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f(Erdős) = 100

Today is the 100th anniversary of the birth of Paul Erdős, or as most people would call it, Erdős’ 100th birthday. So, Happy Birthday Paul. And if you’ve never heard of him, let’s see what people at his birthday party are saying about the Man Who Loved Only Numbers. Please note: all birthday parties are strictly fictional.

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

Born in Hungary in 1913, Paul Erdős was the one of most prolific mathematicians of all time: the honour of most pages published goes to Leonhard Euler, but Erdős has the most papers published in collaboration with others – around 1,525. He worked as a nomad, travelling between conferences and other mathematicians’ hospitality, and wherever he went he created fantastic collaborations with the world’s greatest mathematicians.

Another roof, another proof.

– Erdős’ motto, as quoted in A Tribute to Paul Erdős (1990) edited by Alan Baker, Béla Bollobás, A. Hajnal, Preface, p. ix

Erdős worked in many areas of pure mathematics – combinatorics, graph theory, number theory, set theory and probability theory to name a few. He collaborated with 511 different mathematicians, and was always travelling – his possessions fit in a suitcase, and most of his earnings and awards were generally donated to charity.

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.

– Béla Bollobás, of Trinity College, University of Cambridge in N Is a Number: A Portrait of Paul Erdős (1993)

Erdős is responsible for many recent great developments in mathematics, including the introduction of Ramsey Theory (a branch of graph theory), as well as many proofs in number theory and combinatorics. He was said to have a brilliant mind, and a natural talent for understanding mathematical problems.

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

He also offered prizes for mathematical problems he wanted to see solved – from $25 for problems he thought were within reach, to thousands of dollars for more difficult and significant results. The prizes remain on offer today, administrated by Ron Graham who can send you a cheque signed by Erdős for framing, or a cashable check signed by himself. For a solution to the Collatz conjecture, Erdős offers $500.

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 Erdős (1998), p. 17

Being such a prolific author, and working with so many other mathematicians, means that not only is Erdős a great example of how mathematics is a collaborative and living subject, but he is also a highly connected node in the graph of mathematical authorship. Like Kevin Bacon in the film industry (see Six Degrees of Kevin Bacon), proximity via joint authorship to Erdős is a prized achievement, and a mathematician can calculate their “Erdős Number” to measure it.

Erdős himself has an Erdős Number of zero. Collaborating  directly earns you an Erdős Number of 1, an honour earned by the 511 mathematicians he published papers with. Collaborating with one of these means you have an Erdős Number of 2, and so on. Some have estimated that 90 percent of the world’s active mathematicians have an Erdős number smaller than 8.

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

Many mathematical concepts, theorems and prizes are named after Erdős, including eleven conjectures and thirteen theorems (most were created in collaboration, and so are named Erdős-_). The Paul Erdős Award, given by the World Federation of National Mathematics Competitions, is awarded to those who “have played a significant role in the development of mathematical challenges at the national or international level and which have been a stimulus for the enrichment of mathematics learning”.

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

Erdős died in 1996, leaving behind a huge contribution to his field and many fond memories with the people with whom he met and worked. He sets an example to all of us of someone who knows and loves the subject, as well as loving the people who study it – mathematics is for sharing, and I hope that we can continue to follow his example and enjoy it together.

More birthday cake, anyone?

3 Responses to “f(Erdős) = 100”

  1. Avatar Maciej

    Erdős died in 1996, while attending mathematical congress in Warsaw. He never retired.

  2. Avatar Patrick Vennebush

    My favorite Erdös quote:

    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.

    Thanks for reminding us about his great life, Katie!


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