Ibn al-Haytham, known in Latin as Alhazen (about 965–1040), was a mathematician, astronomer, and physicist from present-day Iraq during the Islamic Golden Age. He is called "the father of modern optics" because of his important work on how light and vision work. His most famous book, Kitāb al-Manāẓir (Book of Optics), was written between 1011 and 1021. A Latin version of this book survived and was used by many scientists during the Scientific Revolution, including Galileo Galilei, René Descartes, Johannes Kepler, and Christiaan Huygens.

Ibn al-Haytham was the first to correctly explain that vision happens when light enters the eye, not when the eye sends out rays. He also showed that vision is processed in the brain and is influenced by personal experiences. He discovered a rule about how light bends, which later became known as Fermat's principle. He studied how light reflects and bends, which helped advance the fields of catoptrics (study of reflection) and dioptrics (study of refraction). He believed that scientific ideas must be tested through experiments or math, a practice that became central to the scientific method. Because of this, he is sometimes called the "first true scientist." He also wrote about philosophy, theology, and medicine.

Ibn al-Haytham was born in Basra and lived most of his working life in Cairo, the capital of the Fatimid Empire. He earned a living by writing books and teaching noble families. He is sometimes called al-Baṣrī (from Basra) or al-Miṣrī (the Egyptian). He was called "the Second Ptolemy" by Abu'l-Hasan Bayhaqi and "The Physicist" by John Peckham. His work laid the foundation for modern physical optics.

Biography

Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham (Alhazen) was born around 965 to a family of Arab or Persian background in Basra, Iraq, which was then part of the Buyid emirate. He first studied religion and worked in his community. At that time, society had many different ideas about religion, and he chose to focus more on mathematics and science instead. He held a high position as a vizier in Basra and became well-known for his skills in applied mathematics, including his work to control the flooding of the Nile.

After returning to Cairo, he was given a job in administration. However, he struggled with this role and angered the caliph, Al-Hakim. It is said that Alhazen had to hide until the caliph died in 1021. After that, his belongings were returned to him. Some stories say he pretended to be mad and was kept under house arrest during this time. During this period, he wrote his important work, the Book of Optics. He later lived in Cairo near the famous University of al-Azhar and earned money from his writing until his death around 1040.

A copy of Apollonius’ Conics, written in Alhazen’s own handwriting, is preserved in Aya Sofya (MS Aya Sofya 2762, 307 fob., dated Safar 415 A.H. [1024]). Among his students were Sorkhab (Sohrab), a Persian from Semnan, and Abu al-Wafa Mubashir ibn Fatek, an Egyptian prince.

Book of Optics

Alhazen's most famous work is a seven-volume book called Kitab al-Manazir (Book of Optics), written between 1011 and 1021. In it, Ibn al-Haytham explained that vision happens when light reflects off an object and enters the eyes. He also argued that vision is processed in the brain, not the eyes, and noted that personal experiences influence how people see things.

The book was translated into Latin by an unknown scholar at the end of the 12th century or the beginning of the 13th century. It became widely respected during the Middle Ages. A Latin version of the work, called De aspectibus, was translated into Italian in the late 14th century under the title De li aspecti.

In 1572, Friedrich Risner printed the book in Latin with the title Opticae thesaurus: Alhazeni Arabis libri septem. Risner also introduced the name "Alhazen," though he was previously known in the West as "Alhacen." In 1834, E. A. Sedillot discovered Alhazen’s writings on geometry in the Bibliothèque nationale in Paris. Today, 18 full or nearly complete manuscripts and five fragments of his work are preserved in 14 locations, including the Bodleian Library at Oxford and the library of Bruges.

Two main theories about vision existed in ancient times. The first, called the emission theory, was supported by thinkers like Euclid and Ptolemy, who believed the eyes sent out light rays to see objects. The second, the intromission theory, was supported by Aristotle and others, who thought light and images from objects entered the eyes. Earlier Islamic writers, such as al-Kindi, followed ideas from Euclid, Galen, or Aristotle. The Book of Optics was strongly influenced by Ptolemy’s Optics, and its description of the eye’s structure was based on Galen’s work. Alhazen combined ideas from Euclid’s mathematical theories, Galen’s medical knowledge, and Aristotle’s intromission theory to create a new explanation for vision.

