N is a Number: A Portrait of Paul Erdős (1913-1996)

“The purpose of life is to conjecture and prove”

~ Paul Erdős

If you’ve never heard of the Hungarian mathematician, Paul Erdős (pronounced “air dish”), it’s time you have, for the sheer implausibility of his life – colorful and drab at the same time, and for his prodigious gift of genius to mathematics. When asked how to best describe his friend, mathematician Joel Spencer (1946-) said:

Mathematical truth is immutable; it lies outside physical reality … This is our belief; this is our core motivating force. Yet our attempts to describe this belief to our nonmathematical friends are akin to describing the Almighty to an atheist. Paul embodied this belief in mathematical truth. His enormous talents and energies were given entirely to the Temple of Mathematics. He harbored no doubts about the importance, the absoluteness, of his quest.

Paul Erdos is to this day remembered as the man who devoted his entire life to mathematics. For an engrossing book on the life of this quaint mathematician, I recommend The Man Who Loved Only Numbers (1998) by Paul Hoffman.

An excerpt from the book:

“Paul Erdős had managed to think about more problems than any other mathematician in history. He wrote or co-authored 1,475 academic papers, many of them monumental, and all of them substantial. Mathematicians now compute their “Erdős number,” a six-degrees-of-separation number that describes how many people it would take to connect you to an Erdős paper. It wasn’t just the quantity of work that was impressive but the quality: “There is an old saying,” said Erdős. “Non numerantur, sed ponclerantur (They are not counted but weighed).

Erdős structured his life to maximize the amount of time he had for mathematics. He had no wife or children, no job, no hobbies, not even a home, to tie him down. He lived out of a shabby suitcase and a drab orange plastic bag from Centrum Aruhaz (“Central Warehouse”), a large department store in Budapest. 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 “Another roof, another proof.” He did mathematics in more than twenty-five different countries, completing important proofs in remote places and sometimes publishing them in equally obscure journals.”

Paul Erdős at the University of Cambridge in 1990. Photo: Simons Foundation, 1990.
Erdős influenced many young mathematicians. In this 1985 photo taken at the University of Adelaide, Erdős explains a problem to Terence Tao — who was 10 years old at the time. Tao received the Fields Medal in 2006 and was elected a Fellow of the Royal Society in 2007.
Erdős in deep thought, 1960.
Erdős and Vera Sos in Princeton in 1985, during a period of intense collaboration on extremal graph theory.
Erdős enjoyed working with several mathematicians on entirely different problems simultaneously. Left to right: G. Grätzer, Erdős, Paul Turán, and Alfréd Rényi at Dobogóko˝, Hungary, 1959. Turán was one of his closest friends and his first major collaborator. Hw and Turán worked together on a variety of subjects in number theory, classical analysis, combinatorics, and statistical group theory.
Erdős giving a lecture.
“A mathematician is a device for turning coffee into theorems” Paul Erdős


Erdős was fond of the idea that God has a volume containing the perfect proof of every mathematical theorem. “This one is from The Book,” he would declare when he wanted to bestow his highest praise on a beautiful proof. Never mind that Erdős doubted God’s very existence.

Erdős’s whimsical idea piqued the mathematician Martin Aigner, and in 1994, during conversations with Erdős at the Oberwolfach Research Institute for Mathematics in Germany, he came up with the idea of compiling a book of the world’s most beautiful mathematical proofs, something that naturally excited Erdős himself. Together with fellow mathematician Günter Ziegler, the two started collecting examples of exceptionally beautiful proofs, with enthusiastic contributions from Erdős which was in 1998 published as Proofs From THE BOOK. Sadly it too late for Erdős to see it – he had died in 1996, at age 83. “Many of the proofs trace directly back to him, or were initiated by his supreme insight in asking the right question or in making the right conjecture,” Aigner and Ziegler, who are now both professors at the Free University of Berlin, write in the preface.

~ Adapted from “In Search of God’s Perfect Proofs”, Quanta Magazine. Mar 19, 2018.

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