As discussed in a previous article, Muslim scholars have made significant contributions through a wide range of scholarly pursuits. This article will continue to highlight key Muslim scientific and philosophical thinkers who have helped shape modern-day knowledge in a range of fields.At the same time as advances in medicine were being made, the Muslims produced some of the most outstanding Mathematicians.
Muhammad ibn Musa al-Khwarizmi, born in 780 A.D., was the founder of modern Algebra. He developed sine, cosine and trigonometrically tables, which were later translated to the West. His book on algebra Hisab al-Jabr waal-Muqabalah (The Calculation of Integration and Equation) was used until the 16th century as the principal textbook of European universities.
In it he writes that given an equation, collecting the unknowns in one side of the equation is called al-Jabr and collecting the knowns in the other side of the equation is called al- Mukabalah. He also described six basic types of equations: nx=m, x^2=nx, x^2=m, m+x^2 =nx, m+nx +x^2 and x^2=m+nx. He also solved the particular equation x^2+21=10x using geometrical arguments.
Al-Khawarizmi also helped introduce Arabic numerals, the decimal position system, and the concept of zero. Algebra and Algorithm are in fact corruptions of his work and name. Interestingly, this first every book on algebra included many examples from the Islamic inheritance laws and how they could be solved using algebra. Under al-Mamun the caliph of the time, he with some others were the first to map the globe.
In the field of Algebra the Muslims continued with Thabit Ibn Qurra’s more general equations solved by geometrical arguments. In 901, Abu Kamil, called “the Egyptian calculator”, did some work on algebra in which he established rules for manipulating
Algebraic expressions. He also proved various laws such as ax*bx-abx^2, a (bx) = (ab) x and (10-x) (10-x) =100+x^2-20x (Mirza, p124). Around 1000, Abu Bakr Al-Karaji, in his book The Marvelous discussed higher order equations such as fourth and fifth order equations, combing geometry and arithmetic. Al-Samawal established the power law x^nx^n=x^ (m+n) in 1180 in his work The Shining which is just one of his 85 books. He also worked on performing multiplication of algebraic expressions involving terms with different powers and division of polynomials. Abu Yunus proved the famous identity cos (a) cos (b) = {cos (a+b) +cos (a-b)}/2 and used spherical trigonometry to set formulas to computer prayer times. Al-Biruni also used spherical trigonometry to find the direction of Mecca or any other city on the globe.
Another outstanding mathematician was Ghiyath al-Din al Kashani of the late fourteenth century. He worked on the theory of numbers and techniques of computations. In 1424, he computed a value of 2pi to sixteen decimal digits of accuracy using an approximation of the circle by 805306368 side polygon. One of his most important works was Miftah elHussab or The Calculators’ Key; in it he described an algorithm for finding the fifth root of any number. The book was used in Persian schools until the seventeenth century. Later in his life he moved to Samarkand at the request of the then ruler to help direct a new scientific school and observatory and conduct research with other scholars of the time. Kashani also wrote on how to approximate sin (1) by solving a cubic equation accurately.
Umar Khayyam known to the west as only a poet actually also was an excellent mathematician. He criticized Euclid’s theorems, evolved a methodology for the solution of third degree equations, and did research in the field of binomials and their coefficients.
Abu Wafa Muhammad al-Buzanji was born in Buzjan, Nishapur in 940 A. D. He became a great mathematician and astronomer at Baghdad and died in 997 A.D. Al-Buzanji’s main contribution lies in several branches of mathematics, in geometry and trigonometry especially. In geometry he contributed to a solution of geometrical
problems with opening of the compass, construction of a square equivalent to other squares, regular polyhedra, construction of regular hectagon taking for its side of the equilateral triangle inscribed in the same circle, constructions of parabola by points and geometrical solution of the equations x4=a and x4+ax3=b.
Al-Buzanji’s contribution to the development of trigonometry was also extensive. He was the first to show the generality of the sine theorem relative to spherical triangles. He developed a new method of constructing sine tables, the value of sin 30` being correct to the eight decimal place. He also developed relations for sine (a+b) and the formula: 2 sin2 (a/2) = 1 -cos a and sin a = 2 sin (a/2) cos (a/2). In addition he studied tangent and calculated tables for them. He introduced the secant and cosecant for the first time. He wrote a large number of books on mathematics and other subjects, most of which have been lost or exist in modified forms. He also wrote rich commentaries on Euclid, Diophanatos and al-Khwarizmi. A sizable part of today’s trigonometry can be traced back to him.
