I still remember reading for the first time about Grisha Perelman’s solution to the Poincaré Conjecture on Slashdot back in 2004. I knew nothing about the Poincaré Conjecture other than it was famous—one of those big question marks in mathematics like Fermat’s Last Theorem1—and therefore big news.
What generated even more press than the solution to the math itself—which, by most journalistic standards, is a dead end—is the fact that the genius behind the proof is a very odd duck indeed. By the time this review is posted, Grigori “Grisha” Perelman has become a near-total recluse at his apartment in St. Petersberg, Russa, which he shares with his mother. He doesn’t talk to anyone—even his old friends—and has claimed to have left the field of mathematics entirely.
It would be disappointing indeed if Perfect Rigor ended up being a puff piece—the sort of pseudo-journalism that so angered Perelman in the slow rumbling response to his proof. Luckily, Masha Gessen is a much better writer than that2. Gessen is perfect for this subject not simply because she is already a good writer, but because she, like Perelman, grew up Jewish in Russia, and from what I can gather from her narrative, she also spent some time in school for advanced mathematics, though obviously she became a writer and not a tormented mathematical genius.
If Perelman were German, or Spanish, or French, Gessen would not need to explain to her readers how mathematical education worked in those countries. Germany and Spain and France, for all their distinctiveness, probably all attack math—indeed, most education—the same way. But Russia is always different, especially when you’re talking about the Soviet era3. It therefore becomes necessary for Gessen to expend a great deal of expository verbiage on Perelman’s predecessors and teachers, and how they came to be a part of that system. Perelman was Jewish (or at least had a Jewish name), and so the very strong Soviet culture of anti-Semitism was always working against him, exerted as it was through ridiculous official quotas on the number of Jews who could be admitted to top-tier universities, and the less official quotas on the number of Jewish-sounding kids who could compete in mathematics contests for the Russian teams. Because Perelman was always the brightest student, his teachers and coaches generally conspired to include him, sometimes at the expense of other very bright Jewish kids.
Because of this sometimes treacherous system, Perelman owes as much for his eventual success4 to his patrons as to his own unquestioned genius. Otherwise, a quiet kid with severe Asperger syndrome might have gotten swallowed up in a world—especially a Soviet one—that doesn’t care if you’re in the autism spectrum unless you’re also a useful prodigy.
Interestingly, Gessen doesn’t even broach the subject of Asperger syndrome until the end of the book, though readers familiar with the syndrome will be thinking about it all along. Perelman’s strict adherence to rules—even if he doesn’t like them, such as mandatory gym class in math school—and his single-minded pursuit of the problems set before him strike both Gessen and myself as textbook Asperger syndrome, though Gessen herself is quick to disclaim that such a diagnosis is impossible without actually talking to Perelman5. What bothers me is that while Perelman was both dedicated and successful in his study and practice of mathematics, there was never anything said either by Gessen or those she interviewed about whether doing math actually made Perelman happy. His Asperger syndrome (if, indeed, he has it) seems so severe is to preclude any emotions but angry frustration; and, if his own statements are to be believed, he has now entirely eschewed the study of math to which he devoted the first forty years of his life. What does Perelman want? Gessen’s best guess is that he wants genuine recognition and appreciation for his mathematical achievements—not the million-dollar Clay Institute prize, not “co-authorship” recognition with the two slimy Chinese mathematicians who tried to piggyback on Perelman’s proof, and not the simpering, simplistic kind of recognition he got from the mainstream press (which, in its typical droll fashion, fixated far more on the monetary award than on the importance of the theorem6). The mixed reaction to his proof—partly attributable to his refusal to publish via a refereed journal and partly attributable to the bruised egos of other mathematicians who and tried to and even partly succeeded in proving the Poincaré conjecture—was enough to drive the somewhat unstable Perelman into a meltdown of frustration.
Though I’ve painted Perelman as a person who follows a strict set of internal rules, he is not without contradiction. Whereas Grisha the young boy obediently participated in gym class despite his distaste for it because it was an known rule, Grigori the man refused to publish his proof in a refereed math journal, even though this is also a known rule in the academic world. Despite having become a near-recluse by 2006 who would tell interested visitors “I see no reason for us to meet,” he nonetheless granted a rather frank interview with two writers for The New Yorker that year. Gessen notes Perelman’s flouting of some rules but not others, but never offers much of an explanation for it, implicitly committing it to the “Troubled Genius” file in the back of the drawer. I like to think the answer lies in one of Gessen’s first precepts: though he may seem like a Russian robot which cranks out answers to math problems and can’t function in the real world, there is much more to Perelman that is “normal”—that is, occasionally irrational like the rest of us—than we initially expect.
Considering that Gessen, unlike the two New Yorker writers, never got to interview Perelman personally, I think she’s done a fantastic job at painting a picture of him. Importantly, she’s painted a picture of him, and not simply of the Poincaré conjecture, or the post-proof brouhaha, or Grigori qua unkempt wunderkind. Read the linked New Yorker article to whet your appetite; if you want the full story, context and all, read Perfect Rigor. You won’t regret it.
- Which was, incidentally, proved in 1995 by Andrew Wiles[↩]
- Also, she is the sister of Keith Gessen, author of All the Sad Young Literary Men[↩]
- For a brief adapted excerpt about the rise of mathematics in the post-war Soviet Union, see Gessen’s piece in the Wall Street Journal.[↩]
- I’m not convinced that such a word is appropriate here.[↩]
- This disclaimer quite endears Gessen to me: too many writers would throw diagnoses around, considering themselves pop psychologists.[↩]
- In fairness to MSM, there’s not much to be gained attempting to explain the importance of a topological conjecture.[↩]