This book provides a comprehensive introduction to the role of infinity in mathematics, from ancient to modern times. It is aimed at a general audience and introduces most of the required techniques from scratch. While the mathematical requirements do not extend very far beyond high school mathematics, the author succeeds in explaining the critical philosophical issues connected to the concept of infinity and their relevance for the foundations of mathematics.

John Stillwell was born in Melbourne, Australia in 1942 and educated at Melbourne High School, the University of Melbourne (M.Sc. 1965), and MIT (Ph.D. 1970). From 1970 to 2001 he taught at Monash University in Melbourne, and since 2002 he has been Professor of Mathematics at the University of San Francisco. He has been an invited speaker at several international conferences, including the International Congress of Mathematicians in Zurich 1994. His works cover a wide spectrum of mathematics, from translations of classics by Dirichlet, Dedekind, Poincare, and Dehn to books on algebra, geometry, topology, number theory, and their history. For his expository writing he was awarded the Chauvenet Prize of the Mathematical Association of America in 2005, and the AJCU National Book Award in 2009. Recent titles by Stillwell include Yearning for the Impossible, Mathematics and Its History, The Four Pillars of Geometry, and Geometry of Surfaces.

The Diagonal ArgumentOrdinalsLogicArithmeticNatural Unprovable SentencesAxioms of Infinity