The Proof is in the Pudding

This book takes the reader on a journey around the globe and through centuries of history, exploring the transformations that mathematical proof has undergone from its inception at the time of Euclid and Pythagoras to its versatile, present-day use.

An extensive evolution of the proof presented for the first time in book form. Topics cover centuries of mathematical history, dating back to Eudoxus and Euclid and span the ages to conclude with the some versatile, present-day use of the proof. Author expresses keen insights and a wealth of historical knowledge. Proofs are presented and accompanied by figures, equations and examples. Includes supplementary material: sn.pub/extras

Autorentext
Steven Krantz is a well-known Springer author. He has written nine books with Springer (1-931914-59-1, 0-8176-4339-7, 0-8176-4011-8, 0-8176-4339-7, 0-8176-4220-X, 0-8176-4097-5, 1-930190-87-5, 0-8176-4264-1, 0-8176-4285-4 ) with sales accumulating almost $130,000 in North America. Prof. Krantz is the editor-in-chief of the "society" journal (published in cooperation with Springer) "The Journal of Geometric Analysis" and is also the present editor-in-chief of the AMS Notices. "The Proof is in the Pudding, is the first of its kind. It details the history of the proof from its beginnings to its place in present-day mathematics. (This was presented as a "hot topic" in an article in the Notices of the AMS.)

Klappentext

Krantz's book covers the full history and evolution of the proof concept. The notion of rigorous thinking has evolved over time, and this book documents that development. It gives examples both of decisive developments in the technique of proof and also of magnificent blunders that taught us about how to think rigorously. Many historical vignettes illustrate the concepts and acquaint the reader with how mathematicians think and what they care about.

In modern times, strict rules for generating and recording proof have been established. At the same time, many new vectors and forces have had an influence over the way mathematics is practiced. Certainly the computer plays a fundamental role in many mathematical investigations.

But there are also fascinating social forces that have affected the way that we now conceive of proof. Daniel Gorenstein's program to classify the finite simple groups, Thomas Hales's resolution of the Kepler sphere-packing problem, Louis de Branges's proof of the Bieberbach conjecture, and Thurston's treatment of the geometrization program are but some examples of mathematical proofs that were generated in ways inconceivable 100 years ago. Krantz treats all of them---and more---in some detail; he names the players and tells all the secrets.

Many of the proofs treated in this book are described in some detail, with figures and explanatory equations. The reader is given a dose of modern mathematics, and h ow mathematicians think. Both the joy and the sorrow of mathematical exploration are communicated dynamically and energetically in this exciting new book.

Inhalt

1. What is a Proof and Why?.- 2. The Ancients.- 3. The Middle Ages and Calculation.- 4. The Dawn of the Modern Age.- 5. Hilbert and the Twentieth Century.- 6. The Four-Color Theorem.- 7. Computer-Generated Proofs.- 8. The Computer as a Mathematical Aid.- 9. Aspects of Mathematical Life.- 10. The Sociology of Mathematical Proof.- 11. A Legacy of Elusive Proofs.- 12. John Horgan and "The Death of Proof".- 13. Closing Thoughts.- Index of Names.- References.- Index.