Paul Erdős (1913–1996) was the most prolific mathematician in history — author of around 1,500 papers with more than 500 collaborators — and very possibly the most eccentric. He owned almost nothing, had no home and no job, and spent the last decades of his life as a mathematical nomad, showing up on colleagues' doorsteps around the world with a half-empty suitcase and the greeting "my brain is open."

A Hungarian prodigy, he could multiply three-digit numbers in his head at three and had discovered negative numbers for himself at four. He would go on to leave fingerprints on nearly every corner of discrete mathematics — number theory, combinatorics, graph theory, probability, set theory.

A language all his own

Erdős spoke a private dialect. Children were "epsilons" (the mathematician's symbol for something very small); women were "bosses," men were "slaves"; to stop doing mathematics was to "die," while to actually die was to "leave." God — whom he was not sure he believed in — kept a book, "The Book," containing the most elegant proof of every theorem, and the highest praise Erdős could give was that an argument was "straight from The Book." A whole volume, Proofs from THE BOOK, was later written in his honour.

Fuelled, in his own joking words, by coffee — "a mathematician is a machine for turning coffee into theorems" — and later by amphetamines, he worked nineteen-hour days into his eighties. When a friend bet him he couldn't quit the pills for a month, he won the bet, then complained that mathematics had been set back a month because he'd just sat staring at a blank page.

The Erdős number

Because he collaborated so widely, mathematicians play a game of academic "six degrees": your Erdős number is your collaboration distance from him. Erdős himself has number 0; his direct co-authors have 1; their co-authors 2, and so on. A surprising fraction of all working scientists — including several Nobel laureates and even Einstein (number 2) — have a small, finite Erdős number. It is a running joke and a genuine tribute to how connected he made the mathematical world.

Ideas that bear his name

Erdős loved elementary problems with deep answers, and elegant proofs above all. A teenage Erdős gave the famous slick proof of Bertrand's postulate (there is always a prime between n and 2n), and he and Atle Selberg later found the astonishing "elementary" proof of the Prime Number Theorem that avoids complex analysis entirely. His name is attached to the probabilistic method, the Erdős–Ko–Rado theorem, the Erdős–Szekeres theorem, and his beloved large-gaps problem, for which he offered a cash prize — one of hundreds he posted for questions he could not crack himself, the hardest still unclaimed.