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A devout Muslim, Ibn al-Haitham believed that human beings are flawed and only God is perfect. To discover the truth about nature, Ibn a-Haitham reasoned, one had to eliminate human opinion and allow the universe to speak for itself through physical experiments. “The seeker after truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them,” the first scientist wrote, “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.”

In his massive study of light and vision, *Kitâb al-Manâzir* (*Book of Optics* ), Ibn al-Haytham submitted every hypothesis to a physical test or mathematical proof. To test his hypothesis that “lights and colors do not blend in the air,” for example, Ibn al-Haytham devised the world’s first camera obscura, observed what happened when light rays intersected at its aperture, and recorded the results. Throughout his investigations, Ibn al-Haytham followed all the steps of the scientific method.

*Kitab al-Manazir* was translated into Latin as *De aspectibus* and attributed to Alhazen in the late thirteenth century in Spain. Copies of the book circulated throughout Europe. Roger Bacon, who sometimes is credited as the first scientist, wrote a summary of *Kitab al-Manazir* entitled *Perspectiva* (*Optics*) some two hundred years after the death of the scholar known as Alhazen.

Ibn al-Haytham conducted many of his experiments investigating the properties of light during a ten-year period when he was stripped of his possessions and imprisoned as a madman in Cairo. How Ibn al-Haytham came to be in Egypt, why he was judged insane, and how his discoveries launched the scientific revolution are just some of the questions Bradley Steffens answers in *Ibn al-Haytham: First Scientist*, the world’s first biography of the Muslim polymath.

Source.

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.

A seven volume work on optics, *Kitab al-Manazir,* is considered by many to be ibn al-Haytham’s most important contribution. It was translated into Latin as *Opticae thesaurus Alhazeni* in 1270. The previous major work on optics had been Ptolemy‘s *Almagest* and although ibn al-Haytham’s work did not have an influence to equal that of Ptolemy‘s, nevertheless it must be regarded as the next major contribution to the field. The work begins with an introduction in which ibn al-Haytham says that he will begin “the inquiry into the principles and premises”. His methods will involve “criticising premises and exercising caution in drawing conclusions” while he aimed “to employ justice, not follow prejudice, and to take care in all that we judge and criticise that we seek the truth and not be swayed by opinions”.

Also in Book I, ibn al-Haytham makes it clear that his investigation of light will be based on experimental evidence rather than on abstract theory. He notes that light is the same irrespective of the source and gives the examples of sunlight, light from a fire, or light reflected from a mirror which are all of the same nature. He gives the first correct explanation of vision, showing that light is reflected from an object into the eye. Most of the rest of Book I is devoted to the structure of the eye but here his explanations are necessarily in error since he does not have the concept of a lens which is necessary to understand the way the eye functions. His studies of optics did led him, however, to propose the use of a camera obscura, and he was the first person to mention it.

Book II of the *Optics* discusses visual perception while Book III examines conditions necessary for good vision and how errors in vision are caused. From a mathematical point of view Book IV is one of the most important since it discusses the theory of reflection. Ibn al-Haytham gave [1]:-

*… experimental proof of the specular reflection of accidental as well as essential light, a complete formulation of the laws of reflection, and a description of the construction and use of a copper instrument for measuring reflections from plane, spherical, cylindrical, and conical mirrors, whether convex or concave.*

Alhazen’s problem, quoted near the beginning of this article, appears in Book V. Although we have quoted the problem for spherical mirrors, ibn al-Haytham also considered cylindrical and conical mirrors. The paper [36] gives a detailed description of six geometrical lemmas used by ibn al-Haytham in solving this problem. Huygens reformulated the problem as:-

*To find the point of reflection on the surface of a spherical mirror, convex or concave, given the two points related to one another as eye and visible object.*

Huygens found a good solution which Vincenzo Riccati and then Saladini simplified and improved.

Book VI of the *Optics* examines errors in vision due to reflection while the final book, Book VII, examines refraction [1]:-

*Ibn al-Haytham does not give the impression that he was seeking a law which he failed to discover; but his “explanation” of refraction certainly forms part of the history of the formulation of the refraction law. The explanation is based on the idea that light is a movement which admits a variable speed *(*being less in denser bodies*)* …*

Ibn al-Haytham’s study of refraction led him to propose that the atmosphere had a finite depth of about 15 km. He explained twilight by refraction of sunlight once the Sun was less than 19° below the horizon.

