Masha Gessen’s Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century (2009) is the story of Russian mathematician Grigory Perelman and his quest to solve the Poincaré Conjecture, a problem that eluded the most brilliant minds in the field for nearly a century. She describes his rise to mathematical brilliance, his genius, his perfection, his habits, his idiosyncrasies, and most bizarrely, his self-induced seclusion from the world after solving the Poincaré.
Very carefully, Gessen notes that the book is not a biography “in the usual sense,” for she did not―and could not―interview Perelman. His isolation prevented such a meeting from happening. Instead, the book uses the testimonies of Perelman’s few friends and associates.
A highly insightful and lively written account, Perfect Rigor the investigation of a man who chooses to avoid public exposure at all costs. He declined two very prestigious prizes: the Fields Medal, which is considered the equivalent of a Nobel in mathematics (there is no Nobel prize in mathematics); and the Millennium Prize, an even greater disctinction, which offers one million dollars for the first rigorous solution to any of seven Millennium Problems, one of them being the Poincaré―Perelman was well aware of, but deliberately failed to meet, the eligibility requirements for this prize.
Gessen prefaces with an introduction to the Millennium Prize, and then begins with mathematical and Soviet history. No advanced knowledge of mathematics is required to read this book, but a bit of familiarity with topology can certainly enhance the read. In fact, the opening chapters are of more use to a historian than to a mathematician; a brilliant account of the specific social and political conditions that led to Perelman’s rise (and later seclusion) is given.
The book then picks up on Perelman, his mother, and his math coaches and teachers. As a child, Perelman excelled at math, and was always ahead of his classmates. In 1982 he won the gold medal at the International Mathematics Olympiad, an international math competition for high school students, by earning a perfect score.
Perelman was no ordinary mathematician―he was a genius. There was no math problem that he could not solve. But he had (and has) a very peculiar and rigorous value system. What is right to him is obviously right to him, yet no one else seems to understand what he considers right. When he published the solution to the Poincaré in 2002, he did not do so in a refereed math journal; in fact, he posted his solution on the Internet and available to the public. Because of this, he was ineligible, and intentionally so, for the million-dollar Millennium Prize.
He dedicated literally his entire life to mathematics, and spent almost a decade working on the problem. His contribution back to mathematics community was solving a problem that no one else could solve. In his Olympiad days, he would solve a problem, submit it, and have his answer acknowledged as correct. But now, the one community he trusted―the mathematics community, for he mostly avoided talking to anyone else―was telling him that his solution was ineligible for recognition. The mathematicians who did support him verified the solution, but still, no Millennium Prize was announced. He did not care about the money; rather, he was shocked that the people whom he trusted most were now refusing to acknowledge him in the greatest mathematical achievement of the century.
In 2006 the mathematics community tried to make up for this by awarding Perelman the Fields Medal. To any other mathematician, it would have been the greatest achievement, but to Perelman, it was almost an insult―the reason for his award was carefully worded as to avoid the statement that Perelman had solved the Poincaré; he was merely congratulated “for his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow.” In his mind, and the minds of most mathematicians, he solved the Poincaré Conjecture. He declined the Fields Medal.
In all, Perelman’s story is a complex one, filled with brilliance, genius, luck, tension. Gessen’s account portrays clearly the life of a man totally estranged from the world, and at this point, even from the mathematics community. It delves into the historical elements that affected Perelman and the ways people seldomly interacted with him, but more importantly, it explores how his environment shaped his mind, and how he used it―how he solved problems perfectly―and how he formed a rigorous idea of correctness in his mind, a set of rules that only he could understand. Perfect Rigor is a perfect read.