Abu al-Hassan al Haitham (965-1039 AD) was one of the most eminent physicists, whose contribution to optics and the scientific method were great. Originally from Basra, he went to Egypt where he was asked to find ways of controlling the flood of the Nile. Being unsuccessful in this, he feigned madness until the death of Caliph al-Hakim. He also traveled to Spain and during this time also had time for his scientific pursuits. He wrote treatises such as Kital al-Manzir on light, worked with mirrors and lenses, reflection, refraction, and magnifying and burning glasses. He discussed the propagation of light and colors, optic illusions and opposed the view of Euclid and Ptolemy that the eye sent out visual rays. From studying motion, he discovered the principle of inertia.
In mathematics, al-Battani was the first to replace the use of Greekchords by sines and the first to develop the concept of cotangent and furnished their table in degrees. He wrote a number of books on astronomy and trigonometry. His most famous book was his
Astronomical treatise with tables which was translated into Latin in the 12th century, called De Sceinta Stellerum De numeris Stellerum ET Motibus. This was extremely influential in Europe until the Renaissance, with translations available in several languages. His original discoveries in both astronomy and trigonometry were of great consequence in the development of those sciences.
In the related field of Physics, Abu al-Fath Abd al-Rahman al-Khazini studied mechanics and hydrostats and wrote books on physics and astronomy. Al-Biruni, a geographer, chronologist, mathematician, astronomer, was also a physicist. His Elements of Astrology remained a textbook for centuries and he also wrote on specific gravity, and developed formulas to determine absolute and specific weights of all objects.
Abu al-Hassan al Haitham (965-1039 AD) was one of the most eminent physicists, whose contribution to optics and the scientific method were great. Originally from Basra, he went to Egypt where he was asked to find ways of controlling the flood of the Nile. Being unsuccessful in this, he feigned madness until the death of Caliph al-Hakim. He also traveled to Spain and during this time also had time for his scientific pursuits. He wrote treatises such as Kital al-Manzir on light, worked with mirrors and lenses, reflection, refraction, and magnifying and burning glasses. He discussed the propagation of light and colors, optic illusions and opposed the view of Euclid and Ptolemy that the eye sent out visual rays. From studying motion, he discovered the principle of inertia.
He contradicted Ptolemy’s and Euclid’s theory of vision that objects are seen by rays of light emanating from the eyes. According to Haitham, the rays originated in the object of vision and not in the eye. Through this kind of extensive research on optics, he has been considered the father of modern Optics. Roger Bacon and all medieval Western writers on optics based their work largely on his Opticae Thesaurus and it even influenced Leonardo da Vinci, Johann Kepler and Newton. Haitham also studied the phenomena of sunrise and sunset and explained rainbows through the principle of reflection. He was known for the earliest use of the camera obscura as well.
Al-Kindi (d. 873 AD) considered the first philosopher of the Arabs, also contributed to Physics, Optics, reflection of light, specific weights, tides and metallurgy.
Muslims also made discoveries in Chemistry by discovering many new substances such as potash, nitrate of silver, corrosive sublimate and nitrate and sulfuric acid as well as improving methods for evaporation, filtration, sublimation, calcinations, melting, distillation, and crystallization.
Jabir, otherwise known as the father of Arab alchemy contributed in the fields of Pharmacology and Toxicology.
Al-Asma’i (740-882 AD) was a philologist who contributed to Zoology, Botany and Animal Husbandry. Other Muslim botanists described plants in detail, medicinal herbs, Physiology of plants and wrote books on horses, camels, sheep, birds, the history of bees and locusts, the effect of climate on the behavior of animals and men. Also working on the subject of Botany, Suri al- Dimashqi researched plants around Damascus and Lebanon at different stages of growth.
Sources:
Brend, Barbara. Islamic Art. Cambridge: Harvard University Press, 1991.
Fakhry, Majid. A History of Islamic Philosophy. New York: Columbia University Press, 1970.
Haye, Kh. A. Stories of Great Muslims. Brentwood: American Trust Publications, 1991.
Hitti, K. Phillip. History of the Arabs. New York: St. Martins Press, 1970.
Irving, T.B. The Tide of Islam. Cedar Rapids: Igrams Press, 1982.
Michell, George. Architecture of the Islamic World. London: Thames and Hudson, 1995.
Mirza, Dr. Muhammad R. and Sidiiqi, Muhammad Iqbal. Muslim Contribution to Science. Chicago: Kazi Publications, 1986.
Nasr, Seyyed Hossein. A Young Muslim’s Guide to the Modern World. Chicago:Kazi Publications, 1994.
Qadir, C.A. Philosophy and Science in the Muslim World. London: Croom Helm, 1988.
Science: The Islamic Legacy: Worlds fair issue, 1987.