Perfect Rigor

October 1, 2009
The story of Russian mathematical prodigy Grigory Perelman, who solved a problem that had stumped everyone for a century—then walked away from his chosen field.

Gessen (Blood Matters: From Inherited Illness to Designer Babies, How the World and I Found Ourselves in the Future of the Gene, 2008, etc.) tells Perelman's story from the viewpoint of a former student in the educational system of which he was a product. Soviet mathematicians worked in isolation from their Western counterparts during the Stalinist era, but were encouraged because of their value to the state. Perelman, an unusually gifted student, was identified early and his talent nurtured, even though, as a Jew, he faced crippling handicaps under the Soviets. He won the attention of an innovative math coach, Sergei Rukshin. The coach and student bonded early, and Perelman was accepted at a prestigious university and then at a top graduate school. As a star, he was allowed an unusual degree of eccentricity, which in his case included an almost total disregard of other people. Numerous contemporaries attest to his fanatical adherence to a set of ideals that essentially ignored the realities of the Soviet state. Politics, prejudice, making friends and getting ahead in the world—these meant nothing to Perelman. During postdoctoral work in the United States, he refused to cut his hair and nails and turned down job offers because he felt it beneath his dignity to apply for them. Meanwhile, he was homing in on a solution to the Poincar Conjecture, a topological riddle so puzzling that the Clay Institute in Boston offered a $1 million prize to anyone who could solve it. When, in 2002, Perelman posted a solution on the Internet, he seemed to expect instant recognition. Instead, the world's mathematicians meticulously checked his proof, which Perelman took it as an insult and turned down a Fields medal, the math equivalent of a Nobel. To this day, there is significant doubt about whether he will accept the Clay prize. Though Gessen was unable to interview her subject, she paints a fascinating picture of the Soviet math establishment and of the mind of one of its most singular products.

An engrossing examination of an enigmatic genius.

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November 1, 2009
The "genius" here is Russian mathematician Grigory Perelman, who announced in 2002 a proof of the Poincar Conjecture, a complex problem that had resisted the best efforts of the world's mathematicians for almost a full century. Strangely, since that moment of apparent triumph, Perelman has progressively withdrawn from contact with the mathematics community and with most other humans as well. Russian American journalist and author Gessen ("Slate, New Republic; Blood Matters") now tells of Perelman's very unconventional life and career. Denied access to Perelman himself, she interviewed many people who knew him as a student and (later) as a researcher. Gessen details the special Russian schools for young mathematical prospects that Perelman attended and describes apparently incorrigible Russian anti-Semitism. Most important, the gist of her excellent discussion of the Poincar Conjecture and its proof should be intelligible even to readers lacking a background in higher mathematics. VERDICT General science buffs curious about how researchers go about creating "new" mathematics or about the eccentric personalities in this field will be fascinated by Gessen's book. More advanced readers can also turn to Donal O'Shea's "The Poincar Conjecture: In Search of the Shape of the Universe".Jack W. Weigel, Ann Arbor, MI

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