Jacques Hadamard

Jacques Hadamard (1865–1963) was a French mathematician who lived almost a hundred years and left his fingerprints on nearly every corner of the subject. He was also a rare thing — a great researcher who thought hard about how discoveries happen, writing a whole book on the psychology of mathematical invention after quizzing scientists like Einstein about the pictures in their heads.

What the world remembers

In 1896 Hadamard achieved one of the great triumphs of number theory: a proof of the prime number theorem, which tells us roughly how the primes thin out as numbers get larger — that near a big number n, primes appear about once every \ln n steps. The proof had eluded mathematicians for a century and required daring new ideas from complex analysis. Charmingly, another mathematician, Charles de la Vallée Poussin, proved it independently the very same year.

Both Hadamard and de la Vallée Poussin, the two men who cracked the prime number theorem, went on to live into their late 90s — leading to a running joke among mathematicians that anyone who proves the theorem is rewarded with a very long life. Hadamard's own century was not all mathematics: he was drawn into the notorious Dreyfus Affair (a relative was involved), becoming a passionate campaigner for justice, and he later fled France during the Second World War. A gentle, curious, deeply humane man who never stopped wondering how ideas are born.