url=https://web.archive.org/web/20180803223823/http://www-personal.umich.edu/~jbourj/money4.htm |date=3 August 2018 }}
	*
	*		*
			*
	* Roshdi Rashed. , '']'', 297 (2002): 773
			*
	* ],
			* {{webarchive |url=https://web.archive.org/web/19991013041615/http://www.ionet.net/~usarch/WTB-Services/MiddleEast/WTB-ME-Thinkers-IbnAlHaitham.shtml |date=13 October 1999 |title=Biography from ioNET }}
	* (in Persian)
			* {{cite web |url=https://www.bbc.co.uk/history/historic_figures/alhazen.shtml |title=Biography from the BBC |access-date=16 September 2008 |archive-url=https://web.archive.org/web/20060211032459/http://www.bbc.co.uk/history/historic_figures/alhazen.shtml |archive-date=11 February 2006 }}
	*
			*
	{{DEFAULTSORT:Ibn Haytham}}
			*
			* from BBC News
			* From The UNESCO Courier on the occasion of the International Year of Astronomy 2009
			* , Muslim Heritage
			* Alhazen's (1572) {{Webarchive|url=https://web.archive.org/web/20180924145526/http://lhldigital.lindahall.org/cdm/ref/collection/color/id/16985 |date=24 September 2018 }} (English) – digital facsimile from the ]
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Latest revision as of 12:46, 4 January 2025

Arab physicist, mathematician and astronomer (c. 965 – c. 1040) "Alhazen" and "Alhaitham" redirect here. For other uses, see Alhazen (disambiguation). For the fictional character, see List of Genshin Impact characters § Alhaitham.

Alhazen Ḥasan Ibn al-Haytham
ابن الهيثم
Born	c. 965 (0965) (c. 354 AH) Basra, Buyid Emirate
Died	c. 1040 (1041) (c. 430 AH) (aged around 75) Cairo, Fatimid Caliphate
Known for	Book of Optics, Doubts Concerning Ptolemy, Alhazen's problem, analysis, Catoptrics, horopter, Spherical aberration, intromission theory of visual perception, moon illusion, experimental science, scientific methodology, animal psychology
Scientific career
Fields	Physics, mathematics, astronomy

Ḥasan Ibn al-Haytham (Latinized as Alhazen; /ælˈhæzən/; full name Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham أبو علي، الحسن بن الحسن بن الهيثم; c. 965 – c. 1040) was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq. Referred to as "the father of modern optics", he made significant contributions to the principles of optics and visual perception in particular. His most influential work is titled Kitāb al-Manāẓir (Arabic: كتاب المناظر, "Book of Optics"), written during 1011–1021, which survived in a Latin edition. The works of Alhazen were frequently cited during the scientific revolution by Isaac Newton, Johannes Kepler, Christiaan Huygens, and Galileo Galilei.

Ibn al-Haytham was the first to correctly explain the theory of vision, and to argue that vision occurs in the brain, pointing to observations that it is subjective and affected by personal experience. He also stated the principle of least time for refraction which would later become Fermat's principle. He made major contributions to catoptrics and dioptrics by studying reflection, refraction and nature of images formed by light rays. Ibn al-Haytham was an early proponent of the concept that a hypothesis must be supported by experiments based on confirmable procedures or mathematical reasoning – an early pioneer in the scientific method five centuries before Renaissance scientists, he is sometimes described as the world's "first true scientist". He was also a polymath, writing on philosophy, theology and medicine.

Born in Basra, he spent most of his productive period in the Fatimid capital of Cairo and earned his living authoring various treatises and tutoring members of the nobilities. Ibn al-Haytham is sometimes given the byname al-Baṣrī after his birthplace, or al-Miṣrī ("the Egyptian"). Al-Haytham was dubbed the "Second Ptolemy" by Abu'l-Hasan Bayhaqi and "The Physicist" by John Peckham. Ibn al-Haytham paved the way for the modern science of physical optics.

Biography

Ibn al-Haytham (Alhazen) was born c. 965 to a family of Arab or Persian origin in Basra, Iraq, which was at the time part of the Buyid emirate. His initial influences were in the study of religion and service to the community. At the time, society had a number of conflicting views of religion that he ultimately sought to step aside from religion. This led to him delving into the study of mathematics and science. He held a position with the title of vizier in his native Basra, and became famous for his knowledge of applied mathematics, as evidenced by his attempt to regulate the flooding of the Nile.

Upon his return to Cairo, he was given an administrative post. After he proved unable to fulfill this task as well, he contracted the ire of the caliph Al-Hakim, and is said to have been forced into hiding until the caliph's death in 1021, after which his confiscated possessions were returned to him. Legend has it that Alhazen feigned madness and was kept under house arrest during this period. During this time, he wrote his influential Book of Optics. Alhazen continued to live in Cairo, in the neighborhood of the famous University of al-Azhar, and lived from the proceeds of his literary production until his death in c. 1040. (A copy of Apollonius' Conics, written in Ibn al-Haytham's own handwriting exists in Aya Sofya: (MS Aya Sofya 2762, 307 fob., dated Safar 415 A.H. ).)

Among his students were Sorkhab (Sohrab), a Persian from Semnan, and Abu al-Wafa Mubashir ibn Fatek, an Egyptian prince.

Book of Optics

Main article: Book of Optics

Alhazen's most famous work is his seven-volume treatise on optics Kitab al-Manazir (Book of Optics), written from 1011 to 1021. In it, Ibn al-Haytham was the first to explain that vision occurs when light reflects from an object and then passes to one's eyes, and to argue that vision occurs in the brain, pointing to observations that it is subjective and affected by personal experience.

Optics was translated into Latin by an unknown scholar at the end of the 12th century or the beginning of the 13th century.

This work enjoyed a great reputation during the Middle Ages. The Latin version of De aspectibus was translated at the end of the 14th century into Italian vernacular, under the title De li aspecti.

It was printed by Friedrich Risner in 1572, with the title Opticae thesaurus: Alhazeni Arabis libri septem, nuncprimum editi; Eiusdem liber De Crepusculis et nubium ascensionibus (English: Treasury of Optics: seven books by the Arab Alhazen, first edition; by the same, on twilight and the height of clouds). Risner is also the author of the name variant "Alhazen"; before Risner he was known in the west as Alhacen. Works by Alhazen on geometric subjects were discovered in the Bibliothèque nationale in Paris in 1834 by E. A. Sedillot. In all, A. Mark Smith has accounted for 18 full or near-complete manuscripts, and five fragments, which are preserved in 14 locations, including one in the Bodleian Library at Oxford, and one in the library of Bruges.

Theory of optics

See also: Horopter

Two major theories on vision prevailed in classical antiquity. The first theory, the emission theory, was supported by such thinkers as Euclid and Ptolemy, who believed that sight worked by the eye emitting rays of light. The second theory, the intromission theory supported by Aristotle and his followers, had physical forms entering the eye from an object. Previous Islamic writers (such as al-Kindi) had argued essentially on Euclidean, Galenist, or Aristotelian lines. The strongest influence on the Book of Optics was from Ptolemy's Optics, while the description of the anatomy and physiology of the eye was based on Galen's account. Alhazen's achievement was to come up with a theory that successfully combined parts of the mathematical ray arguments of Euclid, the medical tradition of Galen, and the intromission theories of Aristotle. Alhazen's intromission theory followed al-Kindi (and broke with Aristotle) in asserting that "from each point of every colored body, illuminated by any light, issue light and color along every straight line that can be drawn from that point". This left him with the problem of explaining how a coherent image was formed from many independent sources of radiation; in particular, every point of an object would send rays to every point on the eye.

What Alhazen needed was for each point on an object to correspond to one point only on the eye. He attempted to resolve this by asserting that the eye would only perceive perpendicular rays from the object – for any one point on the eye, only the ray that reached it directly, without being refracted by any other part of the eye, would be perceived. He argued, using a physical analogy, that perpendicular rays were stronger than oblique rays: in the same way that a ball thrown directly at a board might break the board, whereas a ball thrown obliquely at the board would glance off, perpendicular rays were stronger than refracted rays, and it was only perpendicular rays which were perceived by the eye. As there was only one perpendicular ray that would enter the eye at any one point, and all these rays would converge on the centre of the eye in a cone, this allowed him to resolve the problem of each point on an object sending many rays to the eye; if only the perpendicular ray mattered, then he had a one-to-one correspondence and the confusion could be resolved. He later asserted (in book seven of the Optics) that other rays would be refracted through the eye and perceived as if perpendicular. His arguments regarding perpendicular rays do not clearly explain why only perpendicular rays were perceived; why would the weaker oblique rays not be perceived more weakly? His later argument that refracted rays would be perceived as if perpendicular does not seem persuasive. However, despite its weaknesses, no other theory of the time was so comprehensive, and it was enormously influential, particularly in Western Europe. Directly or indirectly, his De Aspectibus (Book of Optics) inspired much activity in optics between the 13th and 17th centuries. Kepler's later theory of the retinal image (which resolved the problem of the correspondence of points on an object and points in the eye) built directly on the conceptual framework of Alhazen.

