POINCARE CONJECTURE, THE - IN SEARCH OF THE SHAPE OF THE UNIVERSE

The reclusive Russian mathematician Grigory Perelman became a minor media celebrity last summer when he refused the prestigious Fields medal, awarded every four years to a mathematician under the age of 40. Perelman had succeeded in solving the Poincaré conjecture, named for 19th-century French mathematician Henri Poincaré, and which contemporary cosmologists believe has implications for our understanding of the shape of the universe. O'Shea, a professor of mathematics at Mount Holyoke College,begins his account of the long and contentious search for a solution to the puzzle by looking at how we came to understand the shape of the Earth, beginning with the Greeks, in particular Pythagoras and Plato. Writing for generalist science buffs, O'Shea gives a brief course in geometry and in topology and the topological structures called manifolds that are the basis of Poincaré's puzzle. Inexplicably, however, O'Shea doesn't give readers a formal statement of the conjecture itself until well into the book. O'Shea describes mind-bending structures in topology as clearly as most of us can describe a cube, but readers will need to do a little Wikipedia-ing first to find out just what it is they're reading about.