Brahmagupta

Brahmagupta (around 598–668 AD) was a brilliant Indian mathematician and astronomer who did something almost unbelievably bold: he gave the world the number zero as a proper number you could calculate with, and the first real rules for working with negative numbers — which he cheerfully described as "debts" versus "fortunes". Much of the arithmetic you learned as a child traces straight back to him.

The headline achievement

Brahmagupta was a giant of number theory long before Europe caught up. He studied which numbers can be written as sums of squares and discovered a gorgeous identity showing that a product of two such sums is again a sum of two squares. He also found clever methods for what would centuries later be called Pell's equation, and Brahmagupta's formula still gives the area of a four-sided shape inscribed in a circle from its side lengths alone.

Brahmagupta was so far ahead of his time that he tried to define division by zero — and, being a pioneer, he got it a little muddled, suggesting that zero divided by zero was just zero. It took mathematicians another thousand years to sort that out, so we can forgive him. He wrote his great treatise, the Brāhmasphuṭasiddhānta, largely in verse: imagine learning algebra from poetry. His work travelled to the Islamic world and eventually to Europe, quietly shaping the numbers we all use today.