The Proof is in the Pudding: The Changing Nature of Mathematical Proof

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Springer Science & Business Media, 13 de maig 2011 - 264 pàgines

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.

 

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Continguts

1 What Is a Proof and Why?
1
2 The Ancients
37
3 The Middle Ages and An Emphasison Calculation
47
4 The Dawn of the Modern Age
53
5 Hilbert and the Twentieth Century
61
6 The Tantalizing FourColor Theorem
107
7 ComputerGenerated Proofs
116
8 The Computer as an Aid to Teaching and a Substitute for Proof
135
The Sociology of Mathematical Proof
157
11 A Legacy of Elusive Proofs
183
12 John Horgan and The Death of Proof?
218
13 Closing Thoughts
223
Index of Names
229
References
241
Index
250
Copyright

9 Aspects of Modern Mathematical Life
149

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Sobre l'autor (2011)

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.)

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