Discover: July 1987 What happens when hubris meets nemesis By Gary Taubes I have committed the sin of falsely proving Poincare's conjecture. But that was another country; and besides, until now no one has known about it. -- John Stallings Conjectures are what mathematicians call their guesses. Once a conjecture is in print, it becomes a challenge, daring them to prove it, which quite a few will try to do. The more they work at it and the more they fail, the more obsessed they become. After a while, it no longer matters whether the conjecture is still in the mainstream of mathematics, only that it's still unproved. Late last year, after Colin Rourke, an English mathematician, became the latest victim of what's known as the Poincare conjecture, Dave Gabai, of Caltech, explained the obsession. "For a mathematician," said Gabai, who has a reputation for cracking seemingly unsolvable problems, "proving the Poincare conjecture is fame, honor, and prestige." And that's the name of the game. Will Kazez, a Caltech colleague, added, "If you did prove it, maybe some people would say, 'Well, what's it good for?' But they would say it only because they weren't the ones who proved it." Mathematicians speak of Poincare's conjecture like Ahab expounding on the White Whale. And once they get involved, and when the conjecture inevitably wins the first round, they become as obsessed with their pursuit as Ahab was with his. "They say, 'I'm going to be the one to get it,' " says Rourke, who knows all too well whereof he speaks. "And they don't do anything else, and a good mathematician goes down the drain." Considering that the conjecture is only one of many unsolved problems in its field, which is topology, the branch of mathematics concerned with the fundamental properties of structures and spaces, the obsession seems misplaced. The conjecture is so alluring perhaps because it is so fundamental and seems so simple. Tantalizingly so. But it seemed simple 83 ye