Alhazen showed through experiment that light travels in straight lines, and carried out various experiments with lenses, mirrors, refraction, and reflection. His analyses of reflection and refraction considered the vertical and horizontal components of light rays separately.

Alhazen studied the process of sight, the structure of the eye, image formation in the eye, and the visual system. Ian P. Howard argued in a 1996 Perception article that Alhazen should be credited with many discoveries and theories previously attributed to Western Europeans writing centuries later. For example, he described what became in the 19th century Hering's law of equal innervation. He wrote a description of vertical horopters 600 years before Aguilonius that is actually closer to the modern definition than Aguilonius's – and his work on binocular disparity was repeated by Panum in 1858. Craig Aaen-Stockdale, while agreeing that Alhazen should be credited with many advances, has expressed some caution, especially when considering Alhazen in isolation from Ptolemy, with whom Alhazen was extremely familiar. Alhazen corrected a significant error of Ptolemy regarding binocular vision, but otherwise his account is very similar; Ptolemy also attempted to explain what is now called Hering's law. In general, Alhazen built on and expanded the optics of Ptolemy.

In a more detailed account of Ibn al-Haytham's contribution to the study of binocular vision based on Lejeune and Sabra, Raynaud showed that the concepts of correspondence, homonymous and crossed diplopia were in place in Ibn al-Haytham's optics. But contrary to Howard, he explained why Ibn al-Haytham did not give the circular figure of the horopter and why, by reasoning experimentally, he was in fact closer to the discovery of Panum's fusional area than that of the Vieth-Müller circle. In this regard, Ibn al-Haytham's theory of binocular vision faced two main limits: the lack of recognition of the role of the retina, and obviously the lack of an experimental investigation of ocular tracts.

Alhazen's most original contribution was that, after describing how he thought the eye was anatomically constructed, he went on to consider how this anatomy would behave functionally as an optical system. His understanding of pinhole projection from his experiments appears to have influenced his consideration of image inversion in the eye, which he sought to avoid. He maintained that the rays that fell perpendicularly on the lens (or glacial humor as he called it) were further refracted outward as they left the glacial humor and the resulting image thus passed upright into the optic nerve at the back of the eye. He followed Galen in believing that the lens was the receptive organ of sight, although some of his work hints that he thought the retina was also involved.

Alhazen's synthesis of light and vision adhered to the Aristotelian scheme, exhaustively describing the process of vision in a logical, complete fashion.

His research in catoptrics (the study of optical systems using mirrors) was centred on spherical and parabolic mirrors and spherical aberration. He made the observation that the ratio between the angle of incidence and refraction does not remain constant, and investigated the magnifying power of a lens.

Law of reflection

Main article: Specular reflection

Alhazen was the first physicist to give complete statement of the law of reflection. He was first to state that the incident ray, the reflected ray, and the normal to the surface all lie in a same plane perpendicular to reflecting plane.

Alhazen's problem

Main article: Alhazen's problem

His work on catoptrics in Book V of the Book of Optics contains a discussion of what is now known as Alhazen's problem, first formulated by Ptolemy in 150 AD. It comprises drawing lines from two points in the plane of a circle meeting at a point on the circumference and making equal angles with the normal at that point. This is equivalent to finding the point on the edge of a circular billiard table at which a player must aim a cue ball at a given point to make it bounce off the table edge and hit another ball at a second given point. Thus, its main application in optics is to solve the problem, "Given a light source and a spherical mirror, find the point on the mirror where the light will be reflected to the eye of an observer." This leads to an equation of the fourth degree. This eventually led Alhazen to derive a formula for the sum of fourth powers, where previously only the formulas for the sums of squares and cubes had been stated. His method can be readily generalized to find the formula for the sum of any integral powers, although he did not himself do this (perhaps because he only needed the fourth power to calculate the volume of the paraboloid he was interested in). He used his result on sums of integral powers to perform what would now be called an integration, where the formulas for the sums of integral squares and fourth powers allowed him to calculate the volume of a paraboloid. Alhazen eventually solved the problem using conic sections and a geometric proof. His solution was extremely long and complicated and may not have been understood by mathematicians reading him in Latin translation. Later mathematicians used Descartes' analytical methods to analyse the problem. An algebraic solution to the problem was finally found in 1965 by Jack M. Elkin, an actuarian. Other solutions were discovered in 1989, by Harald Riede and in 1997 by the Oxford mathematician Peter M. Neumann. Recently, Mitsubishi Electric Research Laboratories (MERL) researchers solved the extension of Alhazen's problem to general rotationally symmetric quadric mirrors including hyperbolic, parabolic and elliptical mirrors.

Camera Obscura

The camera obscura was known to the ancient Chinese, and was described by the Han Chinese polymath Shen Kuo in his scientific book Dream Pool Essays, published in the year 1088 C.E. Aristotle had discussed the basic principle behind it in his Problems, but Alhazen's work contained the first clear description of camera obscura. and early analysis of the device.

Ibn al-Haytham used a camera obscura mainly to observe a partial solar eclipse. In his essay, Ibn al-Haytham writes that he observed the sickle-like shape of the sun at the time of an eclipse. The introduction reads as follows: "The image of the sun at the time of the eclipse, unless it is total, demonstrates that when its light passes through a narrow, round hole and is cast on a plane opposite to the hole it takes on the form of a moonsickle."

It is admitted that his findings solidified the importance in the history of the camera obscura but this treatise is important in many other respects.

Ancient optics and medieval optics were divided into optics and burning mirrors. Optics proper mainly focused on the study of vision, while burning mirrors focused on the properties of light and luminous rays. On the shape of the eclipse is probably one of the first attempts made by Ibn al-Haytham to articulate these two sciences.

Very often Ibn al-Haytham's discoveries benefited from the intersection of mathematical and experimental contributions. This is the case with On the shape of the eclipse. Besides the fact that this treatise allowed more people to study partial eclipses of the sun, it especially allowed to better understand how the camera obscura works. This treatise is a physico-mathematical study of image formation inside the camera obscura. Ibn al-Haytham takes an experimental approach, and determines the result by varying the size and the shape of the aperture, the focal length of the camera, the shape and intensity of the light source.

In his work he explains the inversion of the image in the camera obscura, the fact that the image is similar to the source when the hole is small, but also the fact that the image can differ from the source when the hole is large. All these results are produced by using a point analysis of the image.

Refractometer

Main article: Refractometer

In the seventh tract of his book of optics, Alhazen described an apparatus for experimenting with various cases of refraction, in order to investigate the relations between the angle of incidence, the angle of refraction and the angle of deflection. This apparatus was a modified version of an apparatus used by Ptolemy for similar purpose.

Unconscious inference

Main article: Unconscious inference

Alhazen basically states the concept of unconscious inference in his discussion of colour before adding that the inferential step between sensing colour and differentiating it is shorter than the time taken between sensing and any other visible characteristic (aside from light), and that "time is so short as not to be clearly apparent to the beholder." Naturally, this suggests that the colour and form are perceived elsewhere. Alhazen goes on to say that information must travel to the central nerve cavity for processing and:

the sentient organ does not sense the forms that reach it from the visible objects until after it has been affected by these forms; thus it does not sense color as color or light as light until after it has been affected by the form of color or light. Now the affectation received by the sentient organ from the form of color or of light is a certain change; and change must take place in time; .....and it is in the time during which the form extends from the sentient organ's surface to the cavity of the common nerve, and in (the time) following that, that the sensitive faculty, which exists in the whole of the sentient body will perceive color as color...Thus the last sentient's perception of color as such and of light as such takes place at a time following that in which the form arrives from the surface of the sentient organ to the cavity of the common nerve.

Color constancy

Main article: Color constancy

Alhazen explained color constancy by observing that the light reflected from an object is modified by the object's color. He explained that the quality of the light and the color of the object are mixed, and the visual system separates light and color. In Book II, Chapter 3 he writes:

Again the light does not travel from the colored object to the eye unaccompanied by the color, nor does the form of the color pass from the colored object to the eye unaccompanied by the light. Neither the form of the light nor that of the color existing in the colored object can pass except as mingled together and the last sentient can only perceive them as mingled together. Nevertheless, the sentient perceives that the visible object is luminous and that the light seen in the object is other than the color and that these are two properties.

Other contributions

The Kitab al-Manazir (Book of Optics) describes several experimental observations that Alhazen made and how he used his results to explain certain optical phenomena using mechanical analogies. He conducted experiments with projectiles and concluded that only the impact of perpendicular projectiles on surfaces was forceful enough to make them penetrate, whereas surfaces tended to deflect oblique projectile strikes. For example, to explain refraction from a rare to a dense medium, he used the mechanical analogy of an iron ball thrown at a thin slate covering a wide hole in a metal sheet. A perpendicular throw breaks the slate and passes through, whereas an oblique one with equal force and from an equal distance does not. He also used this result to explain how intense, direct light hurts the eye, using a mechanical analogy: Alhazen associated 'strong' lights with perpendicular rays and 'weak' lights with oblique ones. The obvious answer to the problem of multiple rays and the eye was in the choice of the perpendicular ray, since only one such ray from each point on the surface of the object could penetrate the eye.

Sudanese psychologist Omar Khaleefa has argued that Alhazen should be considered the founder of experimental psychology, for his pioneering work on the psychology of visual perception and optical illusions. Khaleefa has also argued that Alhazen should also be considered the "founder of psychophysics", a sub-discipline and precursor to modern psychology. Although Alhazen made many subjective reports regarding vision, there is no evidence that he used quantitative psychophysical techniques and the claim has been rebuffed.

Alhazen offered an explanation of the Moon illusion, an illusion that played an important role in the scientific tradition of medieval Europe. Many authors repeated explanations that attempted to solve the problem of the Moon appearing larger near the horizon than it does when higher up in the sky. Alhazen argued against Ptolemy's refraction theory, and defined the problem in terms of perceived, rather than real, enlargement. He said that judging the distance of an object depends on there being an uninterrupted sequence of intervening bodies between the object and the observer. When the Moon is high in the sky there are no intervening objects, so the Moon appears close. The perceived size of an object of constant angular size varies with its perceived distance. Therefore, the Moon appears closer and smaller high in the sky, and further and larger on the horizon. Through works by Roger Bacon, John Pecham and Witelo based on Alhazen's explanation, the Moon illusion gradually came to be accepted as a psychological phenomenon, with the refraction theory being rejected in the 17th century. Although Alhazen is often credited with the perceived distance explanation, he was not the first author to offer it. Cleomedes (c. 2nd century) gave this account (in addition to refraction), and he credited it to Posidonius (c. 135–50 BCE). Ptolemy may also have offered this explanation in his Optics, but the text is obscure. Alhazen's writings were more widely available in the Middle Ages than those of these earlier authors, and that probably explains why Alhazen received the credit.

Scientific method

Further information: Scientific method

Therefore, the seeker after the truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them, but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration, and not to the sayings of a human being whose nature is fraught with all kinds of imperfection and deficiency. The duty of the man who investigates the writings of scientists, if learning the truth is his goal, is to make himself an enemy of all that he reads, and ... attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency.

— Alhazen

An aspect associated with Alhazen's optical research is related to systemic and methodological reliance on experimentation (i'tibar)(Arabic: اختبار) and controlled testing in his scientific inquiries. Moreover, his experimental directives rested on combining classical physics (ilm tabi'i) with mathematics (ta'alim; geometry in particular). This mathematical-physical approach to experimental science supported most of his propositions in Kitab al-Manazir (The Optics; De aspectibus or Perspectivae) and grounded his theories of vision, light and colour, as well as his research in catoptrics and dioptrics (the study of the reflection and refraction of light, respectively).

According to Matthias Schramm, Alhazen "was the first to make a systematic use of the method of varying the experimental conditions in a constant and uniform manner, in an experiment showing that the intensity of the light-spot formed by the projection of the moonlight through two small apertures onto a screen diminishes constantly as one of the apertures is gradually blocked up." G. J. Toomer expressed some skepticism regarding Schramm's view, partly because at the time (1964) the Book of Optics had not yet been fully translated from Arabic, and Toomer was concerned that without context, specific passages might be read anachronistically. While acknowledging Alhazen's importance in developing experimental techniques, Toomer argued that Alhazen should not be considered in isolation from other Islamic and ancient thinkers. Toomer concluded his review by saying that it would not be possible to assess Schramm's claim that Ibn al-Haytham was the true founder of modern physics without translating more of Alhazen's work and fully investigating his influence on later medieval writers.

Other works on physics

Optical treatises

Besides the Book of Optics, Alhazen wrote several other treatises on the same subject, including his Risala fi l-Daw' (Treatise on Light). He investigated the properties of luminance, the rainbow, eclipses, twilight, and moonlight. Experiments with mirrors and the refractive interfaces between air, water, and glass cubes, hemispheres, and quarter-spheres provided the foundation for his theories on catoptrics.

Celestial physics

Alhazen discussed the physics of the celestial region in his Epitome of Astronomy, arguing that Ptolemaic models must be understood in terms of physical objects rather than abstract hypotheses – in other words that it should be possible to create physical models where (for example) none of the celestial bodies would collide with each other. The suggestion of mechanical models for the Earth centred Ptolemaic model "greatly contributed to the eventual triumph of the Ptolemaic system among the Christians of the West". Alhazen's determination to root astronomy in the realm of physical objects was important, however, because it meant astronomical hypotheses "were accountable to the laws of physics", and could be criticised and improved upon in those terms.

He also wrote Maqala fi daw al-qamar (On the Light of the Moon).

Mechanics

In his work, Alhazen discussed theories on the motion of a body.

Astronomical works

On the Configuration of the World

In his On the Configuration of the World Alhazen presented a detailed description of the physical structure of the earth:

The earth as a whole is a round sphere whose center is the center of the world. It is stationary in its middle, fixed in it and not moving in any direction nor moving with any of the varieties of motion, but always at rest.

The book is a non-technical explanation of Ptolemy's Almagest, which was eventually translated into Hebrew and Latin in the 13th and 14th centuries and subsequently had an influence on astronomers such as Georg von Peuerbach during the European Middle Ages and Renaissance.

Doubts Concerning Ptolemy

In his Al-Shukūk ‛alā Batlamyūs, variously translated as Doubts Concerning Ptolemy or Aporias against Ptolemy, published at some time between 1025 and 1028, Alhazen criticized Ptolemy's Almagest, Planetary Hypotheses, and Optics, pointing out various contradictions he found in these works, particularly in astronomy. Ptolemy's Almagest concerned mathematical theories regarding the motion of the planets, whereas the Hypotheses concerned what Ptolemy thought was the actual configuration of the planets. Ptolemy himself acknowledged that his theories and configurations did not always agree with each other, arguing that this was not a problem provided it did not result in noticeable error, but Alhazen was particularly scathing in his criticism of the inherent contradictions in Ptolemy's works. He considered that some of the mathematical devices Ptolemy introduced into astronomy, especially the equant, failed to satisfy the physical requirement of uniform circular motion, and noted the absurdity of relating actual physical motions to imaginary mathematical points, lines and circles:

Ptolemy assumed an arrangement (hay'a) that cannot exist, and the fact that this arrangement produces in his imagination the motions that belong to the planets does not free him from the error he committed in his assumed arrangement, for the existing motions of the planets cannot be the result of an arrangement that is impossible to exist... or a man to imagine a circle in the heavens, and to imagine the planet moving in it does not bring about the planet's motion.

Having pointed out the problems, Alhazen appears to have intended to resolve the contradictions he pointed out in Ptolemy in a later work. Alhazen believed there was a "true configuration" of the planets that Ptolemy had failed to grasp. He intended to complete and repair Ptolemy's system, not to replace it completely. In the Doubts Concerning Ptolemy Alhazen set out his views on the difficulty of attaining scientific knowledge and the need to question existing authorities and theories:

Truth is sought for itself the truths, are immersed in uncertainties not immune from error...

He held that the criticism of existing theories – which dominated this book – holds a special place in the growth of scientific knowledge.

Model of the Motions of Each of the Seven Planets

Alhazen's The Model of the Motions of Each of the Seven Planets was written c. 1038. Only one damaged manuscript has been found, with only the introduction and the first section, on the theory of planetary motion, surviving. (There was also a second section on astronomical calculation, and a third section, on astronomical instruments.) Following on from his Doubts on Ptolemy, Alhazen described a new, geometry-based planetary model, describing the motions of the planets in terms of spherical geometry, infinitesimal geometry and trigonometry. He kept a geocentric universe and assumed that celestial motions are uniformly circular, which required the inclusion of epicycles to explain observed motion, but he managed to eliminate Ptolemy's equant. In general, his model didn't try to provide a causal explanation of the motions, but concentrated on providing a complete, geometric description that could explain observed motions without the contradictions inherent in Ptolemy's model.

