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＜電子ブック＞
The Proof is in the Pudding : The Changing Nature of Mathematical Proof / by Steven G. Krantz

版	1st ed. 2011.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2011
大きさ	XVII, 264 p. 88 illus., 5 illus. in color : online resource
著者標目	*Krantz, Steven G author SpringerLink (Online service)
件　名	LCSH:Mathematics LCSH:History LCSH:Engineering LCSH:Life sciences LCSH:Social sciences LCSH:Humanities LCSH:Science FREE:History of Mathematical Sciences FREE:Technology and Engineering FREE:Life Sciences FREE:Humanities and Social Sciences FREE:Physical Sciences FREE:Mathematics and Computing
一般注記	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 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 mathemati cians think.   Both the joy and the sorrow of mathematical exploration are communicated dynamically and energetically in this exciting new book HTTP:URL=https://doi.org/10.1007/978-0-387-48744-1

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