The Spell of Mathematics

Poincare’s Prize, by George Szpiro

For those who are mathematically inclined, a good math problem has the power to take over the mind like nothing else. George Szpiro’s book Poincare’s Prize describes how attempts to prove the Poincare Conjecture had just this effect on many mathematicians. The Poincare Conjecture was finally proved by the reclusive Russian mathematician Grigori Perelman, who refused the \$1 million prize that the Clay Institute wanted to award for his  proof.

The spell of mathematics is nicely illustrated by a hair-raising story about RH Bing, who was one of the many mathematicians who contributed to the solution of the Poincare Conjecture. George Szpiro quotes a a University of Texas at Austin memorial tribute to Bing as follows:

It was a dark and stormy night when RH Bing volunteered to drive some stranded mathematicians from the fogged-in Madison airport to Chicago. Freezing rain pelted the windscreen and iced the roadway as Bing drove on—concentrating deeply on the mathematical theorem he was explaining. Soon the windshield was fogged from the energetic explanation. The passengers too had beaded brows, but their sweat arose from fear. As the mathematical description got brighter, the visibility got dimmer. Finally, the conferees felt a trace of hope for their survival when Bing reached forward—apparently to wipe off the moisture from the windshield. Their hope turned to horror when, instead, Bing drew a figure with his finger on the foggy pane and continued his proof—embellishing the illustration with arrows and helpful labels as needed for the demonstration. (p. 128)

I don’t recommend RH Bing’s driving while proving, but this story reminds me of the feeling I have often had that a math problem promises sparkling hidden knowledge just beyond the next obstacle, or that proving a long-sought-after result will briefly make me something more than merely human. That kind of mathematical spell can easily keep me up at night. Indeed, chasing a mathematical will-o’-the-wisp that seemed to promise—but did not deliver—a powerful proof, kept me up most of the night through the wee hours of this past Tuesday.

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