before even starting school, and many have read widely throughout their lives. For example, in his article "On Proof and Progress in Mathematics," Bill Thurston wrote: My mathematical education was rather independent and idiosyncratic, where for a number of years I learned things on my own, developing pers

e earth could have been shaped like a doughnut or a pretzel and Magellan would never have been the wiser. But a very rich monarch, says Princeton's Bill Thurston, the topologist who's the odds-on favorite to prove the Poincare conjecture, can establish that the earth is a sphere without ever leaving home. Le