🇭🇺Paul
Erdős

He arrived at your door with a half-empty suitcase and a single sentence: "My brain is open." If you were a mathematician — and he only visited mathematicians — this meant work was about to begin. Paul Erdős had no home, no fixed address, no possessions beyond what fit in the suitcase, and no interest in anything except mathematics. He moved between the houses of colleagues, university departments, and conference hotels on every continent for the last six decades of his life, solving problems in exchange for hospitality, occasionally leaving small amounts of prize money at the doors of colleagues who had helped him, and publishing, year after year, decade after decade, the greatest sustained output of mathematical research in history. When he died in Warsaw in 1996, aged eighty-three, he had published more than 1,500 papers. He had been working the day before he died.

Pál Erdős was born on March 26, 1913, in Budapest, into a Jewish family of remarkable intellectual density. His father Lajos was a high school mathematics teacher, his mother Anna a teacher as well. Four days after his birth, both of his older sisters died of scarlet fever while his mother was in the maternity ward. The effect on his mother, who subsequently almost never let Paul out of her sight, was profound. He grew up almost entirely educated at home, largely by his father, and showed mathematical gifts so early and so pronounced — he could multiply three-digit numbers in his head at age three — that his parents made no attempt to normalize his education. He was still unable to butter his own bread at age twenty. He never learned to cook, never drove a car, never managed a bank account. None of these things interested him. Mathematics was enough.

He published his first paper at age eighteen, in 1931, giving a new and more elegant proof of Chebyshev's theorem — the result that there is always a prime number between n and 2n for any integer n greater than one. The proof was a harbinger of everything to come: it was simple, surprising, and beautiful. Chebyshev had proved the theorem in 1852 using analytic methods. Erdős proved it with pure combinatorics and elementary arithmetic. This preference for elementary methods — proofs that used only basic tools, nothing borrowed from more powerful branches of mathematics — became his trademark. He believed that the most beautiful proofs were those that a child could follow if explained carefully enough.

The Erdős number is a cultural institution in mathematics. Paul Erdős's co-authors have an Erdős number of 1. Anyone who co-authored with a co-author of Erdős has an Erdős number of 2. And so on. Because Erdős collaborated with 511 different mathematicians — across combinatorics, number theory, graph theory, set theory, geometry, and probability — the entire mathematical world is linked through him. Albert Einstein has an Erdős number of 2. Stephen Hawking has a number of 4. The system is, at its core, a map of mathematical collaboration, and Erdős is its center not because he was the greatest mathematician but because he was the most connected, the most generous with his time and ideas, and the most committed to collaboration as a way of life.

He survived the twentieth century's catastrophes through a combination of circumstance and restlessness. He was in England on a fellowship when Hungary fell under German influence, and he never returned permanently. Several of his Jewish relatives were murdered in the Holocaust. His mother, to whom he was extraordinarily close and who traveled with him during his later years, died in 1971 — a blow from which, by his own account, he never fully recovered. He began taking amphetamines after her death and continued until the end of his life, famously wagering a colleague five hundred dollars that he could stop for a month (he won the bet, then immediately resumed). He was eccentric, childlike, mathematically ferocious, and incapable of hypocrisy.

His mathematical legacy spans an extraordinary range. His work with Atle Selberg on the elementary proof of the prime number theorem (1949) was a sensation. His contributions to Ramsey theory, probabilistic combinatorics, graph theory, and additive number theory were foundational. He posted prize money for unsolved problems — sometimes fifty dollars, sometimes ten thousand — and many remain unsolved today. He is buried in Budapest. His gravestone reads, in Hungarian: "I have finally become stupider than usual."