Alhazen argued that light and color from every point of a colored object travel in straight lines. This created a problem: how could the eye form a clear image if every point of an object sent light to every part of the eye? To solve this, he suggested that the eye only perceived light rays that hit it directly, not those that were bent by other parts of the eye. He compared this to a ball hitting a board straight on, which breaks it, while a ball hitting it at an angle bounces off. He believed only these direct rays were strong enough to be seen. Later, he claimed that other rays were bent inside the eye and appeared as if they were direct. However, his reasoning did not fully explain why only direct rays were perceived. Despite these issues, his work was highly influential in Western Europe and inspired many later studies in optics, including Kepler’s theory of how images form on the retina.

Alhazen proved through experiments that light travels in straight lines. He studied how light behaves with lenses, mirrors, refraction, and reflection. He analyzed light rays by considering their vertical and horizontal movements separately.

Alhazen studied how the eye works, how images form inside it, and how the visual system functions. Ian P. Howard wrote in 1996 that many discoveries and theories later credited to Western Europeans were actually first described by Alhazen. For example, he explained a principle later called Hering’s law of equal innervation. He also described vertical horopters 600 years before Aguilonius, with a definition closer to modern science. His work on binocular vision was repeated by Panum in 1858. Craig Aaen-Stockdale noted that while Alhazen made many advances, some of his ideas were similar to those of Ptolemy, with whom he was familiar. Alhazen corrected one of Ptolemy’s errors about binocular vision but otherwise followed similar ideas.

Raynaud’s research showed that Alhazen’s work included early concepts like correspondence, homonymous and crossed diplopia. However, he did not describe the circular shape of the horopter and was closer to explaining Panum’s fusional area than the Vieth-Müller circle. His theory had two main limitations: it did not recognize the role of the retina, and it lacked experiments on the eye’s nerves.

Alhazen’s most original idea was to explain how the eye’s structure functions as an optical system. His experiments with pinhole projection influenced his understanding of how images are formed in the eye. He believed that light entering the eye perpendicularly was bent outward by the lens and passed upright to the optic nerve. He followed Galen’s belief that the lens was the main part of the eye responsible for vision, though some of his work hinted at the retina’s role.

Alhazen’s work on light and vision followed the Aristotelian method, describing the process of seeing in a logical and complete way.

His research on catoptrics (the study of mirrors) focused on spherical and parabolic mirrors and a problem called spherical aberration. He observed that the ratio of the angle of incidence to the angle of refraction is not constant.

Scientific method

Alhazen's work in optics focused on using experiments and controlled testing to study light and vision. He combined knowledge from classical physics and mathematics, especially geometry, to support his scientific ideas. These methods helped shape his theories about light, color, and how vision works, as well as his research on how light reflects and bends.

Matthias Schramm said Alhazen was the first to use a planned method to change conditions in an experiment. He showed that when light from the moon passes through two small holes and hits a screen, the brightness of the light spot decreases as one hole is covered. However, G. J. Toomer questioned this view because, in 1964, the full translation of Alhazen's Book of Optics was not yet available. Toomer believed that without more context, parts of Alhazen's work might be misunderstood. He also noted that Alhazen's contributions should be seen alongside the ideas of other scientists from Islamic and ancient traditions. Toomer concluded that more of Alhazen's writings need to be translated and studied to fully understand his influence on later scientific thinkers.

Other works on physics

Alhazen wrote many books about light and vision, including his Treatise on Light. He studied the brightness of light, rainbows, eclipses, twilight, and moonlight. He performed experiments with mirrors and how light bends when moving between air, water, and glass shapes like cubes and spheres. These experiments helped him develop ideas about how light reflects, known as catoptrics.

In his Epitome of Astronomy, Alhazen explained that models of the universe, like those created by Ptolemy, should be based on real objects instead of imaginary ideas. He believed that physical models could show how celestial bodies move without colliding. This idea helped the Ptolemaic system become more accepted among Christians in the West. Alhazen’s focus on using physical objects in astronomy made sure that ideas about the stars and planets could be tested and improved using physics rules.

He also wrote a book called On the Light of the Moon. In his work, Alhazen explored how objects move.

Astronomical works

In his book On the Configuration of the World, Alhazen provided a detailed explanation of Earth’s physical structure.

The book offered a simple explanation of Ptolemy’s Almagest, which was later translated into Hebrew and Latin during the 13th and 14th centuries. These translations influenced astronomers like Georg von Peuerbach during the European Middle Ages and Renaissance.

