Though born in what is now modern-day Iraq around the year 965, he spent most of his life in Cairo, Egypt, dying there at the age of 76. In his over-confidence about the practical application of his mathematical knowledge, he assumed that he could regulate the floods caused by the overflow of the Nile. After being ordered by Al-Hakim bi-Amr Allah, the sixth ruler of the Fatimid caliphate, to carry out this operation, he quickly perceived the inanity of what he was attempting to do, and retired from engineering. Fearing for his life, he feigned madness and was placed under house arrest, during and after which he devoted himself to his scientific work until his death.
Ibn al-Haytham is regarded as the "father of modern optics for his influential Book of Optics (written while he was under house arrest), which correctly explained and proved the modern intromission theory of vision. He is also recognized so for his experiments on optics, including experiments on lenses, mirrors, refraction, reflection, and the dispersion of light into its constituent colours. He studied binocular vision and the Moon illusion, described the finite speed of light, and argued that it is made of particles travelling in straight lines. Due to his formulation of a modern quantitative and empirical approach to physics and science, he is considered the pioneer of the modern scientific method and the originator of the experimental nature of physics and science. Author Bradley Steffens describes him as the "first scientist". He is also considered by A. I. Sabra to be the founder of experimental psychology for his approach to visual perception and optical illusions, and a pioneer of the philosophical field of phenomenology or the study of consciousness from a first-person perspective. His Book of Optics has been ranked with Isaac Newton's Philosophiae Naturalis Principia Mathematica as one of the most influential books in the history of physics, for starting a revolution in optics and visual perception.
Ibn al-Haytham's achievements include many advances in physics and mathematics. He gave the first clear description and correct analysis of the camera obscura. He enunciated Fermat's principle of least time and the concept of inertia (Newton's first law of motion), and developed the concept of momentum. He described the attraction between masses and was aware of the magnitude of acceleration due to gravity at-a-distance. He stated that the heavenly bodies were accountable to the laws of physics and also presented a critique and reform of Ptolemaic astronomy. He was the first to state Wilson's theorem in number theory, and he formulated the Lambert quadrilateral and a concept similar to Playfair's axiom now used in non-Euclidean geometry. Moreover, he formulated and solved Alhazen's problem geometrically using early ideas related to calculus and mathematical induction. In his optical research, he laid the foundations for the later development of telescopic astronomy, as well as for the microscope and the use of optical aids in Renaissance art.
One account of his career has him summoned to Egypt by the mercurial Al-Hakim bi-Amr Allah, ruler of the Fatimid Caliphate, to regulate the flooding of the Nile, a task requiring an early attempt at building a dam at the present site of the Aswan Dam. After his field work made him aware of the impracticality of this scheme, and fearing the caliph's anger, he feigned madness. He was kept under house arrest from 1011 until al-Hakim's death in 1021. During this time, he wrote his influential Book of Optics.
Although there are stories that Ibn al-Haytham fled to Syria, ventured into Baghdad later in his life, or was even in Basra when he pretended to be insane, it is certain that he was in Egypt by 1038 at the latest. During his time in Cairo, he became associated with Al-Azhar University, as well the city's "House of Wisdom", known as Dar Al-Hekma (House of Knowledge), which was a library "second in importance" to Baghdad's House of Wisdom. After his house arrest ended, he wrote scores of other treatises on physics, astronomy and mathematics. He later traveled to Islamic Spain. During this period, he had ample time for his scientific pursuits, which included optics, mathematics, physics, medicine, and the development of scientific methods; he left several outstanding books on these subjects.
Richard Powers nominated Ibn al-Haytham's scientific method and scientific skepticism as the most influential idea of the second millennium. Recipient of the Nobel Prize in Physics Abdus Salam considered Ibn-al-Haytham "one of the greatest physicists of all time." George Sarton, the father of the history of science, wrote that "Ibn Haytham's writings reveal his fine development of the experimental faculty" and considered him "not only the greatest Muslim physicist, but by all means the greatest of mediaeval times. Robert S. Elliot considers Ibn al-Haytham to be "one of the ablest students of optics of all times. The author Bradley Steffens considers him to be the "first scientist". The Biographical Dictionary of Scientists wrote that Ibn al-Haytham was "probably the greatest scientist of the Middle Ages" and that "his work remained unsurpassed for nearly 600 years until the time of Johannes Kepler. At a scientific conference in February 2007 as a part of the Hockney-Falco thesis, Charles M. Falco argued that Ibn al-Haytham's work on optics may have influenced the use of optical aids by Renaissance artists. Falco said that his and David Hockney's examples of Renaissance art "demonstrate a continuum in the use of optics by artists from circa 1430, arguably initiated as a result of Ibn al-Haytham's influence, until today.
