Failure™ Magazine

Million Dollar Math Problem

Grigory Perelman and the mathematical breakthrough of the century—the Poincaré Conjecture.

Written by Jason Zasky   Filed under Science & Technology

What is the Poincaré Conjecture?
It is no more, actually. Now that Perelman has proved it, it’s a theorem—a classic theorem of topology, one of the most wonderfully weird mathematical disciplines. Much of topology is concerned with things that are essentially the same as other things, even if at particular moments in time they happen to look different. For example, if you have a blob that can be reshaped into a sphere, then the sphere and the blob are essentially similar, or homeomorphic, as topologists say. Poincaré asked, in essence, whether all three-dimensional blobs that are not twisted and have no holes in them are homeomorphic to a three-dimensional sphere. It took more than a hundred years to prove that yes, they are.

What is the significance of this discovery?
A discovery like this generally has far-reaching repercussions that are rarely evident at the moment of the breakthrough. It will almost certainly have profound consequences for our understanding of space—the universe we inhabit.

How were you able to write Perelman’s biography without ever talking to the man?
It was the only way to do it. When I first began researching the book, the only person he was speaking with was Sergei Rukshin—his lifelong math tutor, his competition coach, and in many ways, the architect of his life. But sometime in the last couple years, Perelman stopped talking to Rukshin as well. As far as I know, the only person with who he is still in contact with is his mother, with whom he shares an apartment on the outskirts of St. Petersburg.

While I had no access to Perelman, I talked to virtually all the people who have been important in his life: Rukshin, his classmates, his math club mates, his high school math teacher, his competition coaches and teammates, his university thesis advisor, his graduate school advisor, and those who surrounded him in his postdoctoral years. I think these people were motivated to speak with me because Perelman himself wouldn’t—and because they felt his story had been misinterpreted in so many ways.

It almost sounds as if not talking to Perelman was an advantage.
In some ways, yes. When you write a biography, you are in constant negotiation with that person’s view of himself. So you are always balancing your own perceptions against the subject’s aspirations, and this can be painful for all involved. All I had was my research material and my own perceptions, so it was a little like writing a novel. I was constructing a character.

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