J. Stillwell Yearning for the Impossible: The Surprising Truths of Mathematics

AK Peters | ISBN 156881254X | Year 2006 | 244 pages | PDF | 15.6 MBJohn Stillwell's Yearning for the Impossible is a new book that seeks to teach some mathematics to an audience of nonspecialists. Its title refers to the idea that mathematical advances tend to come about when researchers manage to understand ideas or constructions once thought to be impossible. So, for example, there are chapters about irrational numbers and imaginary numbers (after all, nobody used to think such things existed), chapters about 4-dimensional geometries and different orders of infinity (because nobody really knew whether one could make sense of such things), and a chapter about unique factorization via prime ideals (because unique factorization without prime ideals is, um, impossible).Stillwell weaves historical details into his writing seamlessly, helping to give the reader the true feeling that mathematics is more than just a bunch of people playing games with symbols, but rather a rich and rewarding intellectual endeavor important to the human enterprise. --MAA ReviewsYearning For The Impossible is as much of a celebration of the greater understanding mathematics has brought to the world as it is a history and discussion of innovative concepts. and is highly recommended for library and personal reading shelves. --Wisconsin Bookwatch