Pythagoras of Samos

Pythagoras (around 570–495 BC) is the most famous name in school mathematics — and also one of the most mysterious. He founded a secretive philosophical brotherhood in ancient Greece whose motto was, more or less, "all is number": they believed whole numbers and their ratios were the hidden harmony behind music, the stars, and reality itself.

The theorem everyone remembers

His name lives on in the one equation almost everybody can recite — the Pythagorean theorem, relating the sides of a right-angled triangle:

a^2 + b^2 = c^2.

It is the seed of an astonishing amount of mathematics: it stretches into three dimensions, it gives the distance between any two points, and it generalises into the cosine rule. In truth the result was known to the Babylonians a thousand years earlier — but Pythagoras (or his followers) got the credit, and the name stuck.

The number that broke the brotherhood

The Pythagoreans staked everything on the belief that every length was a neat ratio of whole numbers. Then their own theorem betrayed them. The diagonal of a simple unit square has length \sqrt{2} — and one of them proved that \sqrt{2} is irrational, expressible as no such ratio at all. Legend says the brotherhood was so appalled by this crack in their worldview that they kept it secret — and that the member who leaked it, Hippasus, was drowned at sea for his heresy. Mathematics' first great scandal was a number that simply refused to be tidy.