Sunday, November 30, 2008
The Poincaré Conjecture : In Search of the Shape of the Universe by Donal O'Shea
The universe is finite but doesn't have walls, apparently, which means that it must be bent or curved in some ingenious, twisty way. But how? In 1904 the French mathematician Henri Poincaré attempted to describe its shape. His conjecture ("Is it possible that the fundamental group of a manifold could be the identity, but that the manifold might not be homeomorphic to the three-dimensional sphere?") remained unproven for more than 100 years, although Alfred North Whitehead briefly thought he'd cracked it. O'Shea has his work cut out providing an idiot's guide to differential geometry and algebraic topology, but it is the human stories that stand out: in particular the lives of the mathematicians Johann Carl Gauss, the enigmatic and brilliant Bernhard Riemann and his intellectual heir Poincaré himself. In 2006 it was confirmed that the publicity-shy Grigory Perelman, a Russian Jew, had finally proved Poincaré's conjecture. Huzzah! But hold on. "The question of the shape of the universe," concludes O'Shea, "is still very much open."