Other astronomical works

Alhazen wrote a total of twenty-five astronomical works, some concerning technical issues such as Exact Determination of the Meridian, a second group concerning accurate astronomical observation, a third group concerning various astronomical problems and questions such as the location of the Milky Way; Alhazen made the first systematic effort of evaluating the Milky Way's parallax, combining Ptolemy's data and his own. He concluded that the parallax is (probably very much) smaller than Lunar parallax, and the Milky way should be a celestial object. Though he was not the first who argued that the Milky Way does not belong to the atmosphere, he is the first who did quantitative analysis for the claim. The fourth group consists of ten works on astronomical theory, including the Doubts and Model of the Motions discussed above.

Mathematical works

In mathematics, Alhazen built on the mathematical works of Euclid and Thabit ibn Qurra and worked on "the beginnings of the link between algebra and geometry". Alhazen made developments in conic sections and number theory.

He developed a formula for summing the first 100 natural numbers, using a geometric proof to prove the formula.

Geometry

Alhazen explored what is now known as the Euclidean parallel postulate, the fifth postulate in Euclid's Elements, using a proof by contradiction, and in effect introducing the concept of motion into geometry. He formulated the Lambert quadrilateral, which Boris Abramovich Rozenfeld names the "Ibn al-Haytham–Lambert quadrilateral". He was criticised by Omar Khayyam who pointed that Aristotle had condemned the use of motion in geometry.

In elementary geometry, Alhazen attempted to solve the problem of squaring the circle using the area of lunes (crescent shapes), but later gave up on the impossible task. The two lunes formed from a right triangle by erecting a semicircle on each of the triangle's sides, inward for the hypotenuse and outward for the other two sides, are known as the lunes of Alhazen; they have the same total area as the triangle itself.

Number theory

Alhazen's contributions to number theory include his work on perfect numbers. In his Analysis and Synthesis, he may have been the first to state that every even perfect number is of the form 2(2 − 1) where 2 − 1 is prime, but he was not able to prove this result; Euler later proved it in the 18th century, and it is now called the Euclid–Euler theorem.

Alhazen solved problems involving congruences using what is now called Wilson's theorem. In his Opuscula, Alhazen considers the solution of a system of congruences, and gives two general methods of solution. His first method, the canonical method, involved Wilson's theorem, while his second method involved a version of the Chinese remainder theorem.

Calculus

Alhazen discovered the sum formula for the fourth power, using a method that could be generally used to determine the sum for any integral power. He used this to find the volume of a paraboloid. He could find the integral formula for any polynomial without having developed a general formula.

Other works

Influence of Melodies on the Souls of Animals

Alhazen also wrote a Treatise on the Influence of Melodies on the Souls of Animals, although no copies have survived. It appears to have been concerned with the question of whether animals could react to music, for example whether a camel would increase or decrease its pace.

Engineering

In engineering, one account of his career as a civil engineer has him summoned to Egypt by the Fatimid Caliph, Al-Hakim bi-Amr Allah, to regulate the flooding of the Nile River. He carried out a detailed scientific study of the annual inundation of the Nile River, and he drew plans for building a dam, at the site of the modern-day Aswan Dam. His field work, however, later made him aware of the impracticality of this scheme, and he soon feigned madness so he could avoid punishment from the Caliph.

Philosophy

In his Treatise on Place, Alhazen disagreed with Aristotle's view that nature abhors a void, and he used geometry in an attempt to demonstrate that place (al-makan) is the imagined three-dimensional void between the inner surfaces of a containing body. Abd-el-latif, a supporter of Aristotle's philosophical view of place, later criticized the work in Fi al-Radd 'ala Ibn al-Haytham fi al-makan (A refutation of Ibn al-Haytham's place) for its geometrization of place.

Alhazen also discussed space perception and its epistemological implications in his Book of Optics. In "tying the visual perception of space to prior bodily experience, Alhazen unequivocally rejected the intuitiveness of spatial perception and, therefore, the autonomy of vision. Without tangible notions of distance and size for correlation, sight can tell us next to nothing about such things."

Theology

Alhazen was a Muslim and most sources report that he was a Sunni and a follower of the Ash'ari school. Ziauddin Sardar says that some of the greatest Muslim scientists, such as Ibn al-Haytham and Abū Rayhān al-Bīrūnī, who were pioneers of the scientific method, were themselves followers of the Ashʿari school of Islamic theology. Like other Ashʿarites who believed that faith or taqlid should apply only to Islam and not to any ancient Hellenistic authorities, Ibn al-Haytham's view that taqlid should apply only to prophets of Islam and not to any other authorities formed the basis for much of his scientific skepticism and criticism against Ptolemy and other ancient authorities in his Doubts Concerning Ptolemy and Book of Optics.

Alhazen wrote a work on Islamic theology in which he discussed prophethood and developed a system of philosophical criteria to discern its false claimants in his time. He also wrote a treatise entitled Finding the Direction of Qibla by Calculation in which he discussed finding the Qibla, where prayers (salat) are directed towards, mathematically.

There are occasional references to theology or religious sentiment in his technical works, e.g. in Doubts Concerning Ptolemy:

Truth is sought for its own sake ... Finding the truth is difficult, and the road to it is rough. For the truths are plunged in obscurity. ... God, however, has not preserved the scientist from error and has not safeguarded science from shortcomings and faults. If this had been the case, scientists would not have disagreed upon any point of science...

In The Winding Motion:

From the statements made by the noble Shaykh, it is clear that he believes in Ptolemy's words in everything he says, without relying on a demonstration or calling on a proof, but by pure imitation (taqlid); that is how experts in the prophetic tradition have faith in Prophets, may the blessing of God be upon them. But it is not the way that mathematicians have faith in specialists in the demonstrative sciences.

Regarding the relation of objective truth and God:

I constantly sought knowledge and truth, and it became my belief that for gaining access to the effulgence and closeness to God, there is no better way than that of searching for truth and knowledge.

Legacy

Alhazen made significant contributions to optics, number theory, geometry, astronomy and natural philosophy. Alhazen's work on optics is credited with contributing a new emphasis on experiment.

His main work, Kitab al-Manazir (Book of Optics), was known in the Muslim world mainly, but not exclusively, through the thirteenth-century commentary by Kamāl al-Dīn al-Fārisī, the Tanqīḥ al-Manāẓir li-dhawī l-abṣār wa l-baṣā'ir. In al-Andalus, it was used by the eleventh-century prince of the Banu Hud dynasty of Zaragossa and author of an important mathematical text, al-Mu'taman ibn Hūd. A Latin translation of the Kitab al-Manazir was made probably in the late twelfth or early thirteenth century. This translation was read by and greatly influenced a number of scholars in Christian Europe including: Roger Bacon, Robert Grosseteste, Witelo, Giambattista della Porta, Leonardo da Vinci, Galileo Galilei, Christiaan Huygens, René Descartes, and Johannes Kepler. Meanwhile, in the Islamic world, Alhazen's work influenced Averroes' writings on optics, and his legacy was further advanced through the 'reforming' of his Optics by Persian scientist Kamal al-Din al-Farisi (died c. 1320) in the latter's Kitab Tanqih al-Manazir (The Revision of Optics). Alhazen wrote as many as 200 books, although only 55 have survived. Some of his treatises on optics survived only through Latin translation. During the Middle Ages his books on cosmology were translated into Latin, Hebrew and other languages.

H. J. J. Winter, a British historian of science, summing up the importance of Ibn al-Haytham in the history of physics wrote:

After the death of Archimedes no really great physicist appeared until Ibn al-Haytham. If, therefore, we confine our interest only to the history of physics, there is a long period of over twelve hundred years during which the Golden Age of Greece gave way to the era of Muslim Scholasticism, and the experimental spirit of the noblest physicist of Antiquity lived again in the Arab Scholar from Basra.

Although only one commentary on Alhazen's optics has survived the Islamic Middle Ages, Geoffrey Chaucer mentions the work in The Canterbury Tales:

"They spoke of Alhazen and Vitello,
And Aristotle, who wrote, in their lives,
On strange mirrors and optical instruments."

The impact crater Alhazen on the Moon is named in his honour, as was the asteroid 59239 Alhazen. In honour of Alhazen, the Aga Khan University (Pakistan) named its Ophthalmology endowed chair as "The Ibn-e-Haitham Associate Professor and Chief of Ophthalmology".

