Everything and More: A Compact History of InfinitySince the time of the ancient Greeks, the nature of infinity has perplexed mathematicians and philosophers. Is it a valid mathematical entity or a meaningless abstraction? Plato and Aristotle in their day, Galileo and Newton nearly 2,000 years later, all grappled with it. But it was the 19th-cent. mathematicians Karl Weierstrass, Richard Dedekind, and Georg Cantor whose work established a whole new mathematics of infinity. In particular, Cantor¿s counterintuitive discovery of a progression of larger and larger infinities was both enormously controversial and mind-bendingly beautiful -- a glimpse of a strange landscape where the everyday rules of arithmetic are broken, and where there truly can be found everything and more. |