The Art of the Infinite: The Pleasures of Mathematics

Description

[MR1963099](https://mathscinet.ams.org/mathscinet-getitem?mr=1963099)Taking infinity as a theme and lacing in literary and artistic references, the authors take the reader on an excursion through the real number system, the prime sequence, infinite series, basic results of Euclidean geometry, ruler and compasses constructions, geometry of the complex plane, projective geometry and the arithmetic of cardinals and ordinals. The route is marked with historical milestones and some nice arguments, some relegated to appendices. The book, which does not treat developments much beyond 1900, can be read by laymen with a good background in algebra and geometry at the secondary level. Reviewed by [E. J. Barbeau](https://mathscinet.ams.org/mathscinet/search/author.html?mrauthid=30960)* * *A witty, conversational, and accessible tour of math's profoundest mysteries.Mathematical symbols, for mathematicians, store worlds of meaning, leap continents and centuries. But we need not master symbols to grasp the magnificent abstractions they represent, and to which all art aspires. Through language, anyone can come to delight in the works of mathematical art, which are among our kind's greatest glories.Taking the concept of infinity, in its countless guises, as a starting point and a helpful touchstone, the founders of Harvard's pioneering Math Circle program Robert and Ellen Kaplan guide us through the “Republic of Numbers,” where we meet both its upstanding citizens and its more shadowy dwellers, explore realms where only the imagination can go, and grapple with math's most profound uncertainties, including the question of truth itself-do we discover mathematical principles, or invent them?