Paul Erdős (1913–1996) was one of the most prolific and eccentric mathematicians in history. He had no permanent home, owned almost nothing, collaborated with more than 500 people, and left behind over 1500 published papers — a volume of output that still astonishes.
Life
Erdős was born in Budapest, Hungary, to mathematician parents. He was a child prodigy; at three he could calculate the number of seconds a person had been alive, at four he discovered negative numbers on his own. He received his doctorate at 21.
As a Hungarian Jew, Erdős left Europe in 1938 and spent most of his career in motion. He held no permanent academic position after 1954. Instead, he traveled continuously, visiting mathematicians in cities across the world for weeks or months at a time, then moving on. His suitcase and a small satchel were his only possessions.
He funded himself through small grants, lecture honorariums, and prize money — most of which he gave away, either to support young mathematicians or as rewards for solving the problems he posed.
Eccentricities
Erdős’s personal vocabulary was famous. God was the Supreme Fascist (SF), a mischievous figure who kept the best mathematical proofs hidden in a volume called The Book. Children were epsilons. Women were bosses, men were slaves. Music was noise. To do mathematics was to prove and conjecture; to die was to leave; to stop doing mathematics was to die.
He needed almost no sleep. Fueled by coffee, amphetamines (Benzedrine and later Ritalin), and mathematical problems, he would work twenty hours a day. When a friend bet him he couldn’t stop taking Benzedrine for a month, Erdős stopped — and then complained bitterly: “You’ve set mathematics back a month.”
Contributions
The probabilistic method
Erdős pioneered the probabilistic method in combinatorics: proving that a combinatorial object with certain properties exists by showing that a randomly chosen object has those properties with positive probability. This technique transformed combinatorics and became fundamental to modern discrete mathematics and theoretical computer science.
Elementary proof of the prime number theorem
In 1948, Erdős and Atle Selberg independently found elementary proofs of the prime number theorem — proofs avoiding the complex analysis previously required. The result had long been considered accessible only through the zeta function. Their proof was a surprise, though the priority dispute between them was unhappy.
Ramsey theory, graph theory, number theory
Erdős made foundational contributions to:
- Ramsey theory (how large must a structure be to guarantee a given pattern)
- Random graphs (what does a random graph look like — the Erdős-Rényi model)
- Additive combinatorics and analytic number theory
- The Collatz conjecture, about which he famously said: “Mathematics is not yet ready for such problems.”
The Erdős number
Because of Erdős’s vast collaborative network, mathematicians measure their distance from him by the Erdős number: the length of the shortest chain of co-authorships back to Erdős. Erdős has number 0. His direct co-authors have number 1. Someone who has co-authored with an Erdős collaborator has number 2. The median Erdős number for active mathematicians is about 5.
Even some physicists, economists, and computer scientists have finite Erdős numbers. Albert Einstein has Erdős number 2. Natalie Portman has Erdős number 5 (through a 2000 co-authored neuroscience paper).
Legacy
Erdős published more papers than any mathematician in history — about 1525. His influence on combinatorics, number theory, and discrete mathematics is incalculable. His life was an ongoing experiment in what mathematics could look like if it were treated as a collaborative, gift-economy enterprise.
When asked why he lived the way he did, Erdős replied: “Why is the number 6 a perfect number? Because it is the way it is. The questions are what matter.”
He died in 1996 while attending a conference in Warsaw — appropriate, in retrospect, for a man who lived his life on the move.
Known for
- 1500+ published papers with over 500 collaborators
- Probabilistic method in combinatorics
- Elementary proof of the prime number theorem (with Selberg)
- The Erdős number
Frequently asked
What is an Erdős number?
A measure of collaborative distance from Paul Erdős. Erdős himself has number 0. His direct collaborators have number 1. A mathematician who has published with one of Erdős's collaborators has number 2. And so on. Most working mathematicians have a finite Erdős number; the average is about 5.
Was Erdős really homeless by choice?
Effectively, yes. He owned almost nothing, traveled constantly from one mathematician's home to another, and lived out of a suitcase. He gave most of his earnings and prize money away.
What was his 'SF'?
The Supreme Fascist — Erdős's affectionate, irritated name for the entity who hides the best mathematical proofs. 'The SF has The Book,' he would say, 'in which are written the best proofs of every theorem.' The goal of mathematics is to find those proofs.