The Latin translation of his main work, Kitab al-Manazir (Book of Optics), exerted a great influence on Western science: for example, on the work of Roger Bacon, who cites him by name, and on Johannes Kepler. It brought about a great progress in experimental methods. His research in catoptrics (the study of optical systems using mirrors) 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. His work on catoptrics also contains the problem known as "Alhazen's problem".
Meanwhile in the Islamic world, Ibn al-Haytham'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 (d. ca. 1320) in the latter's Kitab Tanqih al-Manazir (The Revision of [Ibn al-Haytham's] Optics). The correct explanations of the rainbow phenomenon given by al-Fārisī and Theodoric of Freiberg in the 14th Century depended on Ibn al-Haytham's Book of Optics. The work of Ibn al-Haytham and al-Fārisī was also further advanced in the Ottoman Empire by polymath Taqi al-Din in his Book of the Light of the Pupil of Vision and the Light of the Truth of the Sights (1574).
He wrote around 200 books, although very few have survived. Even 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.
The Alhazen crater on the Moon was named in his honour, as was the asteroid "59239 Alhazen". Ibn al-Haytham is featured on the obverse of the Iraqi 10,000 dinars banknote issued in 2003, and on 10 dinar notes from 1982. A research facility that UN weapons inspectors suspected of conducting chemical and biological weapons research in Saddam Hussein's Iraq was also named after him.
Ibn al-Haytham's most famous work is his seven volume Arabic treatise on optics, Kitab al-Manazir (Book of Optics), written from 1011 to 1021. It has been ranked alongside Isaac Newton's Philosophiae Naturalis Principia Mathematica as one of the most influential books in physics for introducing an early scientific method, and for initiating a revolution in optics and visual perception.
Optics was translated into Latin by an unknown scholar at the end of the 12th century or the beginning of the 13th century. 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. 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. This work enjoyed a great reputation during the Middle Ages. Works by Ibn al-Haytham on geometric subjects were discovered in the Bibliothèque nationale in Paris in 1834 by E. A. Sedillot. Other manuscripts are preserved in the Bodleian Library at Oxford and in the library of Leiden. Ibn al-Haytham's optical studies were influential in several later developments, including the telescope, which laid the foundations of telescopic astronomy, as well as of the modern camera, the microscope, and the use of optical aids in Renaissance art.
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. Ibn al-Haytham argued that the process of vision occurs neither by rays emitted from the eye, nor through physical forms entering it. He reasoned that a ray could not proceed from the eyes and reach the distant stars the instant after we open our eyes. He also appealed to common observations such as the eye being dazzled or even injured if we look at a very bright light. 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 experimentation. His unification of geometrical optics with philosophical physics forms the basis of modern physical optics.
Ibn al-Haytham proved that rays of light travel in straight lines, and carried out various experiments with lenses, mirrors, refraction, and reflection. 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. He also discovered a result similar to Snell's law of sines, but did not quantify it and derive the law mathematically.
Ibn al-Haytham also gave the first clear description and correct analysis of the camera obscura and pinhole camera. While Aristotle, Theon of Alexandria, Al-Kindi (Alkindus) and Chinese philosopher Mozi had earlier described the effects of a single light passing through a pinhole, none of them suggested that what is being projected onto the screen is an image of everything on the other side of the aperture. Ibn al-Haytham was the first to demonstrate this with his lamp experiment where several different light sources are arranged across a large area. He was thus the first to successfully project an entire image from outdoors onto a screen indoors with the camera obscura.
In addition to physical optics, The Book of Optics also gave rise to the field of "physiological optics". Ibn al-Haytham discussed the topics of medicine, ophthalmology, anatomy and physiology, which included commentaries on Galenic works. He described the process of sight, the structure of the eye, image formation in the eye, and the visual system. He also described what became known as Hering's law of equal innervation, vertical horopters, and binocular disparity, and improved on the theories of binocular vision, motion perception and horopters previously discussed by Aristotle, Euclid and Ptolemy.
