• Scientist and Polymath Abu Ali al-Hasan ibn al-Hasan ibn al-Haytham (Alhazen), 965
• Philosopher and Theologian Albertus Magnus, 1193

Born circa 965, in Basra, present day Iraq, he lived mainly in Cairo, Egypt, dying there at age 74. Over - confident about practical application of his mathematical knowledge, he assumed that he could regulate the floods 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 impossibility 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.

Alhazen was born in Basra, in the Iraq province of the Buyid Empire. Many historians have different opinions about his ethnicity whether he was Arab or Persian. He probably died in Cairo, Egypt. During the Islamic Golden Age, Basra was a "key beginning of learning", and he was educated there and in Baghdad, the capital of the Abbasid Caliphate, and the focus of the "high point of Islamic civilization". During his time in Buyid Iran, he worked as a civil servant and read many theological and scientific books.

One account of his career has him called to Egypt by 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. 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 the modern experimental scientific method.

Some biographers have claimed that Alhazen fled to Syria, ventured into Baghdad later in his life, or was in Basra when he pretended to be insane. In any case, he was in Egypt by 1038. During his time in Cairo, he became associated with Al-Azhar University, as well the city's "House of Wisdom", known as Dar al-`Ilm (House of Knowledge), which was a library "first in importance" to Baghdad's House of Wisdom.

Among his students were Sorkhab (Sohrab), a Persian student who was one of the greatest people of Iran's Semnan and was his student for over 3 years, and Abu al-Wafa Mubashir ibn Fatek, an Egyptian scientist who learned mathematics from Alhazen.

Alhazen made significant improvements in optics, physical science, and the scientific method. Alhazen's work on optics is credited with contributing a new emphasis on experiment. His influence on physical sciences 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.

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. His research in catoptrics (the study of optical systems using mirrors) centered 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, 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 (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 Alhazen's Book of Optics. The work of Alhazen 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 as many as 200 books, although only 55 have survived, and many of those have not yet been translated from Arabic. 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 crater Alhazen on the Moon is named in his honor, 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".

Alhazen (by the name 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.

Alhazen's most famous work is his seven volume Arabic treatise on optics, Kitab al-Manazir (Book of Optics), written from 1011 to 1021.

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 Alhazen 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.

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. Alhazen 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.

Alhazen 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 proposed a causal model for the refraction of light that could have been extended to yield a result similar to Snell's law of sines, however Alhazen did not develop his model sufficiently to attain that result.

Alhazen 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. Alhazen 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". Alhazen 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.

Neuroscientist Rosanna Gorini notes that "according to the majority of the historians al-Haytham was the pioneer of the modern scientific method." From this point of view, Alhazen developed rigorous experimental methods of controlled scientific testing to verify theoretical hypotheses and substantiate inductive conjectures. Other historians of science place his experiments in the tradition of Ptolemy and see in such interpretations a "tendency to 'modernize' Alhazen ... [which] serves to wrench him slightly out of proper historical focus."

An aspect associated with Alhazen'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 color, 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 superfluous and useless."

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 cue ball at a given point must be aimed in order to carom off the edge of the table 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 the earliest formula for the sum of fourth powers; by using an early proof by mathematical induction, he developed a method that can be readily generalized to find the formula for the sum of any integral powers. He applied his result of sums on integral powers to find the volume of a paraboloid through integration. He was thus able to find the integrals for polynomials up to the fourth degree. Alhazen eventually solved the problem using conic sections and a geometric proof, though many after him attempted to find an algebraic solution to the problem, which was finally found in 1997 by the Oxford mathematician Peter M. Neumann. Recently, Mitsubishi Electric Research Labs (MERL) researchers Amit Agrawal, Yuichi Taguchi and Srikumar Ramalingam solved the extension of Alhazen's problem to general rotationally symmetric quadric mirrors including hyperbolic, parabolic and elliptical mirrors. They showed that the mirror reflection point can be computed by solving an eighth degree equation in the most general case. If the camera (eye) is placed on the axis of the mirror, the degree of the equation reduces to six. Alhazen's problem can also be extended to multiple refractions from a spherical ball. Given a light source and a spherical ball of certain refractive index, the closest point on the spherical ball where the light is refracted to the eye of the observer can be obtained by solving a tenth degree equation.

The Book of Optics describes several early experimental observations that Alhazen made in mechanics and how he used his results to explain certain optical phenomena using mechanical analogies. He conducted experiments with projectiles, and concluded that "it was only the impact of perpendicular projectiles on surfaces which was forceful enough to enable them to penetrate whereas the oblique ones were deflected. 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 would break the slate and pass through, whereas an oblique one with equal force and from an equal distance would not." This result explained how intense direct light hurts the eye: "Applying mechanical analogies to the effect of light rays on the eye, 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 there could only be one such ray from each point on the surface of the object which could penetrate the eye."

