The Prolific Machine
Erdős published his first paper at 20 — a new proof of Chebyshev's theorem that there is always a prime between n and 2n. By his death he had published more papers than any mathematician in history. He wrote until the end, producing significant work in his 80s.
Number Theory and Combinatorics
Erdős's primary domains were number theory, combinatorics, and graph theory. With Atle Selberg, he found an elementary proof of the prime number theorem — a result many thought required complex analysis. In combinatorics he essentially invented the probabilistic method: proving objects exist by showing a random construction yields them with positive probability.
The Erdős Number
Because Erdős collaborated so widely, mathematicians invented the Erdős number: a direct collaborator has Erdős number 1; a collaborator's collaborator has number 2; and so on. Having a low Erdős number became a mark of mathematical achievement. Einstein's Erdős number was 2.
Amphetamines and Mathematics
Erdős took amphetamines for decades, maintaining they allowed him to work productively. When a friend bet him $500 he couldn't stop for a month, he did — then said he had set mathematics back by a month and resumed immediately.
Frequently Asked Questions
How many papers did Paul Erdős publish?
Erdős published over 1,500 mathematical papers with more than 500 co-authors, making him the most prolific mathematician in history. His output spanned number theory, combinatorics, graph theory, and probability.
What is the Erdős number?
The Erdős number measures a mathematician's collaborative distance from Erdős. A direct co-author has Erdős number 1; their co-authors have number 2; and so on. It became a measure of proximity to the mathematical community's center.
Why did Erdős have no home?
Erdős deliberately chose a nomadic life, owning almost nothing and traveling constantly between mathematical collaborators worldwide. He gave away most money he received to students and charities. He believed possessions were a distraction from mathematics.
