# Paul Erdős

### Learn more about Paul Erdős

Born | March 26, 1913 Budapest, Hungary <tr><th>Died</th><td>September 20, 1996 |
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**Paul Erdős**, also **Pál Erdős**, in English **Paul Erdos** or **Paul Erdös** (March 26, 1913 – September 20, 1996), was an immensely prolific (and famously eccentric) Hungarian mathematician who, with hundreds of collaborators, worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory and probability theory.

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## [edit] Biography

He was born in Budapest, Hungary as **Erdős Pál**. (Erdős is pronounced as IPA /ɛrdøːʃ/.) After his siblings died before his birth at the ages of 3 and 5, he was the only child of Anna and Lajos Erdős. His parents were both Jewish mathematicians, from a vibrant intellectual community.<ref>The Budapest Jewish community of that day produced at least six remarkable thinkers besides Erdős: Eugene Wigner (or Wigner Jenő in Hungarian), the physicist and engineer; Edward Teller (or Teller Ede in Hungarian), the physicist; Leó Szilárd, the physicist; John von Neumann (or Neumann János in Hungarian), the mathematician and polymath; Dénes Gábor, the physicist; and Georg Lukács (or Lukács György in Hungarian), the philosopher.</ref> He could add at age 3 and at age 4 he could calculate for friends of the family how many seconds they had lived (Hoffman 1998). Erdős showed early promise as a prodigy, and soon became regarded as a mathematical genius by his peers.

In 1934, he was awarded a doctorate in mathematics.<ref>Erdős's thesis advisor at Eötvös Loránd University was Leopold Fejér (or Fejér Lipót), who was also the thesis advisor for John von Neumann, George Pólya and Paul (Pál) Turán.</ref> Because anti-semitism was increasing, he moved that same year to Manchester, England to be a guest lecturer. In 1938, he accepted his first American position as a scholarship holder at Princeton University. At this time, he began to develop the habit of traveling from campus to campus. He would not stay long in one place and traveled back and forth between mathematical institutions until his death.

Possessions meant little to Erdős; most of his belongings would fit in a suitcase, as dictated by his itinerant lifestyle. Awards and other earnings were in general donated to people in need and various worthy causes. He spent most of his life as a vagabond, travelling between scientific conferences and the homes of colleagues all over the world. He would typically show up at a colleague's doorstep and announce "my brain is open", staying long enough to collaborate on a few papers before moving on a few days later. In many cases, he would ask the current collaborator about whom he (Erdős) should visit next. His working style has been humorously compared to traversing a linked list.

As his colleague Alfréd Rényi said, "a mathematician is a machine for turning coffee into theorems", and Erdős drank copious quantities. (This quote is often attributed to Erdős, but does seem to originate with Rényi.) <ref>Biography of Alfréd Rényi by J.J. O'Connor and E.F. Robertson</ref> After 1971 he also took amphetamines, despite the concern of his friends, one of whom (Ron Graham) bet him $500 that he could not stop taking the drug for a month. Erdős won the bet, but complained that mathematics had been set back by a month: "Before, when I looked at a piece of blank paper my mind was filled with ideas. Now all I see is a blank piece of paper." The bet won, he promptly resumed his amphetamine habit.

He had his own idiosyncratic vocabulary: he spoke of "The Book," an imaginary book in which God had written down the best and most elegant proofs for mathematical theorems. Lecturing in 1985 he said, "You don't have to believe in God, but you should believe in *The Book*." He himself doubted the existence of God, whom he called the "Supreme Fascist" (SF), but accused the SF of hiding his socks and Hungarian passports, and of keeping the most elegant mathematical proofs to himself. When he saw a particularly beautiful mathematical proof he would exclaim, "This one's from *The Book*!".

Other idiosyncratic elements of Erdős' vocabulary include: children were referred to as "epsilons"; women were "bosses"; men were "slaves"; people who stopped doing math had "died"; people who died had "left"; alcoholic drinks were "poison"; music was "noise"; and, to give a mathematical lecture was "to preach." Also, all countries which he thought failed to provide freedom to individuals as long as they did no harm to anyone else were classified as imperialist and given a name that began with a lowercase letter. For example, the U.S. was "samland" (after Uncle Sam), the Soviet Union was "joedom" (after Joseph Stalin), and Israel was "israel". For his epitaph he suggested, "I've finally stopped getting dumber." (Hungarian: "Végre nem butulok tovább").

He died "in action" of a heart attack on September 20, 1996 at the age of 83, while attending a conference in Warsaw, Poland. Erdős never married and left no offspring. Since Erdős' "leaving", a book entitled *Proofs from the Book* has been published, intended as a collection of the most beautiful mathematical proofs in the spirit of Erdős.