Chapters 15 – 16 of the Book of Optics covered astronomy. Alhazen was the first to discover that the celestial spheres do not consist of solid matter. He also discovered that the heavens are less dense than the air. These views were later repeated by Witelo and had a significant influence on the Copernican and Tychonic systems of astronomy.

Sudanese psychologist Omar Khaleefa has argued that Alhazen should be considered to be the "founder of experimental psychology", for his pioneering work on the psychology of visual perception and optical illusions. In the Book of Optics, Alhazen 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. Khaleefa has also argued that Alhazen should also be considered the "founder of psychophysics", a subdiscipline 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, a debate that is still unresolved. 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 BC). 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.

Some have suggested that Alhazen's views on pain and sensation may have been influenced by Buddhist philosophy. He writes that every sensation is a form of 'suffering' and that what people call pain is only an exaggerated perception; that there is no qualitative difference but only a quantitative difference between pain and ordinary sensation.

Besides the Book of Optics, Alhazen wrote several other treatises on optics. 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 luminance and its radiant dispersion through various transparent and translucent media. He also carried out further examinations into anatomy of the eye and illusions in visual perception. He built the first camera obscura and pinhole camera, and investigated the meteorology of the rainbow and the density of the atmosphere. Various celestial phenomena (including the eclipse, twilight and moonlight) were also examined by him. He also made investigations into refraction, catoptrics, dioptrics, spherical mirrors, and magnifying lenses.

In his treatise, Mizan al-Hikmah (Balance of Wisdom), Alhazen 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.

In astrophysics and the celestial mechanics field of physics, Alhazen, in his Epitome of Astronomy, discovered that the heavenly bodies "were accountable to the laws of physics". Alhazen's Mizan al-Hikmah (Balance of Wisdom) covered statics, astrophysics and celestial mechanics. He discussed the theory of attraction between masses, and it seems that he was also aware of the magnitude of acceleration due to gravity at a distance. His Maqala fi'l-qarastun is a treatise on centers of gravity. Little is known about the work, except for what is known through the later works of al-Khazini in the 12th century. In this treatise, Alhazen formulated the theory that the heaviness of bodies varies with their distance from the center of the Earth.

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, Alhazen 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.

In the dynamics and kinematics fields of mechanics, Alhazen's Risala fi’l-makan (Treatise on Place) discussed theories on the motion of a body. He maintained that a body moves perpetually unless an external force stops it or changes its direction of motion. Alhazen's concept of inertia was not verified by experimentation, however. Galileo Galilei repeated Alhazen's principle, centuries later, but introduced the concept of frictional force and provided experimental results.

In his Treatise on Place, Alhazen 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.

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 many of Ptolemy's works, including the Almagest, 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 equant, 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:

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... [F]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.

Alhazen 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 Alhazen 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, Alhazen was mainly concerned with empirical observation and the internal contradictions in Ptolemy's works.

In his Aporias against Ptolemy, Alhazen commented on the difficulty of attaining scientific knowledge:

Truth is sought for itself [but] the truths, [he warns] are immersed in uncertainties [and the scientific authorities (such as Ptolemy, whom he greatly respected) are] 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:

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.

In his On the Configuration of the World, despite his criticisms directed towards Ptolemy, Alhazen continued to accept the physical reality of the geocentric model of the universe, presenting a detailed description of the physical structure of the celestial spheres in his On the Configuration of the World:

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

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.

Alhazen's The Model of the Motions of Each of the Seven Planets, written in 1038, was a 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, Alhazen described the first non - Ptolemaic model in The Model of the Motions. His reform was not concerned with cosmology, as he developed a systematic study of celestial kinematics that was completely geometric. This in turn led to innovative developments in infinitesimal geometry.

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 centers of motion were geometric points without any physical significance, like Johannes Kepler's model centuries later.

In the text, Alhazen 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.

Alhazen distinguished astrology from astronomy, and he refuted the study of astrology, due to the methods used by astrologers being conjectural rather than empirical, and also due to the views of astrologers conflicting with that of orthodox Islam.

Alhazen 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." Alhazen 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 Alhazen 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 Alhazen.

In mathematics, Alhazen built on the mathematical works of Euclid and Thabit ibn Qurra. He systematized conic sections and number theory, carried out some early work on analytic geometry, and worked on "the beginnings of the link between algebra and geometry." This in turn had an influence on the development of René Descartes's geometric analysis and Isaac Newton's calculus.

