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More About This Textbook
Overview
This text explores the many transformations that the mathematical proof has undergone from its inception to its versatile, present-day use, considering the advent of high-speed computing machines. Though there are many truths to be discovered in this book, by the end it is clear that there is no formalized approach or standard method of discovery to date. Most of the proofs are discussed in detail with figures and equations accompanying them, allowing both the professional mathematician and those less familiar with mathematics to derive the same joy from reading this book.
Editorial Reviews
From the Publisher
From the reviews:“The author traces the development of the idea of proof from Euclid through computer-aided and computer-generated proofs, pointing out the way some current social trends in mathematics affect the construction of nonstandard proofs. … This work provides good outside class reading for students—and not just mathematics majors; one could easily imagine this as a supplement to courses on the history or philosophy of science. Summing Up: Recommended. Lower-division undergraduates through researchers/faculty; general readers.” (D. Robbins, Choice, Vol. 49 (2), October, 2011)
“In this book Steven Krantz undertakes the Miltonic task of justifying the ways of (pure) mathematicians to the world at large. … The concept of mathematical proof is at the heart of Krantz’s book. … mathematicians should find the book interesting, illuminating, provocative … .” (J. M. Plotkin, Mathematical Reviews, Issue 2012 b)
“Krantz’s book is entertaining, can be read by the early undergraduate and puts forward some serious issues. There are few math books that are useful and valuable reading for all mathematicians, but this is one of them.” (Charles Ashbacher, The Mathematical Association of America, June, 2011)
Product Details
Meet the Author
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.)
Table of Contents
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.