What is so special about the number 30? How many colors are needed to color a map? Do the prime numbers go on forever? Are there more whole numbers than even numbers? These and other mathematical puzzles are explored in this delightful book by two eminent mathematicians. Requiring no more background than plane geometry and elementary algebra, this book leads the reader into some of the most fundamental ideas of mathematics, the ideas that make the subject exciting and interesting. Explaining clearly how each problem has arisen and, in some cases, resolved, Hans Rademacher and Otto Toeplitz's deep curiosity for the subject and their outstanding pedagogical talents shine through. Originally published in 1957. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

"A thoroughly enjoyable sampler of fascinating mathematical problems and their solutions."--Science "Each chapter is a gem of mathematical exposition... [The book] will not only stretch the imagination of the amateur, but it will also give pleasure to the sophisticated mathematician."--American Mathematical Monthly

Hans Rademacher was an Affiliate of Rockefeller University and Professor Emeritus of Mathematics in the University of Pennsylvania before his death in 1969. Otto Toeplitz was Professor of Mathematics in Kiel and Bonn.