The 2015 International Year of Light celebrated the 1000th anniversary of the works on optics by Ibn Al-Haytham.

In 2014, the "Hiding in the Light" episode of Cosmos: A Spacetime Odyssey, presented by Neil deGrasse Tyson, focused on the accomplishments of Ibn al-Haytham. He was voiced by Alfred Molina in the episode.

Over forty years previously, Jacob Bronowski presented Alhazen's work in a similar television documentary (and the corresponding book), The Ascent of Man. In episode 5 (The Music of the Spheres), Bronowski remarked that in his view, Alhazen was "the one really original scientific mind that Arab culture produced", whose theory of optics was not improved on till the time of Newton and Leibniz.

UNESCO declared 2015 the International Year of Light and its Director-General Irina Bokova dubbed Ibn al-Haytham 'the father of optics'. Amongst others, this was to celebrate Ibn Al-Haytham's achievements in optics, mathematics and astronomy. An international campaign, created by the 1001 Inventions organisation, titled 1001 Inventions and the World of Ibn Al-Haytham featuring a series of interactive exhibits, workshops and live shows about his work, partnering with science centers, science festivals, museums, and educational institutions, as well as digital and social media platforms. The campaign also produced and released the short educational film 1001 Inventions and the World of Ibn Al-Haytham.

Ibn al-Haytham appears on the 10,000 dinar banknote of the Iraqi dinar, series 2003.

List of works

According to medieval biographers, Alhazen wrote more than 200 works on a wide range of subjects, of which at least 96 of his scientific works are known. Most of his works are now lost, but more than 50 of them have survived to some extent. Nearly half of his surviving works are on mathematics, 23 of them are on astronomy, and 14 of them are on optics, with a few on other subjects. Not all his surviving works have yet been studied, but some of the ones that have are given below.

1. Book of Optics (كتاب المناظر)
2. Analysis and Synthesis (مقالة في التحليل والتركيب)
3. Balance of Wisdom (ميزان الحكمة)
4. Corrections to the Almagest (تصويبات على المجسطي)
5. Discourse on Place (مقالة في المكان)
6. Exact Determination of the Pole (التحديد الدقيق للقطب)
7. Exact Determination of the Meridian (رسالة في الشفق)
8. Finding the Direction of Qibla by Calculation (كيفية حساب اتجاه القبلة)
9. Horizontal Sundials (المزولة الأفقية)
10. Hour Lines (خطوط الساعة)
11. Doubts Concerning Ptolemy (شكوك على بطليموس)
12. Maqala fi'l-Qarastun (مقالة في قرسطون)
13. On Completion of the Conics (إكمال المخاريط)
14. On Seeing the Stars (رؤية الكواكب)
15. On Squaring the Circle (مقالة فی تربیع الدائرة)
16. On the Burning Sphere (المرايا المحرقة بالدوائر)
17. On the Configuration of the World (تكوين العالم)
18. On the Form of Eclipse (مقالة فی صورة ‌الکسوف)
19. On the Light of Stars (مقالة في ضوء النجوم)
20. On the Light of the Moon (مقالة في ضوء القمر)
21. On the Milky Way (مقالة في درب التبانة)
22. On the Nature of Shadows (كيفيات الإظلال)
23. On the Rainbow and Halo (مقالة في قوس قزح)
24. Opuscula (Minor Works)
25. Resolution of Doubts Concerning the Almagest (تحليل شكوك حول الجست)
26. Resolution of Doubts Concerning the Winding Motion
27. The Correction of the Operations in Astronomy (تصحيح العمليات في الفلك)
28. The Different Heights of the Planets (اختلاف ارتفاع الكواكب)
29. The Direction of Mecca (اتجاه القبلة)
30. The Model of the Motions of Each of the Seven Planets (نماذج حركات الكواكب السبعة)
31. The Model of the Universe (نموذج الكون)
32. The Motion of the Moon (حركة القمر)
33. The Ratios of Hourly Arcs to their Heights
34. The Winding Motion (الحركة المتعرجة)
35. Treatise on Light (رسالة في الضوء)
36. Treatise on Place (رسالة في المكان)
37. Treatise on the Influence of Melodies on the Souls of Animals (تأثير اللحون الموسيقية في النفوس الحيوانية)
38. كتاب في تحليل المسائل الهندسية (A book in engineering analysis)
39. الجامع في أصول الحساب (The whole in the assets of the account)
40. قول فی مساحة الکرة (Say in the sphere)
41. القول المعروف بالغریب فی حساب المعاملات (Saying the unknown in the calculation of transactions)
42. خواص المثلث من جهة العمود (Triangle properties from the side of the column)
43. رسالة فی مساحة المسجم المکافی (A message in the free space)
44. شرح أصول إقليدس (Explain the origins of Euclid)
45. المرايا المحرقة بالقطوع (The burning mirrors of the rainbow)
46. مقالة في القرصتن (Treatise on Centers of Gravity)

Lost works

1. A Book in which I have Summarized the Science of Optics from the Two Books of Euclid and Ptolemy, to which I have added the Notions of the First Discourse which is Missing from Ptolemy's Book
2. Treatise on Burning Mirrors
3. Treatise on the Nature of Sight and on How Vision is Achieved Through It

See also

• Ibn Sufi
• "Hiding in the Light"
• History of mathematics
• Theoretical physics
• History of optics
• History of physics
• History of science
• History of scientific method
• Hockney–Falco thesis
• Mathematics in medieval Islam
• Physics in medieval Islam
• Science in the medieval Islamic world
• Fatima al-Fihri
• Islamic Golden Age

Notes

1. A. Mark Smith has determined that there were at least two translators, based on their facility with Arabic; the first, more experienced scholar began the translation at the beginning of Book One, and handed it off in the middle of Chapter Three of Book Three. Smith 2001 91 Volume 1: Commentary and Latin text pp.xx–xxi. See also his 2006, 2008, 2010 translations.

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• Smith, A. Mark, ed. (2006), Alhacen on the principles of reflection : a critical edition, with English translation and commentary, of books 4 and 5 of Alhacen's De aspectibus, , Transactions of the American Philosophical Society, vol. 95–4, 95–5, translated by Smith, A. Mark, Philadelphia: American Philosophical Society (Books 4–5 (2006) 95 4 – Vol 1 Commentary and Latin text via JSTOR Archived 24 September 2018 at the Wayback Machine; 95 5 – Vol 2 English translation IV: TOC pp. 289–94, V: TOC pp. 377–84, Notes, Bibl. via JSTOR Archived 6 October 2016 at the Wayback Machine)
• Smith, A. Mark, ed. (2008), Alhacen on Image-formation and distortion in mirrors: a critical edition, with English translation and commentary, of Book 6 of Alhacen's De aspectibus, , Transactions of the American Philosophical Society, vol. 98–1, translated by Smith, A. Mark, Philadelphia: American Philosophical Society (Book 6 (2008) 98 (#1, section 1) – Vol 1 Commentary and Latin text via JSTOR Archived 24 September 2018 at the Wayback Machine; 98 (#1, section 2) – Vol 2 English translation VI:TOC pp. 155–160, Notes, Bibl. via JSTOR Archived 6 October 2016 at the Wayback Machine)
• Smith, A. Mark, ed. (2010), Alhacen on Refraction: a critical edition, with English translation and commentary, of Book 7 of Alhacen's De aspectibus, , Transactions of the American Philosophical Society, vol. 100–3, translated by Smith, A. Mark, Philadelphia: American Philosophical Society (Book 7 (2010) 100(#3, section 1) – Vol 1 Commentary and Latin text via JSTOR Archived 24 September 2018 at the Wayback Machine; 100(#3, section 2) – Vol 2 English translation VII: TOC pp. 213–18, Notes, Bibl. via JSTOR Archived 6 October 2016 at the Wayback Machine)
• Smith, A. Mark (2015), From Sight to Light: The Passage from Ancient to Modern Optics, Chicago: University of Chicago Press, Bibcode:2014fslp.book.....S, ISBN 978-0-226-17476-1
• Smith, John D. (1 March 1992), "The Remarkable Ibn al-Haytham", The Mathematical Gazette, 76 (475), Mathematical Association: 189–198, doi:10.2307/3620392, ISSN 0025-5572, JSTOR 3620392, S2CID 118597450
• Toomer, G. J. (December 1964), "Review: Ibn al-Haythams Weg zur Physik by Matthias Schramm", Isis, 55 (4): 463–465, doi:10.1086/349914
• Topdemir, Huseyin Gazi (18 July 2007), Ibn al-Haytham (965–1039): His Life and Works
• Vernet, J. (1996) , "Ibn al-Haytham", in Gibb, H. A. R.; Bearman, P. (eds.), Encyclopaedia of Islam (First ed.), Leiden: Brill Publishers, ISBN 978-9004161214, archived from the original on 9 January 2012, retrieved 11 February 2016
• Vernet, J. (2012), "Ibn al-Haytham", in Bearman, P.; Bianquis, Th.; Bosworth, C. E.; van Donzel, E.; Heinrichs, W. P. (eds.), Encyclopaedia of Islam (Second ed.), Brill Online: Brill Publishers, archived from the original on 9 January 2012, retrieved 16 September 2008
• Wade, Nicholas J. (1998), A Natural History of Vision, Cambridge, MA: MIT Press
• Wade, Nicholas J.; Finger, Stanley (2001), "The eye as an optical instrument: from camera obscura to Helmholtz's perspective", Perception, 30 (10): 1157–1177, doi:10.1068/p3210, PMID 11721819, S2CID 8185797
• Weisstein, Eric (2008), Alhazen's Billiard Problem, Mathworld, archived from the original on 17 April 2021, retrieved 24 September 2008
• Whitaker, Brian (23 September 2004), "Centuries in the House of Wisdom", The Guardian, archived from the original on 16 September 2014, retrieved 16 September 2008
• Zewail, Ahmed H.; Thomas, John Meurig (2010), 4D Electron Microscopy: Imaging in Space and Time, World Scientific, ISBN 978-1-84816-390-4

