The doorbell would ring — in Princeton, Budapest, Manchester or Canberra — and on the step would stand a small, stooped man in thick spectacles, clutching a half-empty suitcase that held nearly everything he owned. "My brain is open," he would announce. Paul Erdős had arrived. He would sleep in your spare room, wake you before dawn with a conjecture, empty your coffee pot, and stay until the two of you had proved something. Then he would fly off and do the same to someone else.
Erdős was born in Budapest on 26 March 1913, the son of two mathematics teachers. Tragedy framed him from his first day: his two sisters died of scarlet fever days before his birth, and his mother, terrified of infection, kept him out of school for years. The hothouse produced a prodigy who could multiply three-digit numbers in his head at three and who, at four, worked out for himself that subtracting a larger number from a smaller one lands you below zero. He completed his doctorate at 21 and left an increasingly hostile Hungary in 1934 for a fellowship in Manchester; much of his family was later murdered in the Holocaust.
From then on he simply never stopped moving. He owned no house, held no permanent post, and let his friend Ronald Graham manage his money and his mail from New Jersey. His motto was "another roof, another proof": for six decades he criss-crossed four continents from one mathematician's guest room to the next, working up to nineteen hours a day. After his mother's death in 1971 sank him into depression, doctors prescribed amphetamines, and he took them for the rest of his life. In 1979 Graham bet him $500 that he could not stop for a month. Erdős won, then complained that the experiment had set mathematics back a month — every time he looked at a blank page, he said, he saw nothing — and went straight back to the pills.
The number that maps mathematics
The output of this vagabond life was roughly 1,500 papers — more than any other mathematician in history has published, though Euler wrote more pages — produced with more than 500 different co-authors. The collaboration network is so vast that mathematicians turned it into a parlour game. Your Erdős number is your distance from him in the graph of joint papers: his co-authors have Erdős number 1, their co-authors 2, and so on. Albert Einstein's is 2. Among published mathematicians who connect to him at all, the typical number is about 5. The joke has long since escaped the discipline: the Erdős–Bacon number adds an actor's distance from Kevin Bacon, and a handful of scientist-performers hold respectably small totals of both. There is even a cherished piece of whimsy from 1995, when Erdős and the baseball great Hank Aaron received honorary degrees at Emory University on the same day and signed the same baseball — giving Aaron, fans like to say, an honorary Erdős number of 1.
He spoke his own private language. Children were "epsilons", after the vanishingly small quantities of calculus. God was "the SF" — the Supreme Fascist — who hid the best proofs from mortals and kept a transfinite Book containing the perfect proof of every theorem; the highest compliment Erdős could pay an argument was that it came straight from the Book. And he seeded the subject with cash prizes for unsolved problems, from $25 for the merely hard to thousands of dollars for the monsters, with Graham underwriting the cheques. Some of those problems remain open, and the bounties still stand.
The myth in the coffee cup
The line forever pinned to him — "a mathematician is a machine for turning coffee into theorems" — is one he embodied but, the record suggests, did not coin: it is generally credited to his friend and fellow Hungarian Alfréd Rényi. Money interested him even less than sleep did. When he shared the Wolf Prize in 1983–84, he gave nearly all of his $50,000 share away to relatives, students and good causes, reportedly keeping about $720 for himself. Property, he liked to say, was a nuisance.
He died as he had wished, with his boots on: on 20 September 1996, aged 83, he suffered a heart attack while attending a mathematics conference in Warsaw, conjecturing almost to the last. Paul Hoffman's 1998 biography took its title from the truth everyone already knew — he was the man who loved only numbers. The suitcase has stopped travelling; the graph it built never will, because every new joint paper, anywhere on Earth, still shifts someone's distance to a man decades dead.
Quiz nuggets
- Paul Erdős published roughly 1,500 mathematical papers with more than 500 co-authors — more papers than any other mathematician in history.
- An Erdős number measures collaborative distance from Erdős via joint papers; Albert Einstein's is 2, and a typical connected mathematician's is about 5.
- In 1979 Ronald Graham bet Erdős $500 that he could not give up amphetamines for a month; Erdős won, then said the bet had set mathematics back a month.
- The quip that a mathematician is "a machine for turning coffee into theorems" is generally credited to Alfréd Rényi, not to Erdős himself.
- Erdős died of a heart attack on 20 September 1996, aged 83, while attending a mathematics conference in Warsaw.