# Paul Erdős

Paul Erdős [also Erdős Pál, Pál Erdős, Erdos or Erdös] (26 March 1913 – 20 September 1996) was an immensely prolific and famously eccentric mathematician who, with hundreds of collaborators, worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory and probability theory.

## Quotes

* I think that, as Shelah, a very clever young Israeli mathematician, once said, "I am an opportunist. I do what I can do." If there is anything in number theory that I can do, I certainly do it. But you see some of the problems in number theory are enormously difficult and many of these classic problems are very, very hard to make any progress in.
** as quoted by Donald J. Albers and Gerald L. Alexanderson, Mathematical People: Profiles and Interviews. Contemporary Books. 1985. p. 86. ISBN 978-0-8092-4976-3.
* I'm not competent to judge. But no doubt he was a great man.
** Response to a question by an agent of the US Immigration and Naturalization Service in 1954 as to what he thought of Karl Marx, often cited as an indication of his detachment from political sensibilities and the situations of the McCarthy era. He was afterwards denied a return visa for re-entering the US until 1959, after attending the International Congress of Mathematicians in Amsterdam; as quoted in The Man Who Loved Only Numbers : The Story of Paul Erdős and the Search for Mathematical Truth (1998) by Paul Hoffman, p. 128
* Another roof, another proof.
** His motto, as he roamed about the world, as the guest of other mathematicians, as quoted in A Tribute to Paul Erdős (1990) edited by Alan Baker, Béla Bollobás, A. Hajnal, Preface, p. ix
* Suppose aliens invade the earth and threaten to obliterate it in a year's time unless human beings can find the Ramsey number for red five and blue five. We could marshal the world's best minds and fastest computers, and within a year we could probably calculate the value. If the aliens demanded the Ramsey number for red six and blue six, however, we would have no choice but to launch a preemptive attack.
** As quoted in "Ramsey Theory" by Ronald L. Graham and Joel H. Spencer, in Scientific American (July 1990), p. 112-117
* Television is something the Russians invented to destroy American education.
** As quoted in Comic Sections : The Book of Mathematical Jokes, Humour, Wit, and Wisdom (1993) by Des MacHale
* The SF created us to enjoy our suffering. … The sooner we die, the sooner we defy His plans.
** SF was an abbreviation for "Supreme Fascist" — the term Erdős often used to refer to God, as quoted in The Man Who Loved Only Numbers : The Story of Paul Erdős and the Search for Mathematical Truth (1998) by Paul Hoffman, p. 4
* Some French socialist said that private property was theft … I say that private property is a nuisance.
** Referring to a famous statement by the French anarchist Pierre-Joseph Proudhon that "Property is theft!", as quoted in The Man Who Loved Only Numbers (1998) by Paul Hoffman, p. 7
* My brain is open!
** A standard greeting he would make when he was not contemplating some mathematical problem, as quoted in My Brain Is Open : The Mathematical Journeys of Paul Erdos (1998) by Bruce Schechter, p. 10
* If numbers aren't beautiful, I don't know what is.
** Frequent remark, as quoted in My Brain Is Open : The Mathematical Journeys of Paul Erdos (1998) by Bruce Schechter, p. 14
* It is not enough to be in the right place at the right time. You should also have an open mind at the right time.
** My Brain Is Open : The Mathematical Journeys of Paul Erdos (1998) by Bruce Schechter, p. 99
* Végre nem butulok tovább
** Finally I am becoming stupider no more.
** A suggestion for his own epitaph, as quoted in Variety in Religion and Science: Daily Reflections (2005) by Varadaraja Raman, p. 256
* We'll continue tomorrow — if I live.
** Common remark when breaking off work for the night, as quoted in "The Magician of Budapest" in The Edge of the Universe : Celebrating Ten Years of Math Horizons (2007) by Deanna Haunsperger and Stephen Kennedy, p. 111
* This one's from the Book!
** Said in regard to any particularly beautiful or elegant proof, referring to a mythical "book" in which God wrote the proofs for all theorems, as quoted in Philosophy of Mathematics (2008) by John Francis, p. 51
* SF means Supreme Fascist — this would show that God is bad. I don't claim that this is correct, or that God exists, but it is just sort of half a joke. … As a joke I said, "What is the purpose of Life?" "Proof and conjecture, and keep the SF's score low." Now, the game with the SF is defined as follows: If you do something bad the SF gets at least two points. If you don't do something good which you could have done, the SF gets at least one point. And if nothing — if you are okay, then no one gets any point. And the aim is to keep the SF's score low.
** Paul Erdős - SF means Supreme Fascist