In his work Al-Shukūk ‛alā Batlamyūs (also known as Doubts Concerning Ptolemy or Aporias against Ptolemy), published between 1025 and 1028, Alhazen criticized Ptolemy’s Almagest, Planetary Hypotheses, and Optics. He pointed out contradictions in these works, especially in astronomy. Ptolemy’s Almagest explained mathematical theories about planetary motion, while the Hypotheses described what Ptolemy believed was the actual arrangement of planets. Ptolemy admitted his theories and models sometimes disagreed, but he argued this was not a problem as long as it did not cause noticeable errors. Alhazen, however, strongly criticized these contradictions. He argued that Ptolemy’s use of mathematical tools, such as the equant, did not meet the requirement for uniform circular motion. He also noted the problem of using imaginary mathematical points, lines, and circles to explain real physical movements.

Alhazen intended to address the contradictions he found in Ptolemy’s work in a later book. He believed there was a “true configuration” of the planets that Ptolemy had not fully understood. His goal was to improve Ptolemy’s system, not replace it entirely. In Doubts Concerning Ptolemy, he discussed the challenges of gaining scientific knowledge and the importance of questioning established theories. He believed that criticizing existing ideas was essential for scientific progress.

Alhazen’s The Model of the Motions of Each of the Seven Planets was written around 1038. Only one damaged manuscript of this work remains, with only the introduction and the first section on planetary motion surviving. The manuscript originally included a second section on astronomical calculations and a third on astronomical instruments. Building on his earlier work, Alhazen proposed a new planetary model based on geometry. He described planetary motion using spherical geometry, infinitesimal geometry, and trigonometry. He kept the idea of a geocentric universe and assumed celestial motions were uniformly circular, requiring the use of epicycles to explain observed movements. Unlike Ptolemy, he avoided using the equant. His model focused on explaining observed motions geometrically, without attempting to explain their causes.

Alhazen wrote 25 astronomical works. Some addressed technical issues, such as Exact Determination of the Meridian. Others focused on precise astronomical observations, while others explored questions like the location of the Milky Way. Alhazen conducted the first systematic study of the Milky Way’s parallax, combining Ptolemy’s data with his own observations. He concluded that the Milky Way’s parallax was much smaller than the Moon’s and that the Milky Way was a celestial object. Though others had suggested the Milky Way was not part of Earth’s atmosphere, Alhazen was the first to provide a quantitative analysis supporting this idea. His fourth group of works included ten books on astronomical theory, such as Doubts Concerning Ptolemy and The Model of the Motions.

Mathematical works

In mathematics, Alhazen used the ideas from Euclid and Thabit ibn Qurra to explore the connection between algebra and geometry. He made progress in studying conic sections and number theory.

He created a formula to add the first 100 natural numbers, using a geometric proof to show it works.

Alhazen studied what is now called the Euclidean parallel postulate, the fifth rule in Euclid's Elements, by using a proof by contradiction. This method introduced the idea of motion into geometry. He developed the Lambert quadrilateral, which is sometimes called the "Ibn al-Haytham–Lambert quadrilateral." Omar Khayyam criticized him, noting that Aristotle had previously opposed using motion in geometry.

In elementary geometry, Alhazen tried to solve the problem of squaring the circle by calculating the area of lunes (crescent-shaped figures). He later stopped because the task was impossible. The lunes formed from a right triangle by drawing semicircles on each side—toward the inside for the hypotenuse and outward for the other sides—are called the lunes of Alhazen. These lunes have the same total area as the triangle itself.

Alhazen contributed to number theory by studying perfect numbers. In his work Analysis and Synthesis, he may have been the first to suggest that every even perfect number follows the form 2(2ⁿ − 1), where 2ⁿ − 1 is a prime number. However, he could not prove this idea. Later, in the 18th century, Euler proved it, and the result is now known as the Euclid–Euler theorem.

Alhazen solved problems involving congruences using a rule now called Wilson's theorem. In his Opuscula, he described two methods for solving systems of congruences. His first method used Wilson's theorem, while his second method used a version of the Chinese remainder theorem.

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

Other works

Alhazen also wrote a book called Treatise on the Influence of Melodies on the Souls of Animals, but no copies of this work remain today. The book seems to have explored whether animals could respond to music, such as whether a camel would speed up or slow down when hearing music.

In engineering, one story says that Alhazen was called to Egypt by the Fatimid Caliph, Al-Hakim bi-Amr Allah, to manage the flooding of the Nile River. He studied the yearly flooding of the Nile carefully and made plans for building a dam at the location of today’s Aswan Dam. However, after observing the land, he realized the plan was not practical. To avoid punishment from the Caliph, he pretended to be mad.

