My Brain is Open: The Mathematical Journeys of Paul Erdös

  • Bruce Schechter
Oxford University Press/Simon & Schuster: 1998pp. 224 £22.50/$25

When Paul Erdös “left” (as he called it) in 1996, even The New York Times took notice, and printed a front-page obituary calling him “a wayfarer in math's vanguard”. Two years later, Paul Hoffman published an excellent biography about him called The Man Who Loved Only Numbers (Fourth Estate/Hyperion, 1998; reviewed in Nature 394, 535–536; 1998), which reached number three in The Sunday Times best-seller list. Now Bruce Schechter has followed this up with a second biography, My Brain is Open. In his 83 energetic years, this peculiar, obsessive little mathematician has built up a substantial public following.

Erdös was born in 1913 in Hungary, and discovered negative numbers when he was four. He belonged to that extraordinary cluster of scientific geniuses — which included John von Neumann, inventor of the electronic computer and game theory, and the Nobel prizewinners Eugene Wigner, George de Hevesy and George Olah — who emerged from two or three schools in Budapest after the First World War.

During his life, Erdös wrote more than 1,500 papers, books and articles, more than any other mathematician ever. Some of these became the great classics of our century, opening up entirely new fields of study to which generations of mathematicians have devoted their lives. As the mathematician Paul Winkler said, “If I can see a bit farther it is because I stand on the shoulders of Hungarians”.

Schechter is particularly concerned to clarify a few of the basic ideas underlying this astonishing production, such as the sieve of Eratosthenes, Cantor's infinities and Euler's curious problem (the foundation of graph theory) about whether a man could walk across all seven bridges of Königsberg without crossing the same bridge twice. It is inspiring reading, because Schechter, following in the spirit of Erdös, makes clear that much good mathematics can come from whimsical speculation and the clever use of simple ideas. If popular writing about mathematics remains of this quality, there is still enough unused material for a shelf-full of Erdös biographies.

In other respects, Hoffman's book is slightly longer and better on anecdotes, but Schechter's, while not so lively, is less inclined to get distracted from its subject. Although you would never guess it from the acknowledgements, both writers once worked for Discover magazine. Erdös's famous love of creative cooperation has apparently not spilt over into the world of mathematical biographies.

From his teenage years, when he could instantly square a four-digit number and knew 37 proofs of Pythagoras's theorem, Erdös called himself old and decrepit. A few years before his 60th birthday he appended the letters PGOM to his name, which stood for Poor Great Old Man, then added further initials every few years. By the time he was 75 he was PGOMLDADLDCD (Poor Great Old Man, Living Dead, Archaeological Discovery, Legally Dead, Counts Dead).

His output had slowed down a little by then. “One of my greatest regrets,” remarked one of his last collaborators, “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.”