## Misattributed

* God may not play dice with the universe, but something strange is going on with the prime numbers.
** Referencing Albert Einstein's famous remark that "God does not play dice with the universe", this is attributed to Erdős in "Mathematics : Homage to an Itinerant Master" by D. Mackenzie, in Science 275:759 (1997), but has also been stated to be a comment originating in a talk given by Carl Pomerance on the Erdős-Kac theorem, in San Diego in January 1997, a few months after Erdős's death. Confirmation of this by Pomerance is reported in a statement posted to the School of Engineering, Computer Science & Mathematics, University of Exeter, where he states it was a paraphrase of something he imagined Erdős and Mark Kac might have said, and presented in a slide-show, which subsequently became reported in a newspaper as a genuine quote of Erdős the next day. In his slide show he had them both reply to Einstein's assertion: "Maybe so, but something is going on with the primes."
* A mathematician is a machine for turning coffee into theorems.
** Widely attributed to Erdős, this actually originates with Alfréd Rényi, according to My Brain Is Open : The Mathematical Journeys of Paul Erdős (1998) by Bruce Schechter, p. 155
** Variant: A mathematician is a device for turning coffee into theorems.
* The first sign of senility is that a man forgets his theorems, the second sign is that he forgets to zip up, the third sign is that he forgets to zip down.
** Though Erdős used this remark, it is said to have originated with his friend Stanisław Ulam, as reported in The Man Who Loved Only Numbers : The Story of Paul Erdős and the Search for Mathematical Truth (1998) by Paul Hoffman
** Variants:
** The first sign of senility is when a man forgets his theorems. The second sign is when he forgets to zip up. The third sign is when he forgets to zip down.
** As quoted in Wonders of Numbers : Adventures in Mathematics, Mind, and Meaning (2002) by Clifford A. Pickover, p. 64
** There are three signs of senility. The first sign is that a man forgets his theorems. The second sign is that he forgets to zip up. The third sign is that he forgets to zip down.