In his Treatise on Place, Alhazen disagreed with Aristotle’s belief that empty space is impossible. He used geometry to argue that place (al-makan) is the imagined empty space between the inner surfaces of a container. Later, a supporter of Aristotle named Abd-el-latif criticized Alhazen’s work in a book titled A Refutation of Ibn al-Haytham’s Place, saying it incorrectly used geometry to describe place.

Alhazen also wrote about how people perceive space and its connection to knowledge in his Book of Optics. He argued that seeing space is not intuitive and that vision depends on past experiences. Without understanding distance or size, sight alone cannot reveal much about these things.

Alhazen was a Muslim, and most sources say he was a Sunni and followed the Ash’ari school of Islamic theology. Ziauddin Sardar noted that other important Muslim scientists, like Ibn al-Haytham and Abū Rayhān al-Bīrūnī, also followed the Ash’ari school. These scholars believed that faith (taqlid) should apply only to Islamic prophets, not to ancient Greek thinkers. This belief influenced Ibn al-Haytham’s scientific skepticism and his criticism of ancient authors like Ptolemy in works such as Doubts Concerning Ptolemy and Book of Optics.

Alhazen wrote about Islamic theology, discussing prophethood and creating a system to identify false claims about prophets in his time. He also wrote a treatise titled Finding the Direction of Qibla by Calculation, explaining how to mathematically determine the direction of Qibla, where prayers (salat) are directed.

There are occasional mentions of religious ideas or beliefs in his technical writings, such as in Doubts Concerning Ptolemy and The Winding Motion, where he discussed the relationship between objective truth and God.

Legacy

Alhazen made important contributions to optics, number theory, geometry, astronomy, and natural science. His work on optics introduced a new focus on using experiments to learn about light and vision.

His main book, Kitab al-Manazir (Book of Optics), was widely known in the Muslim world, especially through a 13th-century explanation by Kamāl al-Dīn al-Fārisī called Tanqīḥ al-Manāẓir. In al-Andalus, the 11th-century prince al-Mu'taman ibn Hūd, who wrote a significant math text, used the book. A Latin version of Kitab al-Manazir was likely made in the late 12th or early 13th century. This translation influenced many 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. In the Islamic world, the Persian scientist Kamal al-Din al-Farisi (died around 1320) improved Alhazen’s Optics in his book Kitab Tanqih al-Manazir. Alhazen wrote about 200 books, but only 55 remain today. Some of his optical writings survive only in Latin translations. During the Middle Ages, his books on cosmology were translated into Latin, Hebrew, and other languages.

H. J. J. Winter, a British science historian, noted the importance of Ibn al-Haytham in the history of physics. Geoffrey Chaucer, a medieval writer, mentioned Alhazen’s work in The Canterbury Tales.

A crater on the Moon, called Alhazen, honors him, as does the asteroid 59239 Alhazen. The Aga Khan University in Pakistan named its Ophthalmology chair "The Ibn-e-Haitham Associate Professor and Chief of Ophthalmology" in his honor.

The 2015 International Year of Light celebrated the 1000th anniversary of Ibn Al-Haytham’s optical works. In 2014, the Cosmos: A Spacetime Odyssey episode Hiding in the Light, hosted by Neil deGrasse Tyson, highlighted his achievements. He was portrayed by Alfred Molina in the episode.

Forty years earlier, Jacob Bronowski discussed Alhazen’s work in his television series The Ascent of Man and its book. In episode 5, The Music of the Spheres, Bronowski called Alhazen "the one really original scientific mind in Arab culture," noting his optical theories were not surpassed until the time of Isaac Newton and Gottfried Wilhelm Leibniz.

UNESCO declared 2015 the International Year of Light, and its director, Irina Bokova, called Ibn al-Haytham "the father of optics." This honored his work in optics, math, and astronomy. An international campaign by 1001 Inventions promoted his legacy through exhibits, workshops, and films like 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 many different subjects. At least 96 of these works are known to exist. Most of his writings are now lost, but more than 50 have survived in some form. About half of the surviving works are about mathematics, 23 are about astronomy, and 14 are about optics. A few of his works cover other topics. Not all of the surviving works have been studied yet, but some of the ones that have are listed below.

• A Book Summarizing Optics from Euclid and Ptolemy, with Added Ideas
• Treatise on Burning Mirrors
• Treatise on the Nature of Sight and How Vision Works