In geometry, Alhazen developed analytical geometry and established a link between algebra and geometry. He discovered a formula for adding the first 100 natural numbers, using a geometric proof to prove the formula.

Alhazen 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, 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. He also tackled other problems in elementary (Euclidean) and advanced (Apollonian and Archimedean) geometry, some of which he was the first to solve.

His contributions to number theory includes his work on perfect numbers. In his Analysis and Synthesis, Alhazen was the first to realize that every even perfect number is of the form 2ⁿ⁻¹(2ⁿ − 1) where 2ⁿ − 1 is prime, but he was not able to prove this result successfully (Euler later proved it in the 18th century).

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.

In psychology and musicology, Alhazen's Treatise on the Influence of Melodies on the Souls of Animals was the earliest treatise dealing with the effects of music on animals. In the treatise, he demonstrates how a camel's pace could be hastened or retarded with the use of music, and shows other examples of how music can affect animal behavior and animal psychology, experimenting with horses, birds and reptiles. Through to the 19th century, a majority of scholars in the Western world continued to believe that music was a distinctly human phenomenon, but experiments since then have vindicated Alhazen's view that music does indeed have an effect on animals.

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.

According to Al-Khazini, Alhazen also wrote a treatise providing a description on the construction of a water clock.

In early Islamic philosophy, Alhazen's Risala fi’l-makan (Treatise on Place) presents a critique of Aristotle's concept of place (topos). Aristotle's Physics 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. Alhazen 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 space, foreshadowing René Descartes's concept of place in the Extensio in the 17th century. Following on from his Treatise on Place, Alhazen's Qawl fi al-Makan (Discourse on Place) was a treatise which presents geometric demonstrations for his geometrization of place, in opposition to Aristotle's philosophical concept of place, which Alhazen rejected on mathematical grounds. 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. 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."

Alhazen was a devout Muslim, though it is uncertain which branch of Islam he followed. He may have been either a follower of the orthodox Ash'ari school of Sunni Islamic theology according to Ziauddin Sardar and Lawrence Bettany (and opposed to the views of the Mu'tazili school), a follower of the Mu'tazili school of Islamic theology according to Peter Edward Hodgson, or a follower of Shia Islam possibly according to A. I. Sabra.

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 Salah prayers are directed towards, mathematically.

He wrote in his 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...

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.

In The Winding Motion, Alhazen further wrote:

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.

Alhazen described his theology:

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.

Alhazen was a pioneer in many areas of science, making significant contributions in varying disciplines. His optical writings influenced many Western intellectuals such as Roger Bacon, John Pecham, Witelo, Johannes Kepler. His pioneering work on number theory, analytic geometry and the link between algebra and geometry, also had an influence on René Descartes's geometric analysis and Isaac Newton's calculus.

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.

Albertus was born sometime between 1193 and 1206 to the Count of Bollstädt in Lauingen in Bavaria. Contemporaries such as Roger Bacon applied the term "Magnus" to Albertus during his own lifetime, referring to his immense reputation as a scholar and philosopher.

Albertus was educated principally at Padua, where he received instruction in Aristotle's writings. A late account by Rudolph de Novamagia refers to Albertus' encounter with the Blessed Virgin Mary, who convinced him to enter Holy Orders. In 1223 (or 1221) he became a member of the Dominican Order, against the wishes of his family, and studied theology at Bologna and elsewhere. Selected to fill the position of lecturer at Cologne, Germany, where the Dominicans had a house, he taught for several years there, at Regensburg, Freiburg, Strasbourg and Hildesheim. In 1245 he went to Paris, received his doctorate and taught for some time as a master of theology with great success. During this time Thomas Aquinas began to study under Albertus.

Albertus was the first to comment on virtually all of the writings of Aristotle, thus making them accessible to wider academic debate. The study of Aristotle brought him to study and comment on the teachings of Muslim academics, notably Avicenna and Averroes, and this would bring him in the heart of academic debate. He was ahead of his time in his attitude towards science. Two aspects of this attitude deserve to be mentioned: 1) he did not only study science from books, as other academics did in his day, but actually observed and experimented with nature (the rumors starting by those who did not understand this are probably at the source of Albert's supposed connections with alchemy and witchcraft), 2) he took from Aristotle the view that scientific method had to be appropriate to the objects of the scientific discipline at hand (in discussions with Roger Bacon, who, like many 20th century academics, thought that all science should be based on mathematics).

In 1254 Albertus was made provincial of the Dominican Order, and fulfilled the arduous duties of the office with great care and efficiency. During his tenure he publicly defended the Dominicans against attacks by the secular and regular faculty of the University of Paris, commented on St John, and answered what he perceived as errors of the Arabian philosopher Averroes.