Abu al-Qasim ibn Madan was an astronomer who proposed questions to ibn al-Haytham, raising doubts about some of Ptolemy‘s explanations of physical phenomena. Ibn al-Haytham wrote a treatise *Solution of doubts* in which he gives his answers to these questions. They are discussed in [43] where the questions are given in the following form:-

*What should we think of Ptolemy‘s account in “Almagest” *I.3* concerning the visible enlargement of celestial magnitudes *(*the stars and their mutual distances*)* on the horizon? Is the explanation apparently implied by this account correct, and if so, under what physical conditions? How should we understand the analogy Ptolemy draws in the same place between this celestial phenomenon and the apparent magnification of objects seen in water? …*

There are strange contrasts in ibn al-Haytham’s work relating to Ptolemy. In *Al-Shukuk ala Batlamyus* (Doubts concerning Ptolemy), ibn al-Haytham is critical of Ptolemy‘s ideas yet in a popular work the *Configuration,* intended for the layman, ibn al-Haytham completely accepts Ptolemy‘s views without question. This is a very different approach to that taken in his *Optics* as the quotations given above from the introduction indicate.

One of the mathematical problems which ibn al-Haytham attacked was the problem of squaring the circle. He wrote a work on the area of lunes, crescents formed from two intersecting circles, (see for example [10]) and then wrote the first of two treatises on squaring the circle using lunes (see [14]). However he seems to have realised that he could not solve the problem, for his promised second treatise on the topic never appeared. Whether ibn al-Haytham suspected that the problem was insoluble or whether he only realised that he could not solve it, in an interesting question which will never be answered.

In number theory al-Haytham solved problems involving congruences using what is now called Wilson‘s theorem:

*if p is prime then *1 + (*p* – 1) !* is divisible by p .*

In *Opuscula* ibn al-Haytham considers the solution of a system of congruences. In his own words (using the translation in [7]):-

*To find a number such that if we divide by two, one remains; if we divide by three, one remains; if we divide by four, one remains; if we divide by five, one remains; if we divide by six, one remains; if we divide by seven, there is no remainder.*

Ibn al-Haytham gives two methods of solution:-

*The problem is indeterminate, that is it admits of many solutions. There are two methods to find them. One of them is the canonical method: we multiply the numbers mentioned that divide the number sought by each other; we add one to the product; this is the number sought.*

Here ibn al-Haytham gives a general method of solution which, in the special case, gives the solution (7 – 1)! + 1. Using Wilson‘s theorem, this is divisible by 7 and it clearly leaves a remainder of 1 when divided by 2, 3, 4, 5, and 6. Ibn al-Haytham’s second method gives all the solutions to systems of congruences of the type stated (which of course is a special case of the Chinese Remainder Theorem).

Another contribution by ibn al-Haytham to number theory was his work on perfect numbers. Euclid, in the *Elements,* had proved:

*If, for some k > *1, 2^{k} – 1* is prime then *2^{k-1}(2^{k} – 1)* is a perfect number.*

The converse of this result, namely that every even perfect number is of the form 2^{k-1}(2^{k} – 1) where 2^{k} – 1 is prime, was proved by Euler. Rashed ([7], [8] or [27]) claims that ibn al-Haytham was the first to state this converse (although the statement does not appear explicitly in ibn al-Haytham’s work). Rashed examines ibn al-Haytham’s attempt to prove it in *Analysis and synthesis* which, as Rashed points out, is not entirely successful [7]:-

*But this partial failure should not eclipse the essential: a deliberate attempt to characterise the set of perfect numbers.*

Ibn al-Haytham’s main purpose in *Analysis and synthesis* is to study the methods mathematicians use to solve problems. The ancient Greeks used analysis to solve geometric problems but ibn al-Haytham sees it as a more general mathematical method which can be applied to other problems such as those in algebra. In this work ibn al-Haytham realises that analysis was not an algorithm which could automatically be applied using given rules but he realises that the method requires intuition. See [18] and [26] for more details.

**Article by:** *J J O’Connor* and *E F Robertson*

*Source.*

Using math in physics and astronomy, Ibn Al-Haytham wrote treaties on the light of the Moon, in which he argues that the moon shines like a self luminous object, though its light is borrowed from the Sun.

He wrote on the Halo and Rainbow, on Spherical Burning Mirrors, on Paraboloidal Burning Mirrors, and on the Shape of an eclipse, which examines the camera obscura phenomena.

**Camera Obscura**

Karmal al-Din al-Farisi

Istanbul, Fourteenth Century

**source.**

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