Ibn al-Haytham is sometimes called al-Basri, meaning from the city of Basra in Iraq, and sometimes called al-Misri, meaning that he came from Egypt. He is often known as Alhazen which is the Latinised version of his first name "al-Hasan".
In particular this name occurs in the naming of the problem for which he is best remembered, namely Alhazen's problem:
Given a light source and a spherical mirror, find the point on the mirror were the light will be reflected to the eye of an observer.
We shall discuss this problem, and ibn al-Haytham's other work, after giving some biographical details. In contrast to our lack of knowledge of the lives of many of the Arabic mathematicians, we have quite a number of details of ibn al-Haytham's life. However, although these details are in broad agreement with each other, they do contradict each other in several ways. We must therefore try to determine which are more likely to be accurate. It is worth commenting that an autobiography written by ibn al-Haytham in 1027 survives, but it says nothing of the events his life and concentrates on his intellectual development.
Since the main events that we know of in ibn al-Haytham's life involve his time in Egypt, we should set the scene regarding that country. The Fatimid political and religious dynasty took its name from Fatimah, the daughter of the Prophet Muhammad. The Fatimids headed a religious movement dedicated to taking over the whole of the political and religious world of Islam. As a consequence they refused to recognise the 'Abbasid caliphs. The Fatimid caliphs ruled North Africa and Sicily during the first half of the 10th century, but after a number of unsuccessful attempts to defeat Egypt, they began a major advance into that country in 969 conquering the Nile Valley. They founded the city of Cairo as the capital of their new empire. These events were happening while ibn al-Haytham was a young boy growing up in Basra.
We know little of ibn al-Haytham's years in Basra. In his autobiography he explains how, as a youth, he thought about the conflicting religious views of the various religious movements and came to the conclusion that none of them represented the truth. It appears that he did not devote himself to the study of mathematics and other academic topics at a young age but trained for what might be best described as a civil service job. He was appointed as a minister for Basra and the surrounding region. However, ibn al-Haytham became increasingly unhappy with his deep studies of religion and made a decision to devote himself entirely to a study of science which he found most clearly described in the writings of Aristotle. Having made this decision, ibn al-Haytham kept to it for the rest of his life devoting all his energies to mathematics, physics, and other sciences.
Ibn al-Haytham went to Egypt some considerable time after he made the decision to give up his job as a minister and to devote himself to science, for he had made his reputation as a famous scientist while still in Basra. We do know that al-Hakim was Caliph when ibn al-Haytham reached Egypt. Al-Hakim was the second of the Fatimid caliphs to begin his reign in Egypt; al-Aziz was the first of the Fatimid caliphs to do so. Al-Aziz became Caliph in 975 on the death of his father al-Mu'izz. He was very involved in military and political ventures in northern Syria trying to expand the Fatimid empire. For most of his 20 year reign he worked towards this aim. Al-Aziz died in 996 while organising an army to march against the Byzantines and al-Hakim, who was eleven years old at the time, became Caliph.
Al-Hakim, despite being a cruel leader who murdered his enemies, was a patron of the sciences employing top quality scientists such as the astronomer ibn Yunus. His support for science may have been partly because of his interest in astrology. Al-Hakim was highly eccentric, for example he ordered the sacking of the city of al-Fustat, he ordered the killing of all dogs since their barking annoyed him, and he banned certain vegetables and shellfish. However al-Hakim kept astronomical instruments in his house overlooking Cairo and built up a library which was only second in importance to that of the House of Wisdom over 150 years earlier.
Our knowledge of ibn al-Haytham's interaction with al-Hakim comes from a number of sources, the most important of which is the writings of al-Qifti. We are told that al-Hakim learnt of a proposal by ibn al-Haytham to regulate the flow of water down the Nile. He requested that ibn al-Haytham come to Egypt to carry out his proposal and al-Hakim appointed him to head an engineering team which would undertake the task. However, as the team travelled further and further up the Nile, ibn al-Haytham realised that his idea to regulate the flow of water with large constructions would not work.
Ibn al-Haytham returned with his engineering team and reported to al-Hakim that they could not achieve their aim. Al-Hakim, disappointed with ibn al-Haytham's scientific abilities, appointed him to an administrative post. At first ibn al-Haytham accepted this but soon realised that al-Hakim was a dangerous man whom he could not trust. It appears that ibn al-Haytham pretended to be mad and as a result was confined to his house until after al-Hakim's death in 1021. During this time he undertook scientific work and after al-Hakim's death he was able to show that he had only pretended to be mad. According to al-Qifti, ibn al-Haytham lived for the rest of his life near the Azhar Mosque in Cairo writing mathematics texts, teaching and making money by copying texts. Since the Fatimids founded the University of Al-Azhar based on this mosque in 970, ibn al-Haytham must have been associated with this centre of learning.
A different report says that after failing in his mission to regulate the Nile, ibn al-Haytham fled from Egypt to Syria where he spent the rest of his life. This however seems unlikely for other reports certainly make it certain that ibn al-Haytham was in Egypt in 1038. One further complication is the title of a work ibn al-Haytham wrote in 1027 which is entitled Ibn al-Haytham's answer to a geometrical question addressed to him in Baghdad. Several different explanations are possible, the simplest of which being that he visited Baghdad for a short time before returning to Egypt. He may also have spent some time in Syria which would partly explain the other version of the story. Yet another version has ibn al-Haytham pretending to be mad while still in Basra.
Ibn al-Haytham's writings are too extensive for us to be able to cover even a reasonable amount. He seems to have written around 92 works of which, remarkably, over 55 have survived. The main topics on which he wrote were optics, including a theory of light and a theory of vision, astronomy, and mathematics, including geometry and number theory. We will give at least an indication of his contributions to these areas.
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