In 1260 Pope Alexander IV made him Bishop of Regensburg, an office from which he resigned after three years. During the exercise of his duties he enhanced his reputation for humility by refusing to ride a horse — in accord with the dictates of the Dominican order — instead walking back and forth across his huge diocese. This earned him the affectionate sobriquet, "boots the bishop," from his parishioners. After his stint as bishop, he spent the remainder of his life partly in retirement in the various houses of his order, yet often preaching throughout southern Germany. In 1270 he preached the eighth Crusade in Austria. After this, he was especially known for acting as a mediator between conflicting parties (In Cologne he is not only known for being the founder of Germany's oldest university there, but also for "the big verdict" (der Grose Schied) of 1258, which brought an end to the conflict between the citizens of Cologne and the archbishop. Among the last of his labors was the defense of the orthodoxy of his former pupil, Thomas Aquinas, whose death in 1274 grieved Albertus (the story that he traveled to Paris in person to defend the teachings of Aquinas can not be confirmed).

After suffering a collapse of health in 1278, he died on November 15, 1280, in Cologne, Germany. Since November 15, 1954, his relics are in a Roman sarcophagus in the crypt of the Dominican St. Andreas church in Cologne.

Albertus is frequently mentioned by Dante, who made his doctrine of free will the basis of his ethical system. In his Divine Comedy, Dante places Albertus with his pupil Thomas Aquinas among the great lovers of wisdom (Spiriti Sapienti) in the Heaven of the Sun. Albertus is also mentioned, along with Agrippa and Paracelsus, in Mary Shelley's Frankenstein, in which his writings influence a young Victor Frankenstein.

Albertus was beatified in 1622. He was canonized and proclaimed a Doctor of the Church in 1931 by Pope Pius XI and patron saint of the sciences. St Albert's feast day is celebrated on November 15. According to Joan Carroll Cruz, his body is incorrupt.

Albertus' writings collected in 1899 went to thirty - eight volumes. These displayed his prolific habits and literally encyclopedic knowledge of topics such as logic, theology, botany, geography, astronomy, astrology, mineralogy, chemistry, zoology, physiology, phrenology and others; all of which were the result of logic and observation. He was perhaps the most well read author of his time. He digested, interpreted and systematized the whole of Aristotle's works, gleaned from the Latin translations and notes of the Arabian commentators, in accordance with Church doctrine. Most modern knowledge of Aristotle was preserved and presented by Albertus.

Albertus' activity, however, was more philosophical than theological (Scholasticism). The philosophical works, occupying the first six and the last of the twenty - one volumes, are generally divided according to the Aristotelian scheme of the sciences, and consist of interpretations and condensations of Aristotle's relative works, with supplementary discussions upon contemporary topics, and occasional divergences from the opinions of the master.

His principal theological works are a commentary in three volumes on the Books of the Sentences of Peter Lombard (Magister Sententiarum), and the Summa Theologiae in two volumes. The latter is in substance a more didactic repetition of the former.

Albertus's knowledge of physical science was considerable and for the age remarkably accurate. His industry in every department was great, and though we find in his system many gaps which are characteristic of scholastic philosophy, his protracted study of Aristotle gave him a great power of systematic thought and exposition. An exception to this general tendency is his Latin treatise "De falconibus" (later inserted in the larger work, De Animalibus, as book 23, chapter 40), in which he displays impressive actual knowledge of a) the differences between the birds of prey and the other kinds of birds; b) the different kinds of falcons; c) the way of preparing them for the hunt; and d) the cures for sick and wounded falcons. His scholarly legacy justifies his contemporaries' bestowing upon him the honorable surname Doctor Universalis.

In the centuries since his death, many stories arose about Albertus as an alchemist and magician. On the subject of alchemy and chemistry, many treatises relating to Alchemy have been attributed to him, though in his authentic writings he had little to say on the subject, and then mostly through commentary on Aristotle. For example, in his commentary, De mineralibus, he refers to the power of stones, but does not elaborate on what these powers might be. A wide range of Pseudo - Albertine works dealing with alchemy exist, though, showing the belief developed in the generations following Albert's death that he had mastered alchemy, one of the fundamental sciences of the Middle Ages. These include Metals and Materials; the Secrets of Chemistry; the Origin of Metals; the Origins of Compounds, and a Concordance which is a collection of Observations on the philosopher's stone; and other alchemy - chemistry topics, collected under the name of Theatrum Chemicum. He is credited with the discovery of the element arsenic and experimented with photosensitive chemicals, including silver nitrate. He did believe that stones had occult properties, as he related in his work De mineralibus. However, there is scant evidence that he personally performed alchemical experiments. Much of the modern confusion results from the fact that later works, particularly the alchemical work known as the Secreta Alberti or the Experimenta Alberti, were falsely attributed to Albertus by their authors to increase the prestige of the text through association.