Further reading

Primary

• Sabra, A. I, ed. (1983), The Optics of Ibn al-Haytham, Books I–II–III: On Direct Vision. The Arabic text, edited and with Introduction, Arabic-Latin Glossaries and Concordance Tables, Kuwait: National Council for Culture, Arts and Letters
• Sabra, A. I, ed. (2002), The Optics of Ibn al-Haytham. Edition of the Arabic Text of Books IV–V: On Reflection and Images Seen by Reflection. 2 vols, Kuwait: National Council for Culture, Arts and Letters
• Smith, A. Mark, ed. and trans. (2006), "Alhacen on the principles of reflection: A Critical Edition, with English Translation and Commentary, of books 4 and 5 of Alhacen's De Aspectibus, the Medieval Latin Version of Ibn al-Haytham's Kitāb al-Manāẓir, 2 vols.", Transactions of the American Philosophical Society, 95 (2–3), Philadelphia: American Philosophical Society{{citation}}: CS1 maint: multiple names: authors list (link) 2 vols: . (Philadelphia: American Philosophical Society), 2006 – 95(#2) Books 4–5 Vol 1 Commentary and Latin text via JSTOR Archived 24 September 2018 at the Wayback Machine; 95(#3) Vol 2 English translation, Notes, Bibl. via JSTOR Archived 6 October 2016 at the Wayback Machine
• Smith, A. Mark, ed. and trans. (2008) Alhacen on Image-formation and distortion in mirrors : a critical edition, with English translation and commentary, of Book 6 of Alhacen's De aspectibus, , Transactions of the American Philosophical Society, 2 vols: Vol 1 98(#1, section 1 – Vol 1 Commentary and Latin text); 98(#1, section 2 – Vol 2 English translation). (Philadelphia: American Philosophical Society), 2008. Book 6 (2008) Vol 1 Commentary and Latin text via JSTOR Archived 24 September 2018 at the Wayback Machine; Vol 2 English translation, Notes, Bibl. via JSTOR Archived 6 October 2016 at the Wayback Machine
• Smith, A. Mark, ed. and trans. (2010) Alhacen on Refraction : a critical edition, with English translation and commentary, of Book 7 of Alhacen's De aspectibus, , Transactions of the American Philosophical Society, 2 vols: 100(#3, section 1 – Vol 1, Introduction and Latin text); 100(#3, section 2 – Vol 2 English translation). (Philadelphia: American Philosophical Society), 2010. Book 7 (2010) Vol 1 Commentary and Latin text via JSTOR Archived 24 September 2018 at the Wayback Machine;Vol 2 English translation, Notes, Bibl. via JSTOR Archived 6 October 2016 at the Wayback Machine

Secondary

• Belting, Hans, Afterthoughts on Alhazen's Visual Theory and Its Presence in the Pictorial Theory of Western Perspective, in: Variantology 4. On Deep Time Relations of Arts, Sciences and Technologies in the Arabic-Islamic World and Beyond, ed. by Siegfried Zielinski and Eckhard Fürlus in cooperation with Daniel Irrgang and Franziska Latell (Cologne: Verlag der Buchhandlung Walther König, 2010), pp. 19–42.
• El-Bizri, Nader (2009b), "Ibn al-Haytham et le problème de la couleur", Oriens Occidens, 7 (1), Paris: CNRS: 201–226
• El-Bizri, Nader (2016), "Grosseteste's Meteorological Optics: Explications of the Phenomenon of the Rainbow after Ibn al-Haytham", in Cunningham, Jack P.; Hocknull, Mark (eds.), Robert Grosseteste and the Pursuit of Religious and Scientific Knowledge in the Middle Ages, Studies in the History of Philosophy of Mind, vol. 18, Dordrecht: Springer, pp. 21–39, ISBN 978-3-319-33466-0
• Falco, Charles M. (12–15 February 2007), Ibn al-Haytham and the Origins of Modern Image Analysis (PDF), presented at a plenary session at the International Conference on Information Sciences, Signal Processing and its Applications, archived from the original (PDF) on 4 December 2020, retrieved 23 January 2008
• Gazı Topdemır, Hüseyın (2000). İBNÜ'l-HEYSEM – An article published in 21st volume of Turkish Encyclopedia of Islam (in Turkish). Vol. 21. Istanbul: TDV İslâm Ansiklopedisi. pp. 82–87. ISBN 978-97-53-89448-7. Archived from the original on 9 June 2021. Retrieved 14 January 2022.
• Graham, Mark. How Islam Created the Modern World. Amana Publications, 2006.
• Omar, Saleh Beshara (June 1975), Ibn al-Haytham and Greek optics: a comparative study in scientific methodology, PhD Dissertation, University of Chicago, Department of Near Eastern Languages and Civilizations
• Roshdi Rashed, Optics and Mathematics: Research on the history of scientific thought in Arabic, Variorum reprints, Aldershot, 1992.
• Roshdi Rashed, Geometry and Dioptrics the tenth century: Ibn Sahl al-Quhi and Ibn al-Haytham (in French), Les Belles Lettres, Paris, 1993
• Roshdi Rashed, Infinitesimal Mathematics, vols. 1–5, al-Furqan Islamic Heritage Foundation, London, 1993–2006
• Saliba, George (2007), Islamic Science and the Making of the European Renaissance, MIT Press, ISBN 978-0-262-19557-7, archived from the original on 19 April 2017, retrieved 18 April 2017
• Siegfried Zielinski & Franziska Latell, How One Sees, in: Variantology 4. On Deep Time Relations of Arts, Sciences and Technologies in the Arabic-Islamic World and Beyond, ed. by Siegfried Zielinski and Eckhard Fürlus in cooperation with Daniel Irrgang and Franziska Latell (Cologne: Verlag der Buchhandlung Walther König, 2010), pp. 19–42. Buchhandlung Walther-König - KWB 45: Variantology 4

