Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantors answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantors counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology Smart, challenging, and thoroughly rewarding, Wallaces tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.