His most original anatomical contribution was his description of the functional anatomy of the eye as an optical system, or optical instrument. His experiments with the camera obscura provided sufficient empirical grounds for him to develop his theory of corresponding point projection of light from the surface of an object to form an image on a screen. It was his comparison between the eye and the camera obscura which brought about his synthesis of anatomy and optics, which forms the basis of physiological optics. As he conceptualized the essential principles of pinhole projection from his experiments with the pinhole camera, he considered image inversion to also occur in the eye, and viewed the pupil as being similar to an aperture. Regarding the process of image formation, he incorrectly agreed with Avicenna that the lens was the receptive organ of sight, but correctly hinted at the retina being involved in the process.
An aspect associated with Ibn al-Haytham's optical research is related to systemic and methodological reliance on experimentation (i'tibar) 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) in terms of devising the rudiments of what may be designated as a hypothetico-deductive procedure in scientific research. 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 refraction of light). His legacy was further advanced through the 'reforming' of his Optics by Kamal al-Din al-Farisi (d. ca. 1320) in the latter's Kitab Tanqih al-Manazir (The Revision of [Ibn al-Haytham's] Optics).
The concept of Occam's razor is also present in the Book of Optics. For example, after demonstrating that light is generated by luminous objects and emitted or reflected into the eyes, he states that therefore "the extramission of [visual] rays is superflous and useless.
In philosophy, Ibn al-Haytham is considered a pioneer of phenomenology. He articulated a relationship between the physical and observable world and that of intuition, psychology and mental functions. His theories regarding knowledge and perception, linking the domains of science and religion, led to a philosophy of existence based on the direct observation of reality from the observer's point of view.
In Islamic psychology, Ibn al-Haytham is considered the founder of experimental psychology by A. I. Sabra, for his pioneering work on the psychology of visual perception and optical illusions. In the Book of Optics, 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 came up with a theory to explain the Moon illusion, which played an important role in the scientific tradition of medieval Europe. It was an attempt to the solve the problem of the Moon appearing larger near the horizon than it does while higher up in the sky. Arguing against Ptolemy's refraction theory, he redefined 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. With the Moon however, there are no intervening objects. Therefore, since the size of an object depends on its observed distance, which is in this case inaccurate, the Moon appears larger on the horizon. Through works by Roger Bacon, John Pecham and Witelo based on Ibn al-Haytham's explanation, the Moon illusion gradually came to be accepted as a psychological phenomenon, with Ptolemy's theory being rejected in the 17th century.
Omar Khaleefa has argued that Ibn al-Haytham should also be considered the founder of psychophysics, a subdiscipline and precursor to modern psychology. Although Ibn al-Haytham made many subjective reports regarding vision, there is no evidence that he used quantitative psychophysical techniques and the claim has been rebuffed.
In his treatise, Mizan al-Hikmah (Balance of Wisdom), Ibn al-Haytham discussed the density of the atmosphere and related it to altitude. He also studied atmospheric refraction. He discovered that the twilight only ceases or begins when the Sun is 19° below the horizon and attempted to measure the height of the atmosphere on that basis.
Another treatise, Maqala fi daw al-qamar (On the Light of the Moon), which he wrote some time before his famous Book of Optics, was the first successful attempt at combining mathematical astronomy with physics, and the earliest attempt at applying the experimental method to astronomy and astrophysics. He disproved the universally held opinion that the Moon reflects sunlight like a mirror and correctly concluded that it "emits light from those portions of its surface which the sun's light strikes." To prove that "light is emitted from every point of the Moon's illuminated surface," he built an "ingenious experimental device." According to Matthias Schramm, Ibn al-Haytham had
formulated a clear conception of the relationship between an ideal mathematical model and the complex of observable phenomena; in particular, he 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.
Also in his Treatise on Place, Ibn al-Haytham disagreed with Aristotle's view that nature abhors a void, and he thus used geometry to demonstrate that place (al-makan) is the imagined three-dimensional void between the inner surfaces of a containing body.
Ibn al-Haytham further criticized Ptolemy's model on other empirical, observational and experimental grounds, such as Ptolemy's use of conjectural undemonstrated theories in order to "save appearances" of certain phenomena, which Ibn al-Haytham did not approve of due to his insistence on scientific demonstration. Unlike some later astronomers who criticized the Ptolemaic model on the grounds of being incompatible with Aristotelian natural philosophy, Ibn al-Haytham was mainly concerned with empirical observation and the internal contradictions in Ptolemy's works.