External links

• Works by Ibn al-Haytham at Open Library
• Langermann, Y. Tzvi (2007). "Ibn al-Haytham: Abū ʿAlī al-Ḥasan ibn al-Ḥasan". In Thomas Hockey; et al. (eds.). The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 556–5567. ISBN 978-0-387-31022-0. (PDF version)
• 'A Brief Introduction on Ibn al-Haytham' based on a lecture delivered at the Royal Society in London by Nader El-Bizri
• Ibn al-Haytham on two Iraqi banknotes Archived 3 August 2018 at the Wayback Machine
• The Miracle of Light – a UNESCO article on Ibn al-Haytham
• Biography from Malaspina Global Portal
• Short biographies on several "Muslim Heroes and Personalities" including Ibn al-Haytham
• Biography from ioNET at the Wayback Machine (archived 13 October 1999)
• "Biography from the BBC". Archived from the original on 11 February 2006. Retrieved 16 September 2008.
• Biography from Trinity College (Connecticut)
• Biography from Molecular Expressions
• The First True Scientist from BBC News
• Over the Moon From The UNESCO Courier on the occasion of the International Year of Astronomy 2009
• The Mechanical Water Clock Of Ibn Al-Haytham, Muslim Heritage
• Alhazen's (1572) Opticae thesaurus Archived 24 September 2018 at the Wayback Machine (English) – digital facsimile from the Linda Hall Library

v t e Astronomy in the medieval Islamic world
Astronomers by century 8th Ahmad Nahavandi Al-Fadl ibn Naubakht Muḥammad ibn Ibrāhīm al-Fazārī Ibrāhīm al-Fazārī Mashallah ibn Athari Yaʿqūb ibn Ṭāriq 9th Abu Ali al-Khayyat Abu Ma'shar al-Balkhi Abu Said Gorgani Al-Farghani Al-Kindi Al-Mahani Abu Hanifa Dinawari Al-Ḥajjāj ibn Yūsuf Al-Marwazi Ali ibn Isa al-Asturlabi Banū Mūsā brothers Iranshahri Khalid ibn Abd al‐Malik al‐Marwarrudhi Al-Khwarizmi Sahl ibn Bishr Thābit ibn Qurra Yahya ibn Abi Mansur 10th al-Sufi Ibn Al-Adami al-Khojandi al-Khazin al-Qūhī Abu al-Wafa Ahmad ibn Yusuf al-Battani Al-Qabisi Ibn al-A'lam Al-Nayrizi Al-Saghani Aṣ-Ṣaidanānī Ibn Yunus Ibrahim ibn Sinan Ma Yize al-Sijzi Al-ʻIjliyyah Nastulus Abolfadl Harawi Haseb-i Tabari al-Majriti Abu al-Hasan al-Ahwazi 11th Abu Nasr Mansur al-Biruni Ali ibn Ridwan Al-Zarqālī Ibn al-Samh Alhazen Avicenna Ibn al-Saffar Kushyar Gilani Said al-Andalusi Ibrahim ibn Said al-Sahli Ibn Mu'adh al-Jayyani Al-Isfizari Ali ibn Khalaf 12th Al-Bitruji Avempace Ibn Tufail Al-Kharaqī Al-Khazini Al-Samawal al-Maghribi Abu al-Salt Averroes Ibn al-Kammad Jabir ibn Aflah Omar Khayyam Sharaf al-Din al-Tusi 13th Ibn al-Banna' al-Marrakushi Ibn al‐Ha'im al‐Ishbili Jamal ad-Din Alam al-Din al-Hanafi Najm al‐Din al‐Misri Muhyi al-Din al-Maghribi Nasir al-Din al-Tusi Qutb al-Din al-Shirazi Shams al-Din al-Samarqandi Zakariya al-Qazwini al-Urdi al-Abhari Muhammad ibn Abi Bakr al‐Farisi Abu Ali al-Hasan al-Marrakushi Ibn Ishaq al-Tunisi Ibn al‐Raqqam Al-Ashraf Umar II Fakhr al-Din al-Akhlati 14th Ibn al-Shatir Al-Khalili Ibn Shuayb al-Battiwi Abū al‐ʿUqūl Al-Wabkanawi Nizam al-Din al-Nisapuri al-Jadiri Sadr al-Shari'a al-Asghar Fathullah Shirazi 15th Ali Kuşçu Abd al‐Wajid Jamshid al-Kashi Kadızade Rumi Ulugh Beg Sibt al-Maridini Ibn al-Majdi al-Wafa'i al-Kubunani 'Abd al-'Aziz al-Wafa'i 16th Al-Birjandi al-Khafri Baha' al-din al-'Amili Piri Reis Takiyüddin 17th Yang Guangxian Ehmedê Xanî Al Achsasi al Mouakket Muhammad al-Rudani
Topics Works Arabic star names Islamic calendar Aja'ib al-Makhluqat Encyclopedia of the Brethren of Purity Tabula Rogeriana The Book of Healing The Remaining Signs of Past Centuries Zij Alfonsine tables Huihui Lifa Book of Fixed Stars Toledan Tables Zij-i Ilkhani Zij-i Sultani Sullam al-sama' Instruments Alidade Analog computer Aperture Armillary sphere Astrolabe Astronomical clock Celestial globe Compass Compass rose Dioptra Equatorial ring Equatorium Globe Graph paper Mural instrument Navigational astrolabe Octant Planisphere Quadrant Sextant Shadow square Sundial Schema for horizontal sundials Triquetrum Concepts Almucantar Apogee Astrology Astrophysics Axial tilt Azimuth Celestial mechanics Celestial spheres Circular orbit Deferent and epicycle Earth's rotation Eccentricity Ecliptic Elliptic orbit Equant Galaxy Geocentrism Gravitational energy Gravity Heliocentrism Inertia Islamic cosmology Moonlight Multiverse Muwaqqit Obliquity Parallax Precession Qibla Salah times Specific gravity Spherical Earth Sublunary sphere Sunlight Supernova Temporal finitism Trepidation Triangulation Tusi couple Universe Institutions Al-Azhar University House of Knowledge House of Wisdom University of al-Qarawiyyin Observatories Constantinople (Taqi al-Din) Maragheh Samarkand (Ulugh Beg) Influences Babylonian astronomy Egyptian astronomy Hellenistic astronomy Indian astronomy Influenced Byzantine science Chinese astronomy Medieval European science Indian astronomy

v t e Mathematics in the medieval Islamic world
Mathematicians	9th century 'Abd al-Hamīd ibn Turk Sanad ibn Ali al-Jawharī Al-Ḥajjāj ibn Yūsuf Al-Kindi Qusta ibn Luqa Al-Mahani al-Dinawari Banū Mūsā brothers Hunayn ibn Ishaq Al-Khwarizmi Yusuf al-Khuri Ishaq ibn Hunayn Na'im ibn Musa Thābit ibn Qurra al-Marwazi Abu Said Gorgani 10th century Abu al-Wafa al-Khazin Al-Qabisi Abu Kamil Ahmad ibn Yusuf Aṣ-Ṣaidanānī Sinān ibn al-Fatḥ al-Khojandi Al-Nayrizi Al-Saghani Brethren of Purity Ibn Sahl Ibn Yunus al-Uqlidisi Al-Battani Sinan ibn Thabit Ibrahim ibn Sinan Al-Isfahani Nazif ibn Yumn al-Qūhī Abu al-Jud Al-Sijzi Al-Karaji al-Majriti al-Jabali 11th century Abu Nasr Mansur Alhazen Kushyar Gilani Al-Biruni Ibn al-Samh Abu Mansur al-Baghdadi Avicenna al-Jayyānī al-Nasawī al-Zarqālī ibn Hud Al-Isfizari Omar Khayyam Muhammad al-Baghdadi 12th century Jabir ibn Aflah Al-Kharaqī Al-Khazini Al-Samawal al-Maghribi al-Hassar Sharaf al-Din al-Tusi Ibn al-Yasamin 13th century Ibn al‐Ha'im al‐Ishbili Ahmad al-Buni Ibn Munim Alam al-Din al-Hanafi Ibn Adlan al-Urdi Nasir al-Din al-Tusi al-Abhari Muhyi al-Din al-Maghribi al-Hasan al-Marrakushi Qutb al-Din al-Shirazi Shams al-Din al-Samarqandi Ibn al-Banna' Kamāl al-Dīn al-Fārisī 14th century Nizam al-Din al-Nisapuri Ibn al-Shatir Ibn al-Durayhim Al-Khalili al-Umawi 15th century Ibn al-Majdi al-Rūmī al-Kāshī Ulugh Beg Ali Qushji al-Wafa'i al-Qalaṣādī Sibt al-Maridini Ibn Ghazi al-Miknasi 16th century Al-Birjandi Muhammad Baqir Yazdi Taqi ad-Din Ibn Hamza al-Maghribi
Mathematical works	The Compendious Book on Calculation by Completion and Balancing De Gradibus Principles of Hindu Reckoning Book of Optics The Book of Healing Book on the Measurement of Plane and Spherical Figures Encyclopedia of the Brethren of Purity Toledan Tables Tabula Rogeriana Zij
Concepts	Alhazen's problem Islamic geometric patterns
Centers	Al-Azhar University Al-Mustansiriya University House of Knowledge House of Wisdom Constantinople observatory of Taqi ad-Din Madrasa Maragheh observatory University of al-Qarawiyyin
Influences	Babylonian mathematics Greek mathematics Indian mathematics
Influenced	Byzantine mathematics European mathematics Indian mathematics
Related	Hindu–Arabic numeral system Arabic numerals (Eastern Arabic numerals, Western Arabic numerals) Trigonometric functions History of trigonometry History of algebra

