An Arbitrary Number of Years Since Mathematician Paul Erd s Birth

Today would?ve been the 100th anniversary of the Hungary-born mathematician who worked published so many papers and so many with a high impact that a playful measure of one?s academic affiliation with him has been created

By Calla Cofield

Paul Erd?s at a student seminar in Budapest, Fall 1992. Image: Wikimedia Commons/Kmhkmh

I take issue with the celebration of Paul Erd?s? 100^th birthday.

Not the celebration itself, but the number. Why 100? The number 100 was chosen, of course, because 10 is the base unit of our number system: we have 10 unique symbols (0-9) which can be combined to represent any conceivable number. Ten units of 10 is 100, so it?s a nice, neat factor. If we used a base-12 system we would have 12 unique symbols, and we?d be celebrating anniversaries of 144 years. But I can?t find any particular significance about 100 for Erd?s.

Paul Erd?s was born in 1913 in Hungary to Jewish parents, both mathematics teachers. He moved to Manchester in 1934 for a post-doctoral appointment, but also spent time (unofficially) working in London, Cambridge and Bristol: a trend of bouncing from institute to institute that would continue for the rest of his life. Erd?s did not return to Hungary until 1945, when Soviet troops liberated Budapest. Throughout his life he spent time living in the US, Israel and Britain, and visited Hungary often. But he had no permanent residence. He lectured, taught and worked at dozens of universities, but never held a permanent position at any of them. He died in 1996 of a heart attack while attending a conference in Warsaw.?

Next year will mark Erd?s? 101^st birthday, which would be better than celebrating his 100^th birthday because 101 is a prime number. You can?t divide 101 by anything but 1 and itself and still get a whole number (where 100 is the product of 2 x 2 x 5 x 5). Erd?s once told his biographer Paul Hoffman, in a somewhat beautiful and somewhat sad sentiment, that prime numbers were his best friends.

A large portion of Erd?s?s work involved prime numbers. The first significant theorem he ever proved, at age 17, stated that between any number and its double, there is at least one prime number. The Russian mathematical giant Chebyshev had already proven this theorem, called Bertrand?s conjecture, 80 years earlier, but Erd?s proof was simpler and clearer. Erd?s later did a similar job of simplifying the prime number theorem, which reveals how prime numbers will be distributed. Close to zero, prime numbers are common: 2,3,5,7, etc. As one climbs higher and higher, prime numbers occur more infrequently. (The prime number theorem doesn?t? show how to find those numbers, which are infinitely abundant. The largest known prime number is 2^57,885,161 ? 1, which has over 17.4 million digits).

Reducing proofs and theorems to their ?elementary? state was a particular talent of Erd?s?. He once wrote a simpler proof of a theorem in a paper he was supposed to be refereeing. Erd?s believed that ?the Supreme Fascist? (God) kept a book of mathematical proofs in their most perfect, simplified states, and it was the task of mathematicians to transcribe the pages from this book.

In some respects, zero was a rather significant number for Erd?s. He never married, never had children, never bought a home, never had a regular job or very much money, and never stayed in one location for very long. Instead he traveled, carrying all his worldly possessions in two suitcases, making a temporary home with collaborators. This style of living took him all over the U.S. and Europe. At last count, he published papers with 511 people.

Erd?s? terrible behavior as a house guest is a thing of legend: opening a carton of tomato juice by cutting a hole in it and not bothering to clean up the mess; banging pots and pans at 4:30 in the morning to wake everyone so they could continue their work.

Despite his obnoxious behavior, Erd?s was usually welcomed back, and remained friends with most of the people he visited. Reportedly, he was a radiantly happy person, a delightful collaborator, and had a gift for getting people to do the best mathematics they were capable of.? In fact, a more fitting day of celebration for Erd?s might be December 26, 2039, or 1,521 months after his birth; 1,521 is the total number of papers Erd?s collaborated on, which is more than any other mathematician in history.

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