## [edit] Mathematical work

Erdős was one of the most prolific publishers of papers in mathematical history, second only to Leonhard Euler; Erdős published more papers, while Euler published more pages (Hoffman 1998). He wrote around 1,500 mathematical articles in his lifetime, mostly with co-authors. He had about 500 different collaborators, and strongly believed in (and obviously practiced) mathematics as a social activity.

Of his contributions, the development of Ramsey theory and the application of the probabilistic method especially stand out. Extremal combinatorics owes to him a whole approach, derived in part from the tradition of analytic number theory. Erdős found a proof for Bertrand's postulate which proved to be far neater than Chebyshev's original one. He also discovered an elementary proof for the Prime number theorem, along with Atle Selberg, which showed how combinatorics was an efficient method of counting collections.

## [edit] Collaborations

Among his frequent collaborators were

- Yousef Alavi
- Béla Bollobás
- Stefan Burr
- Fan Chung
- Ralph Faudree
- Ron Graham
- András Gyárfás
- András Hajnal
- Eric Milner
- János Pach
- Carl Pomerance
- Richard Rado (one of the co-authors of the famous Erdős–Ko–Rado theorem)
- Alfréd Rényi
- Vojtech Rődl
- C. C. Rousseau
- Andras Sárközy
- Dick Schelp
- Miklós Simonovits
- Vera Sós
- Joel Spencer
- Endre Szemerédi
- Víctor Neumann-Lara
- Paul Turán
- Peter Winkler

## [edit] Erdős number

Because of his prolific output, friends created the **Erdős number** as a humorous tribute; Erdős alone was assigned the Erdős number of 0 (for being himself), while his immediate collaborators could claim an Erdős number of 1, their collaborators have Erdős number at most 2, and so on. Some have estimated that 90% of the world's active mathematicians have an Erdős number smaller than 8 (not surprising in the light of the small world phenomenon). It is jokingly said that Baseball Hall of Famer Hank Aaron has an Erdős number of 1 because they both autographed the same baseball when Emory University awarded them honorary degrees on the same day. Erdős numbers have also been humorously assigned to an infant, a horse and several actors. For details see the "Extended Erdős Number Project" [1]

The Erdős number was most likely first defined by Casper Goffman, an analyst whose own Erdős number is 1.<ref>[2] Michael Golomb's obituary of Paul Erdős</ref> Goffman published his observations about Erdős's prolific collaboration in a 1969 article entitled "*And what is your Erdős number?*"<ref>Template:Cite journal</ref>

## [edit] DVD collection of his works

A collection on DVD of his writings has been compiled, and is currently available under the title "N is a Number - A Portrait of Paul Erdos".

## [edit] Notes

<references/>

## [edit] References

- Aigner, M., Ziegler, G.M., Hofmann, K.H.;
*Proofs from THE BOOK*(3/e). Springer, 2004. ISBN 3540404600. - Hoffman, Paul;
*The man who loved only numbers*. Hyperion, 1998. ISBN 0786863625. - The Mathematics Genealogy Project - Paul Erdős
- Schechter, Bruce;
*My brain is open*. Touchstone, 2000. ISBN 0684859807*(biography)*.

## [edit] See also

- Erdős conjectures
- Erdős–Borwein constant
- Erdős–Gyárfás conjecture
- Erdős–Ko–Rado theorem
- Erdős–Ginzburg–Ziv theorem
- Erdős–Kac theorem
- Erdős–Szekeres theorem
- Erdős–Woods number
- Erdős cardinal
- Erdős number
- Prime number theorem

## [edit] External links

- O'Connor, John J., and Edmund F. Robertson. "Paul Erdős".
*MacTutor History of Mathematics archive*. - Paul Erdős at the Mathematics Genealogy Project
*N is a Number: a portrait of Paul Erdős*- Summary of Erdős's life from the American Mathemactical Society
- Jerry Grossman at Oakland University.
*The Erdös Number Project* - The Man Who Loved Only Numbers - Royal Society Public Lecture by Paul Hoffman (RealVideo)
- His biography at Hungary.hu
- Obituary from the Washington Post
- A tribute to Paul Erdos (anecdotes)

Persondata | |
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NAME | Erdős, Paul |

ALTERNATIVE NAMES | Erdos, Paul (Anglicization); Erdős Pál (Birth name) |

SHORT DESCRIPTION | Mathematician |

DATE OF BIRTH | March 26, 1913 |

PLACE OF BIRTH | Budapest, Hungary |

DATE OF DEATH | September 20, 1996 |

PLACE OF DEATH | Warsaw, Poland |

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Categories: 1913 births | 1996 deaths | 20th century mathematicians | Combinatorists | Hungarian Jews | Hungarian mathematicians | Hungarian people | Atheist mathematicians | Jewish mathematicians | Number theorists | Graph theorists | Wolf Prize recipients