History, or as Hegel would say, the Zeitgeist (or World Spirit), has been kind enough to give birth from time to time to genius. It is likely, though indeterminable, that a great proportion of these geniuses are never appreciated, their potential remaining dormant, or their lives thwarted from fruition. Those left standing are remembered, and serve to inspire and amaze. When we think of the greats, we think first to, among others, Hypatia, Leibniz, DaVinci, Mozart, Wittgenstein, Leonard Euler, Goethe, Newton, and others. Not all of the great geniuses are eccentric in their personal lives, but a great majority are. This is not surprising; it is difficult to flourish both intellectual and socially, when the goals of the former are given disproportionate attention relative to the latter.
It is my relatively unwarranted ‘hunch’ that there is a contemporary mathematician who deserves mention as a genius in the very highest ranks. Perelman is a Russian mathematician whose area of research is topographical geometry. There is a problem in topographical geometry that made the Clay Institute for Mathematics list of the Millenium Problems: a list of the seven ‘great’ open problems in mathematics. One of these problems is the problem of proving a conjecture made by Henri Poincare, which concerns the topography of a three-dimensional sphere. The Clay Institute has offered a million dollars per problem to anyone who solves any of these problems in such a way that the proof is published in a peer-reviewed journal and survives two years of scrutiny. Perelman, working off of the ideas of Richard Hamilton-particularly his proposal of the Ricci Flow-secluded himself in Russia for several years, during which time he proved what many thought might never be proved. Against the norm of self-interest and greed, Perelman was not interested in receiving the monetary reward, or any other type of reward, such as the Field’s medal, for his efforts. It was his view that, if the solution were correct, that would be sufficient reward.
Publishing the Proof
Perelman published his proof in a set of three instalments on ArXiv, which amounts to essentially a mathematical ‘blog’ that hosts unpublished works. This move was considered surprising by peers who are inclined to keep lucrative and original work secret. Perelman, after a brief series of American lectures, has retired to Russia, lives with his mother and is unemployed, having retired from mathematics. He turned down the Fields medal and no longer works in mathematics. All of this from a man who essentially discovered the holy grail of topographical geometry.
Perelman’s place in history
Perelman’s eccentricity, genius and lack of concern for his own self-interest place him in an interesting category of thinkers that includes Wittgenstein and the Hungarian mathematician Paul Erdos. Both Wittgenstein and Erdos were disinterested in material possessions. Erdos lived as a vagabond, carrying his belongings in a humble suitcase, whilst publishing a tome of articles that ranks him second all time behind only Euler. Wittgenstein, on the other hand, had given away an inheritance, earned by his father who had been one of the foremost European industrialists, which would have made him one of the wealthiest men in Austria. Perelman, by virtue of his accomplishments, accompanied by an outright rejection of the fruits that could accrue to them, sets himself, I think, into a league of great company. Such attitudes are as rare these days as genius itself.
