# Paul Erdös

Paul Erdös was one of the greatest mathematicians of our century. He was definitely the most prolific. He was doing mathematics all the way up to his death on September 20th, 1996. He gave a lecture just hours before he died in Warsaw. He lived on coffee, doing mathematics 19 hours a day, 7 days a week. He was quoted as saying "A mathematician is a machine for turning coffee into theorems."

He pioneered the branch of mathematics called Ramsey Theory. It is the belief that total disorder is impossible. A problem in Ramsey Theory is what is the smallest set that contains a certain object. For example: What is the smallest group of people that contains two people of the same sex? The answer is three.

The classic example is the "party problem". What is the smallest party which will contain a certain number of people who know each other or who are all strangers? For three people the answer is six. Consider a party of 6. Let one member of the party be named Brent. Since Brent either knows or doesn't each person he will know at least 3 people or not know at least 3. Assume he knows 3. If any 2 of the people he knows know each other we will have the 3 we needed. If they all are strangers we have 3 that don't know each other and we are done. The reason why 5 would not work is that Brent could know two of the five people and each person he knows could only know one of the people he doesn't know.

Erdös worked with more mathematicians than any other mathematician of our age. He published so many papers that a humorous way of measuring a mathematician was formed called the Erdös number. A mathematician's Erdös number depends on how close one was to publishing a paper with Erdös. If you published a paper with Erdös you had a Erdös number of one. If you published a paper with someone who published a paper with Erdös, your number was 2 and so on.

Erdös has published more papers than any other mathematician, even Euler! He published at least 1512 of them. More importantly, Erdös created more good problems for others to solve than anyone else ever did. He made mathematicians in 25 countries convert conjectures into proofs. He wanted to die like Euler did. Euler died moments after calculating the orbit of Uranus on September 18, 1783. Erdös died a day after solving his last problem or at least the last problem he shared with the world.

This entry contributed by John P. Bush.

**Related pages** (outside of this work)

- The Erdös Number Project A listing of Erdös numbers.

**References:**

- Hoffman1999
P. Hoffman,The man who loved only numbers: the story of Paul Erdös and the search for mathematical truth, Hyperion Press, New York, 1998. pp. viii+302, ISBN 0-7868-6362-5.MR 2001b:01024- Kanigel1992
R. Kanigel,The man who knew infinity, Pocket Books, 1992. New York, NY, ISBN 0671750615.MR 92e:01063- Schechter1998
B. Schechter,My brain is open: the mathematical journeys of Paul Erdös, Simon \& Schuster, 1998. New York, NY, ISBN 0-684-84635-7; 0-684-85980-7.MR 99h:01038