# Mathematician:Paul Erdős

## Mathematician

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.*

## Nationality

Hungarian

## History

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

## Theorems and Inventions

- Erdős Conjecture on Arithmetic Progressions (still unsolved)

- Cameron-Erdős Conjecture (with Peter Cameron)
- Erdős-Anning Theorem (with Norman Herbert Anning)
- Erdős-Kac Theorem (with Mark Kac)
- Erdős-Ko-Rado Theorem (with Ke Zhao (Chao Ko) and Richard Rado)
- Erdős-Menger Conjecture (with Karl Menger)
- Erdős-Moser Conjecture (with Leo Moser)
- Erdős-Nagy Theorem (with Béla Szőkefalvi-Nagy)
- Erdős-Rado Theorem (with Richard Rado)
- Erdős-Straus Conjecture (with Ernst Gabor Straus)
- Erdős-Szekeres Theorem (with George Szekeres)

Results named for **Paul Erdős** can be found here.

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

## Publications

About $1500$ papers, including:

- 1932:
*Beweis eines Satzes von Tschebyschef*(*Acta Sci. Math. (Szeged)***Vol. 5**: pp. 194 – 198)

- 1935:
*A combinatorial problem in geometry*(*Compos. Math.***Vol. 2**: pp. 463 – 470) (with George Szekeres)

- 1935:
*Problems for Solution: 3739-3743*(*Amer. Math. Monthly***Vol. 42**: pp. 396 – 397) (with H.D. Ruderman, Maud Willey and Norman Anning) www.jstor.org/stable/2301373

- 1944:
*On Highly Composite and Similar Numbers*(*Trans. Amer. Math. Soc.***Vol. 56**,*no. 3*: pp. 448 – 469) (with L. Alaoglu) www.jstor.org/stable/1990319

- 1945:
*Integral distances*(*Bull. Amer. Math. Soc.***Vol. 51**: pp. 598 – 600) (with Norman H. Anning) (in which Erdős-Anning Theorem is presented)

- 1946:
*Note on Normal Numbers*(*Bull. Amer. Math. Soc.***Vol. 52**: pp. 857 – 860) (with A.H. Copeland)

- 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**)

- 1953:
*On linear independence of sequences in a Banach space*(with Ernst Gabor Straus)

- 1960:
*On the maximal number of pairwise orthogonal Latin squares of a given order*(with Sarvadaman Chowla and Ernst Gabor Straus)

- 1968:
*A theorem of finite sets*(in*Theory of Graphs*, co-edited with Gyula O.H. Katona)

- 1973:
*The Asymmetric Propeller*(*Math. Mag.***Vol. 46**,*no. 5*: pp. 270 – 272) (with Leon Bankoff and Murray S. Klamkin) www.jstor.org/stable/2688264

- 1988:
*Some diophantine equations with many solutions*(*Compos. Math.***Vol. 66**: pp. 37 – 56) (with C.L. Stewart and R. Tijdeman)

- 1993:
*Estimates of the Least Prime Factor of a Binomial Coefficient*(with J.L. Selfridge and C.B. Lacampagne)

## 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**.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $-1$ and $i$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $-1$ and $i$ - 1998: Paul Hoffman:
*The Man Who Loved Only Numbers* - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Erdős, Paul**(1913-96) - 2005: Clifford A. Pickover:
*A Passion for Mathematics*: Numbers, History, Society, and People: God's math book - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Erdős, Paul**(1913-96) - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**Erdős, Paul**(1913-96)