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EFTA01206797 | EFTA01206798 showed him a proof of a theorem that Rourke figured led directly to the conjecture. The two men went after the proof without even taking time to consider, in the words of topologist John Morgan of Columbia University, "that there was too much history on this one." By February 1986 Rourke and Rego were confident they had a proof and said so. The responses of knowing mathematicians ranged from cynical to cautiously optimistic. Even among those who thought the proof might be valid, Rourke didn't gain any popularity: they objected to the idea that a man working with less than brilliant ideas should have been the one to pull it off. Perhaps for this reason, many topologists chose not to attend the Berkeley seminar. Among the absentees was Mike Freedman of the University of California at San Diego, who had proved the Poincare conjecture for a limited case -- that of a four-dimensional universe, as opposed to the conventional three-dimensional one. Freedman, like a number of his colleagues, had decided that if Rourke's proof was wrong, they would let others expose the flaws. Still, even Freedman admits that his first reaction was disappointment: "Well, there goes the best problem around." Berkeley's John Stallings, who had helped prove the conjecture for universes with six or more dimensions, a more abstract, though easier, task, refused to deal with more of what he called "deluded junk." He attended the first session of Rourke's seminar only, and that, he says, was for the sole purpose of making a "psychological diagnosis": whether Rourke "was crazy or not." Berkeley topologist Andrew Casson went to the seminar, but only to play the role of Grand Inquisitor to Rourke's mathematical heretic. A few participants, including Robion Kirby, the seminar's organizer, who created a technique called Kirby calculus that Rourke had used extensively in his proof, were hoping for the best. But then, Kirby also considered Rourke a friend. And Kirby worked predominantly in the fourth dimension, not the third (mathematicians, like foreign-car mechanics, are highly specialized), and so had no great attachment to a threedimensional conjecture. A few others were also hopeful, thinking that Rourke's proof had a certain elegance and power. But even they came to the inquisition wearing "proof buster" T shirts. In sum, Hubris was about to meet Nemesis. Henri Poincare, the man who left the conjecture like a family curse to his intellectual heirs, was born in 1854. He taught at the University of Paris from 1881 until his death in 1912, dominating the mathematics of his day. Poincare was a universalist. He worked in everything from pure math to physics and astronomy, and he did it all in his head first, which perhaps accounted for his reputation as an absent-minded soul. His greatest creation was topology, or what he called analysis situs, which was regarded at first as more or less trivial, and has since become a preeminent part of twentieth century math. Topologists are concerned with those properties of objects and spaces that transcend mere geometry. To the topologist, a sphere, for instance, can be stretched, compressed, or warped in any number of ways and still remain a sphere, so long as it isn't ripped or torn. "Say you're given a ball," says one Harvard mathematician, "which is a topological object. You push it in on one side, pull it out on another. Twist it a bit. Maybe you run over it with your car a couple of times, let your baby play with it. To a topologist, if it's not ripped, it's still a ball." Topologists, so the joke goes, can't tell the difference between a coffee cup and a doughnut. Both are examples of what they call a torus: a topologist can deform the former into the latter simply by shrinking the depression in the cup and the size of the cup itself, while enlarging the handle. 2 EFTA01206798
May 13, 2026 at 10:00 AM