## Quotes about Erdős

    Sorted alphabetically by author or source
* Erdős knows about more problems than anybody else, and he not only knows about various problems and conjectures, but he also knows the tastes of various mathematicians. So if I get a letter from him giving me three of his conjectures and two of his problems, then it's sure that these are exactly the kind of conjectures and problems I'm interested in, and these are exactly the kind of questions I may be able to answer. Of course, this applies not only to me, but to everybody else. So Erdős has an amazing ability to match problems with people. Which is why so many mathematicians benefit from his presence. Every letter is likely to inspire you to do some work, or every phone call will give you some problems you are interested in.
** Béla Bollobás, of Trinity College, University of Cambridge in N Is a Number: A Portrait of Paul Erdős (1993)
* Paul Erdős is the consummate problem solver: his hallmark is the succinct and clever argument, often leading to a solution from "the book". He loves areas of mathematics which do not require an excessive amount of technical knowledge but give scope for ingenuity and surprise. The mathematics of Paul Erdős is the mathematics of beauty and insight.
** Preface to A Tribute to Paul Erdős (1990) edited by Alan Baker, Béla Bollobás, and A. Hajnal
* One of my greatest regrets is that I didn't know him when he was a million times faster than most people. When I knew him he was only hundreds of times faster.
** Neil Calkin, one of Erdős's last collaborators, as quoted in My Brain Is Open : The Mathematical Journeys of Paul Erdos (1998) by Bruce Schechter, p. 119
* Hungarian mathematician Paul Erdős, although an atheist, spoke of an imaginary book, in which God has written down all the most beautiful mathematical proofs. When Erdős wanted to express particular appreciation of a proof, he would exclaim "This one's from the Book!". This viewpoint expresses the idea that mathematics, as the intrinsically true foundation on which the laws of our universe are built, is a natural candidate for what has been personified as God by different religious mystics.
** John Francis, in Philosophy of Mathematics (2008), p. 51
* He was an absolutely wonderful man. He was interested in everything. You felt right away that you are not dealing with one of your colleagues or an average guy. He was a genius, his thoughts were all over the place. I've met very smart people. I have never met a genius before. … He basically disregarded any disciplined approach to anything.
** Dr. Jonas Gellert, his cardiologist, as quoted in My Brain Is Open : The Mathematical Journeys of Paul Erdos (1998) by Bruce Schechter, p. 119
* Probably the greatest mathematician of the twentieth century, Paul Erdős … was so eccentric that he made Einstein look normal. He was 11 before he ever tied his shoes, 21 before he ever buttered toast, and died without ever boiling an egg. Erdős lived on the road, traveling from conference to conference, owning nothing but math notebooks and a suitcase or two. His life consisted of math, nothing else.
** Clifford Goldstein, in The Mules That Angels Ride (2005), p. 125
* This book is dedicated to Paul Erdos, who not only possessed the art of asking the right question, but of asking it of the right person.
** Richard K. Guy in Unsolved Problems in Number Theory, 3rd Edition (2004)
* The SF is the Supreme Fascist, the Number-One Guy Up There, God, who was always tormenting Erdős by hiding his glasses, stealing his Hungarian passport, or, worse yet, keeping to Himself the elegant solutions to all sorts of intriguing mathematical problems.
** Paul Hoffman, in The Man Who Loved Only Numbers : The Story of Paul Erdős and the Search for Mathematical Truth (1998), p. 4
* He wrote or co-authored 1,475 academic papers, many of them monumental, and all of them substantial. It wasn't just the quantity of work that was impressive but the quality: "There is an old saying," said Erdős. "Non numerantur, sed ponderantur (They are not counted but weighed).
** Paul Hoffman, in The Man Who Loved Only Numbers : The Story of Paul Erdős and the Search for Mathematical Truth (1998), p. 6
* In a never-ending search for good mathematical problems and fresh mathematical talent, Erdős crisscrossed four continents at a frenzied pace, moving from one university or research center to the next. His modus operandi was to show up on the doorstep of a fellow mathematician, declare, "My brain is open," work with his host for a day or two, until he was bored or his host was run down, and then move on to another home. Erdős's motto was not "Other cities, other maidens" but "Another roof, another proof." He did mathematics in more than 25 different countries, completing important proofs in remote places and sometimes publishing them in equally obscure journals.
** Paul Hoffman, in The Man Who Loved Only Numbers : The Story of Paul Erdős and the Search for Mathematical Truth (1998), p. 6
* His language had a special vocabulary — not just "the SF" [God] and "epsilon" [child] but also "bosses" (women), "slaves" (men), "captured" (married), "liberated" (divorced), "recaptured" (remarried), "noise" (music), "poison" (alcohol), "preaching" (giving a mathematics lecture), "Sam" (the United States), and "Joe" (the Soviet Union). When he said someone had "died," Erdős meant that the person had stopped doing mathematics. When he said someone had "left," the person had died.
** Paul Hoffman, in The Man Who Loved Only Numbers : The Story of Paul Erdős and the Search for Mathematical Truth (1998), p. 8
* In the late 1980s Erdős heard of a promising high school student named Glen Whitney who wanted to study mathematics at Harvard but was a little short the tuition. Erdős arranged to see him and, convinced of the young man's talent, lent him $1,000. He asked Whitney to pay him back only when it would not cause financial strain. A decade later Graham heard from Whitney, who at last had the money to repay Erdős. "Did Erdős expect me to pay interest?" Whitney wondered. "What should I do?" he asked Graham. Graham talked to Erdős. "Tell him," Erdős said, "to do with the $1,000 what I did."
** Paul Hoffman, in The Man Who Loved Only Numbers : The Story of Paul Erdős and the Search for Mathematical Truth (1998), p. 10
* As a mathematician Erdös is what in other fields is called a "natural". If a problem can be stated in terms he can understand, though it may belong to a field with which he is not familiar, he is as likely as, or even more likely than, the experts to find a solution.
** Mark Kac, Enigmas Of Chance, p. 93
* Paul Erdős (1913–1996) was once told that a friend of his had shot and killed his wife. Without blinking an eye, Erdős said, "Well, she was probably interrupting him when he was trying to prove a theorem."
** Steven G. Krantz, Mathematical Apocrypha Redux: More Stories and Anecdotes of Mathematicians and the Mathematical. American Mathematical Society. 25 November 2019. p. 4. ISBN 9781470451721. (1st edition, 2005)
* In the early 1960s, when I was a student at University College London … Erdős came to visit us for a year. After collecting his first month's salary he was accosted by a beggar on Euston station, asking for the price of a cup of tea. Erdős removed a small amount from the pay packet to cover his own frugal needs and gave the remainder to the beggar.
** D. G. Larman, as quoted in The Man Who Loved Only Numbers : The Story of Paul Erdős and the Search for Mathematical Truth (1998) by Paul Hoffman, p. 10
* A conjecture both deep and profound Is whether a circle is round. In a paper of Erdős Written in Kurdish A counterexample is found.
** Limerick attributed to Leo Moser, in Handbook of Combinatorics (1995) edited by Ronald L. Graham, Ch. 17
** Variant:
** A conjecture thought to be sound Was that every circle was round In a paper of Erdős written in Kurdish A counterexample is found!
*** Attributed to an unnamed colleague, quoted in "The Magician of Budapest" by Peter Schumer, in The Edge of the Universe : Celebrating Ten Years of Math Horizons (2007) by Deanna Haunsperger and Stephen Kennedy, p. 110
* He was the Bob Hope of mathematics, a kind of vaudeville performer who told the same jokes and the same stories a thousand times. … When he was scheduled to give yet another talk, no matter how tired he was, as soon as he was introduced to an audience, the adrenaline (or maybe amphetamine) would release into his system and he would bound onto the stage, full of energy, and do his routine for the 1001st time.
** Melvyn Nathanson, as quoted in The Man Who Loved Only Numbers : The Story of Paul Erdős and the Search for Mathematical Truth (1998), p. 11
* "Want to meet Erdos?" mathematicians would ask. "Just stay here and wait. He'll show up."
** Bruce Schechter, in My Brain Is Open : The Mathematical Journeys of Paul Erdos (1998), p. 14
* He loved to play silly tricks to amuse children and to make sly jokes and thumb his nose at authority. But most of all, Erdős loved those who loved numbers, mathematicians.
** Bruce Schechter, in My Brain Is Open : The Mathematical Journeys of Paul Erdos (1998), p. 17
* Twenty hours of work a day was not unusual. Upon arriving at a meeting, he would announce, in his thick Hungarian accent, "my brain is open." At parties, he would often stand alone oblivious to all else, deep in thought pondering some difficult argument.
** Peter Schumer in "The Magician of Budapest" in The Edge of the Universe : Celebrating Ten Years of Math Horizons (2007) by Deanna Haunsperger and Stephen Kennedy, p. 110
* Nothing bothered Erdős more than political strictures which did not allow for complete freedom of expression and the ability to travel freely. … Always traveling with a single shabby suitcase which doubled as a briefcase, he had little need or interest in the material world.
** Peter Schumer in "The Magician of Budapest" in The Edge of the Universe : Celebrating Ten Years of Math Horizons (2007) by Deanna Haunsperger and Stephen Kennedy, p. 110

