The greatest scientific contribution Muslims made to the world is the creation of mathematical science. Algebra, geometry, algorithm and arithmetic are at the heart of every scientific and social aspect of life.
There is hardly a single device, business entity, industry, architecture built without the Arabic numerals, the decimal point, the sign and cosine, the ruler and the compass, all of which are Islamic inventions.
Abulwafaa was the first person to demonistrate the sine theorom for spherical triangle: sin (a+b) = sin a cos b - cos a sin b. The word 'sine' is the exact translation of the arabic word Jayb.
Muhammad Ibn Musa Al-Khowarizmi, the father of algebra, was a mathematician and astronomer. He was summoned to Baghdad by Al-Mamun and appointed court astronomer.
The first book on algebra was written by al Khawarzmi, Kitab al Mukhtasir fi Hisab al Jabr wa 'l-muqabalah' The book of Summary Concerning the Process of Calculating Compulsion and Equatin. Al jaber is the restoration and amplification of something incomplete, and Muqabalah is the balancing of the two sides of an equation.