Mathematician:Paul Erdős

From ProofWiki
Jump to navigation Jump to search


Hungarian mathematician known for the vast quantity of work he did (approximately 1500 papers).

Spent his entire life travelling the world looking for interesting mathematical problems to solve.

Interesting to him often meant: easy to state, but difficult to solve.

Perhaps most famous for his widespread collaborations (about 500 collaborators), from which the concept of the Erdős Number emerged.

Found an elementary proof of the Prime Number Theorem at the same time as Atle Selberg. Exactly what happened in $1948$ has been discussed a great deal in the years following. See Erdős-Selberg dispute for a fairly unbiased account.

Because of his widespread influence, there are many stories in circulation about Erdős, not all of which are completely true, so don't believe everything you read about him (even this!) -- its source may be flawed.

Wolf Prize

Paul Erdős was awarded a Wolf Prize for Mathematics in $\text {1983/84}$:

For his numerous contributions to number theory, combinatorics, probability, set theory and mathematical analysis, and for personally stimulating mathematicians the world over.




  • Born: 26 March 1913, Budapest, Hungary
  • Died: September 20, 1996, Warsaw, Poland

Theorems and Inventions

Results named for Paul Erdős can be found here.

Definitions of concepts named for Paul Erdős can be found here.


About $1500$ papers, including:

  • 1949: On a new method in elementary number theory which leads to an elementary proof of the prime number theorem
  • 1950: Az $1 / x_1 + 1 / x_2 + \cdots + 1/x_n = a / b$ egyenlet egész számú megoldásairól (On a Diophantine Equation) (Mat. Lapok Vol. 1)
  • 1968: A theorem of finite sets (in Theory of Graphs, co-edited with Gyula O.H. Katona)

Notable Quotes

If you subtract $250$ from $100$, you get $150$ below zero.
-- at the age of $4$ to his mother

A mathematician is a machine for turning coffee into theorems.

God has a transfinite book with all the theorems and their best proofs. You don't really have to believe in God as long as you believe in the book.

Also known as

In Hungarian, Paul Erdős is Erdős Pál.

His surname can often be seen without its diacritic: Erdos.

Some sources incorrectly use the wrong diacritic: Erdös.