According to legend, Albertus Magnus is said to have discovered the philosopher's stone and passed it to his pupil Thomas Aquinas, shortly before his death. Magnus does not confirm he discovered the stone in his writings, but he did record that he witnessed the creation of gold by "transmutation." Given that Thomas Aquinas died six years before Albertus Magnus' death, this legend as stated is unlikely.

However, it is true that Albertus was deeply interested in astrology, as has been articulated by scholars such as Paola Zambelli. While today we would view this as evidence of superstition, in the high Middle Ages — and well into the early modern period — few intellectuals, if any, questioned the basic assumptions of astrology: humans live within a web of celestial influences that affect our bodies, and thereby motivate us to behave in certain ways. Within this worldview, it was logical to believe that astrology could be used to predict the probable future of a human being. Albertus made this a central component of his philosophical system, arguing that an understanding of the celestial influences affecting us could help us to live our lives more in accord with Christian precepts. The most comprehensive statement of his astrological beliefs is to be found in a work he authored around 1260, now known as the Speculum astronomiae. However, details of these beliefs can be found in almost everything he wrote, from his early Summa de bono to his last work, the Summa theologiae.

Albertus is known for his enlightening commentary on the musical practice of his times. Most of his written musical observations are found in his commentary on Aristotle's Poetics. He rejected the idea of "music of the spheres" as ridiculous: movement of astronomical bodies, he supposed, is incapable of generating sound. He wrote extensively on proportions in music, and on the three different subjective levels on which plainchant could work on the human soul: purging of the impure; illumination leading to contemplation; and nourishing perfection through contemplation. Of particular interest to 20th century music theorists is the attention he paid to silence as an integral part of music.

The iconography of the tympanum and archivolts of the late 13th century portal of Strasbourg Cathedral was inspired by the writings of Albertus Magnus. Albertus is recorded as having made a mechanical automaton in the form of a brass head that would answer questions put to it. Such a feat was also attributed to Roger Bacon.

In The Concept of Anxiety Søren Kierkegaard wrote that Albert Magnus, "arrogantly boasted of his speculation before the deity and suddenly became stupid." Kierkegaard cites G. O. Marbach who he quotes as saying "Albertus repente ex asino factus philosophus et ex philosopho asinus" [Albert was suddenly transformed from an ass into a philosopher and from a philosopher into an ass].

In 1968, he was cited by William F. Buckley as one of several historical figures whose best qualities would be emulated by the ideal President.

The typeface Albertus is named in his memory.

In Mary Shelley's Frankenstein, Albertus Magnus is referred to as one of Victor Frankenstein's chosen readings. He is also referred to in Nathaniel Hawthorne's The Birth - mark and Herman Melville's The Bell Tower. In Terry Pratchett's Discworld novels, the character of Alberto Mallich (founder of the Unseen University and later Death's manservant Albert) is a sly nod to Albertus Magnus in his more legendary and esoteric guise. Walter M. Miller, Jr.'s novel A Canticle for Leibowitz centers on a monastic order called the Albertian Order of Leibowitz, named by its founder after Albertus Magnus and dedicated to preserving scientific knowledge lost after a nuclear war.

A number of schools are named after Albert, including Albertus Magnus High School, in Bardonia, New York, and Albertus Magnus College in New Haven, Connecticut. The main science building at Providence College is named in honor of Albertus Magnus.

The Academy for Science and Design in New Hampshire honored Albertus by naming one of its four houses Magnus House.

As a tribute to the scholar's contributions to the law, the University of Houston Law Center displays a statue of Albertus Magnus. It is located on the campus of the University of Houston.

The Albertus - Magnus - Gymnasium is found in Regensburg, Germany.

In Managua, Nicaragua, the Albertus Magnus International Institute, a business and economic development research center, was founded in 2004.

In the Philippines, the Albertus Magnus Building at the University of Santo Tomas that houses the Conservatory of Music, College of Tourism and Hospitality Management, College of Education, and UST Education High School is named in his honor. The Saint Albert the Great Science Academy in San Carlos City, Pangasinan, which offers preschool, elementary and high school education, takes pride in having St. Albert as their patron saint. Its main building was named Albertus Magnus Hall in 2008.

Due to his contributions to natural philosophy, the plant species Alberta magna and the asteroid 20006 Albertus Magnus were named after him.