## External links

* Searchable collection of (almost) all papers of Erdős
* "Paul Erdős", at the MacTutor History of Mathematics archive
* Profile at Math Geneology
* Jerry Grossman at Oakland University. The Erdős Number Project
* The Man Who Loved Only Numbers - Royal Society Public Lecture by Paul Hoffman (video)
* Erdős in Memphis 1996 part 2
* Erdős in Memphis 1996 part 3
* Radiolab: Numbers, with a story on Paul Erdős
* Paul Erdős anecdotes
Mathematics :
| Mathematicians (by country) | Abel • Anaxagoras • Archimedes • Aristarchus of Samos • Averroes • Arnold • Banach • Cantor • Cartan • Chern • Cohen • Descartes • Diophantus • Erdős • Euclid • Euler • Fourier • Gauss • Gödel • Grassmann • Grothendieck • Hamilton • Hilbert • Hypatia • Lagrange • Laplace • Leibniz • Milnor • Newton • von Neumann • Noether • Penrose • Perelman • Poincaré • Pólya • Pythagoras • Riemann • Russell • Schwartz • Serre • Tao • Tarski • Thales • Turing • Weil • Weyl • Wiles • Witten |
| Numbers | 1 • 23 • 360 • e • π • Fibonacci numbers • Irrational number • Negative number • Number • Prime number • Quaternion • Octonion |
| Concepts | Abstraction • Algorithms • Axiomatic system • Completeness • Deductive reasoning • Differential equation • Dimension • Ellipse • Elliptic curve • Exponential growth • Infinity • Integration • Geodesic • Induction • Proof • Partial differential equation • Principle of least action • Prisoner's dilemma • Probability • Randomness • Theorem • Topological space • Wave equation |
| Results | Euler's identity • Fermat's Last Theorem |
| Pure math | Abstract algebra • Algebra • Analysis • Algebraic geometry (Sheaf theory) • Algebraic topology • Arithmetic • Calculus • Category theory • Combinatorics • Commutative algebra • Complex analysis • Differential calculus • Differential geometry • Differential topology • Ergodic theory • Foundations of mathematics • Functional analysis • Game theory • Geometry • Global analysis • Graph theory • Group theory • Harmonic analysis • Homological algebra • Invariant theory • Logic • Non-Euclidean geometry • Nonstandard analysis • Number theory • Numerical analysis • Operations research • Representation theory • Ring theory • Set theory • Sheaf theory • Statistics • Symplectic geometry • Topology |
| Applied math | Computational fluid dynamics • Econometrics • Fluid mechanics • Mathematical physics • Science |
| History of math | Ancient Greek mathematics • Euclid's Elements • History of algebra • History of calculus • History of logarithms • Indian mathematics • Principia Mathematica |
| Other | Mathematics and mysticism • Mathematics education • Mathematics, from the points of view of the Mathematician and of the Physicist • Philosophy of mathematics • Unification in science and mathematics |