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On Islamic mathematical contributions

This comes from a challenge from a discussion and from the repeated claims by Muslims and Muslim sites that Islam is a mathematical religion and that Islam’s Golden era was also the era of mathematics. This is not for any peer-review but Anand may have it analyzed by anyone. We examine here how much of the Islamic contribution in the said fields was unknown before them.

0. Assumptions

0.1 Knowing/Using a mathematical principal to solve a problem is does NOT mean contributing to it.

1. Algebra

1.1 Mathematical induction: Greeks and ancient Indians were both aware of the principle and have used it in their treatises. Euclid used Induction as something intuitive in his ubiquitous treatises. The first formal statement comes from Pascal in Traité du triangle arithmétique in 17th century. The Muslims knew and used the principle but have made no contribution to it.

1.2 Irrational numbers: Greeks knew of these. So did the Indians. But none had any explicit symbol for say √2 even though they knew that its value can not be correctly stated and estimated its rational approximations. Greeks found the idea difficult to accept even though they (and also Indians!) had ventured as far as complex numbers.

Muslims mathematicians were first to become ‘comfortable’ with irrational numbers. They used Indian numerals (Hindu numerals in their language) to describe the problems confounding the Greeks and Babylonians. The first use of irrational coefficients in quadratic problems (and their solution), extension of Greeks’ geometrical solution of cubic equations by Omar Khayyam to all equations with positive roots followed naturally.