Erdös spent the last half of his life without a place of permanent residence, roaming the world visiting other mathematicians. He arranged his life "with only one purpose, to spend as many hours a day as possible in the essential, lifeaffirming business of proof and conjecture", and published more than 1500 papers, working with almost 500 coauthors. And he had an amusing idiom all of his own: God was "the Supreme Fascist", who would always win but whose score was to be kept as low as possible, mathematicians "died" when they stopped doing mathematics, and children were "epsilons", after a mathematical symbol used to represent small quantities.
Schechter doesn't overemphasize such eccentricities in My Brain Is Open, however. He portrays a man who loved children, played a mean game of pingpong, liked to talk about politics, and possessed an "essential goodness and generosity". And though he describes Erdös' feats as a child prodigy, he doesn't push the individualistic "genius from nowhere" line. Instead he places Erdös in his setting, a product of the Jewish intellectual tradition and the excellent Hungarian education system, and one among a number of brilliant mathematicians, scientists, and artists from that milieu. Schechter also touches on the effects on Erdös of World War Two and the Holocaust and his problems obtaining entry into the United States during the McCarthy era.
Intermingled with the anecdotes and stories and the biographical and historical narrative, My Brain Is Open also tries to give the general reader some idea of how someone could find mathematics so engaging. There are brief accounts of other famous mathematicians connected to Erdös in one way or another: Ramanujan, von Neumann, and Gödel, among others. Some mathematics is included, taken not from the work of Erdös himself, but chosen so as to give some feel for the beauty and fascination of his chosen subject: Euler and the Kongisberg Bridge problem, Pythagoras and the square root of two, Euclid and the infinity of the primes, Cantor diagonalisation, and so forth. And we get a passing glimpse of the workings of mathematics as a discipline, of such things as collaboration and communication networks and disputes over priority. My Brain Is Open should be enjoyed by mathematicians too, though they will have to look elsewhere for any of Erdös' mathematics itself.
November 1998
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