In his Aporias against Ptolemy, Ibn al-Haytham commented on the difficulty of attaining scientific knowledge:
He held that the criticism of existing theories—which dominated this book—holds a special place in the growth of scientific knowledge:
While he attempted to discover the physical reality behind Ptolemy's mathematical model, he developed the concept of a single orb (falak) for each component of Ptolemy's planetary motions. This work 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.
His reformed empirical model was the first to reject the equant and eccentrics, separate natural philosophy from astronomy, free celestial kinematics from cosmology, and reduce physical entities to geometric entities. The model also propounded the Earth's rotation about its axis, and the centres of motion were geometric points without any physical significance, like Johannes Kepler's model centuries later.
In the text, Ibn al-Haytham also describes an early version of Occam's razor, 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 the Earth.
Ibn al-Haytham also wrote a treatise entitled On the Milky Way, in which he solved problems regarding the Milky Way galaxy and parallax. In antiquity, Aristotle believed the Milky Way to be caused by "the ignition of the fiery exhalation of some stars which were large, numerous and close together" and that the "ignition takes place in the upper part of the atmosphere, in the region of the world which is continuous with the heavenly motions. Ibn al-Haytham refuted this and "determined that because the Milky Way had no parallax, it was very remote from the earth and did not belong to the atmosphere. He wrote that if the Milky Way was located around the Earth's atmosphere, "one must find a difference in position relative to the fixed stars." He described two methods to determine the Milky Way's parallax: "either when one observes the Milky Way on two different occasions from the same spot of the earth; or when one looks at it simultaneously from two distant places from the surface of the earth." He made the first attempt at observing and measuring the Milky Way's parallax, and determined that since the Milky Way had no parallax, then it does not belong to the atmosphere.
In 1858, Muhammad Wali ibn Muhammad Ja'far, in his Shigarf-nama, claimed that Ibn al-Haytham wrote a treatise Maratib al-sama in which he conceived of a planetary model similar to the Tychonic system where the planets orbit the Sun which in turn orbits the Earth. However, the "verification of this claim seems to be impossible," since the treatise is not listed among the known bibliography of Ibn al-Haytham.
Ibn al-Haytham made the first attempt at proving the Euclidean parallel postulate, the fifth postulate in Euclid's Elements, using a proof by contradiction, where he introduced the concept of motion and transformation into geometry. He formulated the Lambert quadrilateral, which Boris Abramovich Rozenfeld names the "Ibn al-Haytham–Lambert quadrilateral", and his attempted proof also shows similarities to Playfair's axiom. His theorems on quadrilaterals, including the Lambert quadrilateral, were the first theorems on elliptical geometry and hyperbolic geometry. These theorems, along with his alternative postulates, such as Playfair's axiom, can be seen as marking the beginning of non-Euclidean geometry. His work had a considerable influence on its development among the later Persian geometers Omar Khayyám and Nasīr al-Dīn al-Tūsī, and the European geometers Witelo, Gersonides, Alfonso, John Wallis, Giovanni Girolamo Saccheri and Christopher Clavius.
In elementary geometry, Ibn al-Haytham attempted to solve the problem of squaring the circle using the area of lunes (crescent shapes), but later gave up on the impossible task. Ibn al-Haytham also tackled other problems in elementary (Euclidean) and advanced (Apollonian and Archimedean) geometry, some of which he was the first to solve.
Ibn al-Haytham solved problems involving congruences using what is now called Wilson's theorem. 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 Chinese remainder theorem.
Ibn al-Haytham also discussed space perception and its epistemological implications in his Book of Optics. His experimental proof of the intromission model of vision led to changes in the way the visual perception of space was understood, contrary to the previous emission theory of vision supported by Euclid and Ptolemy. In "tying the visual perception of space to prior bodily experience, Alhacen 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.
Ibn al-Haytham 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 Salah prayers are directed towards, mathematically.
Ibn al-Haytham attributed his experimental scientific method and scientific skepticism to his Islamic faith. The Islamic holy book the Qur'an, for example, placed a strong emphasis on empiricism. He also believed that human beings are inherently flawed and that only God is perfect. He reasoned that to discover the truth about nature, it is necessary to eliminate human opinion and error, and allow the universe to speak for itself. He wrote in his Doubts Concerning Ptolemy:
In The Winding Motion, Ibn al-Haytham further wrote that faith (or taqlid "imitation") should only apply to prophets of Islam and not to any other authorities, in the following comparison between the Islamic prophetic tradition and the demonstrative sciences:
Ibn al-Haytham described his search for truth and knowledge as a way of leading him closer to God:
According to medieval biographers, Ibn al-Haytham 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.