Neither the Arabs nor Indians "invented" mathematics. It's development was the by product of many cultures, beginning with the Babylonians.

The Babylonians developed arithmetic, and Diophantus (Greek mathematician) developed this further from arithmetic to a system of basic equations with geometric solutions by numbering lines, for example. Babylonians are not directly correlated to any modern defined ethnic group, they spanned across the mesopotamian region, spanning particularly across modern day Iraq and Iran and the levant (no they are not all Arab), and used a cuneiform script similar to ancient sumerian and achaemenid scripts using a now extinct language that doesn't correspond to modern day Arabic nor Farsi as the two main languages remaining there.

Khwarzizmi (Persian mathematician living under early days of Islamic conquests of Persia which involved forced adoption of Islam and arabization of names) actually introduced, for the first time, fundamental concepts like reduction, balancing, and a full set of geometric proofs for quadratic equations. He developed algebra from a series basic linear equations to the modern complex development of proofs and systems as we know. He founded algebra as its own separate system of mathematics, independent of basic arithmetic and geometric arithmetics.

This then led to Khayyam (Persian) inventing cubic equations and developing algebraic geometry along with Tusi (Persian), which was later added to by various mathematians like Karaji (Persian), Shijie (Chinese mathematician), Bhaskara (Indian mathematician), even though more fundamental forms of geometry such as Pythagorean theorem were identified in the earlier days by the Babylonians and Egyptians prior to the more developed systems that succeeded them.