v t e Islamic philosophy
Fields Alchemy Aqidah (theology) 'Aql (intellect) Cosmology astrology medieval astronomy Eschatology Ethics Kalam (dialectic) Fiqh (jurisprudence) Logic Metaphysics Natural philosophy (physics) Peace Madrasah (education) Medieval science Medieval psychology Sufism (mysticism) Schools Early Farabism Avicennism Averroism Illuminationism Sufi cosmology metaphysics psychology Transcendent theosophy Traditionalist Contemporary Concepts ʻAṣabīya Ḥāl Iʻjaz ʼIjtihād ʻIlm ʻIrfān Ijmāʿ Maslaha Nafs Qadar Qalb Qiyās Shūrā Tawḥīd Ummah
Philosophers by century (CE) 9th–10th Al-Kindi Ali ibn Sahl Rabban al-Tabari Abu al-Abbas Iranshahri Abu Bakr al-Razi Apharabius Abu Hatim al-Razi Al Amiri Ikhwan al-Safa Abu Sulayman Sijistani Ibn Masarrah Abu Ya'qub al-Sijistani 11th Al-Ghazali Ibn Miskawayh Avicenna Ibn Hazm Bahmanyār Mu'ayyad fi'l-Din al-Shirazi Nasir Khusraw Hamid al-Din al-Kirmani 12th Abu'l-Barakāt al-Baghdādī Afdal al-Din Kashani Ahi Evren Ahmad Yasavi Ayn-al-Quzat Averroes Ibn Tufail Omar Khayyám Suhrawardi Shams Tabrizi 13th Hajji Bektash Wali Jalal ad-Din Muhammad Rumi Ibn Sab’in Ibn Arabi al-Abharī Nasir al-Din Tusi Fakhr al-Din al-Razi Qutb al-Din al-Shirazi Sadr al-Din al-Qunawi Ibn Taymiyya 14th–16th Ibn Khaldun Yunus Emre Hajji Bayram Jalaladdin Davani Sadr ad-Din Dashtaki Aziz Mahmud Hudayi Qadi Mir Husayn al-Maybudi Mahmud Shabistari Sayyid Haydar Amuli Dawūd al-Qayṣarī Jami 17th–19th Mir Damad Mir Fendereski Mulla Sadra Mohsen Fayz Kashani Abd al-Razzaq Lahiji Mujaddid Alf-i-Sani Rajab Ali Tabrizi Qazi Sa’id Qumi Shah Waliullah Dehlawi Hādī Sabzavārī 20th–present Muhammad Husayn Tabatabaei Muhammad Iqbal Gohar Shahi Mohammad Baqir al-Sadr René Guénon Frithjof Schuon Martin Lings Ismail al-Faruqi Seyyed Hossein Nasr Syed Muhammad Naquib al-Attas Abdolkarim Soroush Gholamhossein Ebrahimi Dinani Taha Abdurrahman Mohammed Abed al-Jabri Mohammed Arkoun Fouad Zakariyya Reza Davari Ardakani Ahmad Fardid Mostafa Malekian Hasanzadeh Amoli Javadi Amoli Partawi Shah

v t e Islamic medicine
Physicians	7th century Abu Hafsa Yazid Al-Harith ibn Kalada Bukhtishu Ibn Abi Ramtha al-Tamimi Ibn Uthal Masarjawaih Nafi ibn al-Harith Rufaida Al-Aslamia Zaynab al-Awadiya 8th century Bukhtishu Ja'ar al-Sadiq 9th century Al-Kindi Al-Ruhawi Albubather Ali al-Ridha Ali ibn Sahl Rabban al-Tabari Bukhtishu Hunayn ibn Ishaq Ishaq ibn Hunayn Jabir ibn Hayyan Jabril ibn Bukhtishu Masawaiyh Salmawaih ibn Bunan Shapur ibn Sahl Yahya ibn Sarafyun Yuhanna ibn Bukhtishu Yusuf al-Khuri 10th century 'Ali ibn al-'Abbas al-Majusi Aayon Ibn Aayon Abu Bakr Rabee Ibn Ahmad Al-Akhawyni Bokhari Abu Bakr al-Razi Abu Sahl 'Isa ibn Yahya al-Masihi Abu Zayd al-Balkhi Abu al-Hasan al-Tabari Abu al-Qasim Muqane'i Abu al-Qasim al-Zahrawi Abu ul-Ala Shirazi Al-Kaŝkarī Al-Natili Al-Tamimi, the physician Eutychius of Alexandria Ibn Abi al-Ashʿath Ibn Juljul Ibn al-Jazzar Ibrahim ibn Baks Isaac Israeli ben Solomon Mohammed ibn Abdun al-Jabali Muvaffak Qumri Qusta ibn Luqa 11th century Abdollah ibn Bukhtishu Abu 'Ubayd al-Juzjani Abu al-Hakam al-Kirmani Al-Biruni Ali ibn Isa al-Kahhal Ali ibn Ridwan Ali ibn Yusuf al-Ilaqi Ammar ibn Ali al-Mawsili Avicenna Badi' al-Asturlabi Ibn Abi Sadiq Ibn Al-Thahabi Ibn Butlan Ibn Hindu Ibn Jazla Ibn al-Haytham Ibn al-Kattani Ibn al-Wafid Jonah ibn Janah Masawaih 12th century Abu Jafar ibn Harun al-Turjali Abu al-Bayan ibn al-Mudawwar Abu al-Majd ibn Abi al-Hakam Abu'l-Barakāt al-Baghdādī Ahmad ibn Farrokh Al-Samawal al-Maghribi Avempace Averroes Ibn Habal Ibn Jumay‘ Ibn Tufayl Ibn Zuhr Ibn al-Tilmīdh Moshe ben Maimon Muhammad ibn Aslam Al-Ghafiqi Serapion the Younger Ya'qub ibn Ishaq al-Israili Zayn al-Din Gorgani 13th century Abd al-Latif al-Baghdadi Abraham ben Moses ben Maimon Al-Dakhwar Al-Shahrazuri Amin al-Din Rashid al-Din Vatvat As-Suwaydi Da'ud Abu al-Fadl Hussam al-Din al-Jarrahi Ibn Abi Usaibia Ibn Tumlus Ibn al-Baitar Ibn al-Nafis Ibn al-Quff Ibn al‐Raqqam Joseph ben Judah of Ceuta Najib ad-Din Samarqandi Qutb al-Din al-Shirazi Rashidun al-Suri Sa'ad al-Dawla Zakariya al-Qazwini 14th century Al-Nagawri Aqsara'i Ibn Shuayb Ibn al-Akfani Ibn al-Khatib Jaghmini Mansur ibn Ilyas Mas‘ud ibn Muhammad Sijzi Muhammad ibn Mahmud Amuli Najm al-Din Mahmud ibn Ilyas al-Shirazi Nakhshabi Rashid-al-Din Hamadani Sadid al-Din al-Kazaruni Yusuf ibn Ismail al-Kutubi Zayn-e-Attar 15th century Abu Sa'id al-Afif Burhan-ud-din Kermani Husayni Isfahani Muhammad Ali Astarabadi Muhammad ibn Yusuf al-Harawi Nurbakhshi Shaykh Muhammad ibn Thaleb Şerafeddin Kadir 16th century Rostam Gorgani ʽImad Shirazi Abul Qasim ibn Mohammed al-Ghassani Dawud al-Antaki Hakim-e-Gilani Sultan Ali Khorasani Taqi al-Din Muhammad ibn Ma'ruf 17th century Qiwam al-Din Muhammad al-Hasani Abd El Razzaq Al-Jazaïri Qurayshi al-Shirazi Tunakabuni Maqsud-Ali Tabrizi 18th century Al-Khurasani al-Shirazi
Concepts	Ophthalmology Psychology
Works	Al-Risalah al-Dhahabiah The Canon of Medicine Tacuinum Sanitatis Anatomy Charts of the Arabs The Book of Healing Book of the Ten Treatises of the Eye De Gradibus Al-Tasrif Zakhireye Khwarazmshahi Adab al-Tabib Kamel al-Sanaat al-Tibbyya Al-Hawi Commentary on Anatomy in Avicenna's Canon Lives of the Physicians
Centers	Al-'Adudi Hospital Bimarestan Nur al-Din Bimaristan
Influences	Ancient Greek medicine Ancient Iranian medicine Ayurveda
Influenced	Ibn Sina Academy Learned medicine Medical Renaissance Medieval medicine

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• Ibn al-Haytham
• 960s births
• 1040 deaths
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• Iraqi astronomers
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• Engineers of the medieval Islamic world
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• Scientists who worked on qibla determination
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• 11th-century inventors
• Muslim critics of atheism