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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.
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Preface to A Tribute to Paul Erdős (1990) edited by Alan Baker, Béla Bollobás, and A. Hajnal

 

Paul Erdos

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Hunagarian 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.

 

Paul Erdos

 

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 Erdos

 

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 Erdos

 

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 Erdos

 

The sphere of mathematics is here extended, in accordance with the derivation of its name, to all demonstrative research, so as to include all knowledge strictly capable of dogmatic teaching. Mathematics is not the discoverer of laws, for it is not induction; neither is it the framer of theories, for it is not hypothesis; but it is the judge over both, and it is the arbiter to which each must refer its claims ; and neither law can rule nor theory explain without the sanction of mathematics. It deduces from a law all its consequences, and develops them into the suitable form for comparison with observation, and thereby measures the strength of the argument from observation in favor of a proposed law or of a proposed form of application of a law.
Mathematics, under this definition, belongs to every enquiry, moral as well as physical. Even the rules of logic, by which it is rigidly bound, could not be deduced without its aid. The laws of argument admit of simple statement, but they must be curiously transposed before they can be applied to the living speech and verified by,observation.

 

Benjamin Peirce