Monday, January 21, 2013

Perfect Rigour

The Poincaré conjecture was a great open problem in topology, first posed by Henri Poincaré in 1904. It was an important problem, and was included in the list of seven Millennium problems by the Clay mathematical Institute; each problem carrying a prize of $1M for a successful solution. Most people thought they would not see a millennium problem cracked in their lifetime.

Then in 2002, Grisha Perelman, a mathematician from Russia, posted a solution to the Poincaré conjecture on the Internet, and it was verified to be correct. Incredibly, Perelman refused to publish it in a scholarly journal, refused to vet other's expositions of the proof, declined the Fields medal (the highest honor of Mathematics) which was  subsequently offered to him, and also declined the $1M prize. Perfect Rigour is his story.

The book offers a glimpse into Perelman's life and a light foray into his work. Perelman's is a story of mathematical genius, but also of the troubles a logical mind faces when the 'real world' comes calling. The situation was compounded by Perelman's unique, personal code of conduct, which nearly everyone failed to fathom. After publishing his proof, Perelman severed almost all human contact, mathematical or not, and the book is written based solely on interviews with those who knew Perelman, none with Perelman himself. The book is quite readable, and we are definitely indebted to Perelman for providing a major intellectual advance of our times, but ultimately, it seems a mind like Perelman's cannot find peace in the world as it currently exists, and it is hard not to feel but a little sad about it.

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