Saturday, March 20, 2004

The Man Who Loved Only Numbers: the story of Paul Erdos and the search for mathematical truth by Paul Hoffman

This is the biography of Paul Erdos, probably the most famous mathematician of the 20'th century. The title is unfair. Erdos comes across as a deeply social man, but one who had no language but math. Perhaps he had Aspergers syndrome.

Erdos is credited with making math a social activity, as opposed to the solitary activity most people think it to be. He got along well with children--possibly because young children like someone who takes them seriously. Most touching are the stories of how he tried to cheer up sick mathematician friends by visiting them and talking about interesting math problems. He knew that sickness and depression (depression seems rather common) could destroy a man's confidence in his own mind, and his cure was to try to interest them in something.

Erdos seems to have had a rare skill for calibrating problems to your skill. Most number theory problems I've worked on have been either trivial or impossible (for me, anyway). He could see problems in between, and find one suited to your abilities.

He lived out of a battered suitcase, and donated the prizes he won to funds to support young mathematicians. He never learned to cook, or do laundry, or drive, or most of the ordinary activities of daily life. He would show up at a mathematician's home and ask what unsolved problems he had. They (and other friends who heard Erdos was there) would talk about the math problems and how to deal with them--and as one fellow would slow down to think though what Erdos had said, Erdos would turn to the next, like a chess grandmaster playing a dozen games simultaneously. Meanwhile he was a nightmare to their wives--washing so thoroughly and carelessly that the bathroom would be 1/4 inch deep in water, or deciding that the best way to open a carton of tomato juice was to stab it in the side with a knife. One day he finally learned how to butter toast, and announced that it wasn't so hard after all.

He had a language all his own: epsilon was a child (Remember epsilon/delta proofs from calculus? No? OK, trust me, it's funny.), spoke of God as having "the Book" in which He kept all the math proofs, and called Him the "Supreme Fascist" for not telling us what the proofs are and making us find them out ourselves. He said "A mathematician is a device for turning coffee into proofs," and lived on coffee and amphetamines. (Not recommended, but he lived an active life into his 90's.)

The author tries to make the appeal of math clear to the layman, with examples from Gauss' and Fermat's lives as well. If you never got past algebra you missed the parts of math where mathematicians start having fun. (Yes, fun. Playing around with ideas, and finding out which are true, is fun.) Some very deep problems are very easy to state, and easy to mostly understand--but hard to prove. Go read the book. Have fun!

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