Mathematics or “the queen of the sciences” as Carl Friedrich Gauss called it, plays an important role in our lives. A world without mathematics is unimaginable. Throughout history, many scholars have made important contributions to this science, among them a great number of Muslims. The word “algebra” comes from “Al-Jabr,” which is taken from the title of the book Hisab Al-Jabr wal Muqabala (The Calculation of Integration and Equation) by Muhammad ibn Musa al-Khwarizmi (780 – 850), who is known as the “father of algebra.’’ Europe was first introduced to algebra as a result of the translation of Khwarizmi’s book into Latin by Robert Chester in 1143. Until the 16^{th} century, the book was used as the principal textbook of European universities. In it he composes that given an equation, collecting the unknowns in one side of the equation is called al-Jabr and collecting the known in the other side of the equation is called al-Mukabalah. Also, the book comprised many examples from the Islamic inheritance laws and how they could be answered using algebra.

Al-Khwarizmi developed the Sine, the Cosine, and trigonometric tables which are used in everyday mathematics, modern day architecture, science, and astronomy. Without a proper number theory, how would we conduct our daily financial transactions? It was Khwarizmi that defined the uses of the number “zero,” by capitulating on earlier works made by the Hindus and Chinese. The word “zero” actually comes from Latin “zephirum,” which is derived from the Arabic word “sifr.” Under Al-Mamun the caliph of the time, he with some others was the first to map the globe. Therefore, ‘Algebra’ and ‘Algorithm’ are corruptions of his work and name.

The three sons of Musa ibn Shakir (about 800 – 860) wrote a great book on geometry, Kitab Marifat Masakhat Al-Ashkal (The Book of the Measurement of Plane and Spherical Figures), which was later translated into Latin by Gerard of Cremona. In the book, they considered volumes and areas as numbers, and hence they developed a new approach to mathematics. For example, they described the constant number pi (π) as “the magnitude which, when multiplied by the diameter of a circle, yields the circumference.”

Al-Battani or Albetagnius (about 850 – 929) was a Muslim astronomer and mathematician. In his research on astronomy he used trigonometric methods which were a lot more advanced than the geometric methods used by Claudius Ptolemy (a Greek Mathematician, astronomer and geographer who lived between 90 and 168). He introduced trigonometric ratios. For example, for a right triangle with adjacent sides ‘a’ and ‘b’, he gives the formula:
b sin (A) = a sin (90^{0 }– A), which is equivalent to tan A = a/b. He was the first to introduce the cotangent function.

Muhammad Abu’l Wafa (940 – 998), born at Buzjan in Khorasan, introduced the use of secant, cosecant and tangent functions. He also gave a new method of constructing sine tables. He calculated sin (30^{0}) with an accuracy of up to eight decimal digits. He improved spherical trigonometry and proved the law of sines for general spherical triangles.

Another outstanding mathematician Nasir al-Din al-Tusi (1201 – 1274) wrote “Treatise on the Quadrilateral,” later translated into French by Alexandre Pasha in 1891. In his book, al-Tusi made enormous advances in plane and spherical trigonometry. The Dictionary of Scientific Biography states, “This work is really the first in history on trigonometry as an independent branch of pure mathematics and the first in which all six cases for a right-angled spherical triangle are set forth.” The well-known sine law (a/sin A = b/sin B = c/sin C) is also stated in this work.