Niels Henrik Abel

Niels Henrik Abel (1802–1829) was the Norwegian genius who settled a question mathematicians had chewed on for three centuries: is there a formula, like the quadratic formula, that solves every fifth-degree equation? Abel proved the answer is a flat no — there can be no such formula, ever. He did it at 21, paid a printer out of his own empty pockets, and died of tuberculosis at 26.

The impossible made certain

It is one thing to fail to find a formula; it is another thing entirely to prove that nobody can. Abel's proof of the insolvability of the quintic — now called the Abel–Ruffini theorem — is a landmark of that rarer, harder kind. His name lives on all over mathematics: a commutative group is called abelian in his honour, and the Abel Prize is today mathematics' answer to the Nobel.

Abel spent his short life in poverty, hunting for a university post that never came. Just two days after he died in 1829, a letter reached his home with the news he had waited years for: a professorship in Berlin. His story and Galois's rhyme so eerily — two revolutionaries in the same subject, both dead before 27 — that together they've become mathematics' great emblem of brilliance cut tragically short.