Reviews, Science.

Too simply pure

The Poincaré conjecture, one of the great unsolved topological problems, was finally proven at the end of the 20th century by Grigoriy Perelman, a Russian mathematician of genius. Topology might be described as distilled geometry. The historian Masha Gessen, who grew up herself in the Russian mathematical culture, invites us into the Aspergian milieu of world-class geometers to tease out the tale.

-CC-BY-SA 3.0, Salix alba at English Wikipedia

A homotopy of a circle around a sphere can be reduced to a singe point.. Attrib: Salix alba at English Wikipedia, CC-BY-SA 3.0.

 

While she takes us on the journey of Perelman’s Fields award winning accomplishment, we learn about the closed and edgy culture of those who see themselves as thinkers of pure thoughts, who are unironically direct and honest about all. During Perelman’s coming-of-age, for a brief period the Soviet mathematical world became a safe harbor for those who needed a place to be eccentric. All about them the institutions of the Soviet Union systematically taught and enforced the conformity of its distorted version of communism, while the mathematical elite were trained in schools and math clubs that were as free as was possible of such constraints, a happy accident helped by the immense Cold War arms race, which required skilled mathematicians.

Perelman, who rivaled Candide in his unworldliness, swallowed whole the mathematics of entire fields, and in conquering the up-to-now unconquerable Poincaré conjecture, was swallowed in turn by his pure belief in meritocracy, unable to see that great things can be done in a world colored in the grey of human ambition. His own ambition was ferociously channeled into his mathematics, so much so that when he achieved the unachievable, he forsook the further pursuit of mathematics, at the same time refusing the ordinary rewards of position, money (one million dollars), and fame, turning down the Fields medal, the mathematical equivalent of the Nobel prize. Gessen suggested in topological terms that "like a rubber band slipping inexorably off a sphere, his world was about to shrink to a point" (page 175).

It is the mind of Perelman, a problem solver of the highest order, that Gessen seeks to place in its context, if not to explain. His world was an immense shelter, of which he seemed largely unaware, his gifts slightly larger than his vulnerabilities. Without the convergence of events, without the forbearance and protection of determined people, the gifted Perelman may not have sustained the effort required to complete the pursuit of the conjecture.

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