Friday, April 23, 2010

Review: Perfect Rigor

Perfect Rigor is Masha Gessen's book about Grisha Perelman, the mathematician who proved the Poincaré Conjecture. It's a short book and a compelling read: I got it home from the library at 5pm yesterday, and finished it at 11pm, with a couple of hours off for cooking, eating, and mowing the lawn.

Perelman doesn't do interviews, and hates talking to people, so Gessen was forced to go about writing this book by interviewing his friends, teachers, and associates. Perelman's childhood was filled with mathematics, having been enrolled by his math tutor into a math club, where Perelman did very well. The book does a great job at describing what it was like growing up in the Soviet system for mathematicians during the 80s, with widespread anti-Semetic sentiments. Perelman was brilliant, however, and was lucky in having great mentors who nurtured and developed him as a problem solver. This first part of the book makes for great reading.

After Perelman leaves the Soviet Union, however, the book flounders a bit. First of all, Gessen had to describe that Poincaré Conjecture to laymen. This is not easy to do with text only: there are no diagrams throughout the book. I feel that this is the weakest part of the book, and Gessen made a hash out of it. Fortunately, the Wikipedia entry is thorough and does a good job of explanation.

Because Gessen did not have access to Perelman, we never understand Perelman's view of the whole thing. Why did he decline the Clark medal? We are led to believe that Perelman felt that he did not get the recognition that he deserved. Gessen also implies that Perelman might have Asperger syndrome, or was so idealistic that when the politics (again, really sociology) inside Mathematics came into play with regards to his solution of the problem, he decided to resign from Mathematics rather than put up with the problem. Perelman also declined the Millenium Prize.

Given that even his former mentors and teachers don't really have access to Perelman, we'll never know the complete story behind this.

20 years ago, when Fermat's Last Theorem was declared proven, I remember sitting down at dinner with one of my CS instructors. He told me about the result, and I said, "OK, so does this prove P=NP or anything interesting like that?" "No," came the reply. "Well then, I don't see why it's news." "You have no soul, Piaw!"

Unfortunately, I still feel like that. I don't think Gessen explains why the Poincaré Conjecture was important or interesting, and unfortunately neither this book nor Wikipedia does a good job of explaining the motivation behind the drive to solve this problem, which even after Perelman's publication, took teams of mathematicians nearly two years to fully explain. Nevertheless, a fun read, and worth the 3 hours of your time to read for a good understanding of the sociology behind Mathematics. Not that I could perform at the level these guys regularly do.
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