The Poincare Conjecture: 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. Illus.(Mar.)Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved.