000			03692nam a22004815i 4500
001			978-0-387-48744-1
003			DE-He213
005			20180115171408.0
007			cr nn 008mamaa
008			110512s2011 xxu| s |||| 0|eng d
020			_a9780387487441 _9978-0-387-48744-1
024	7		_a10.1007/978-0-387-48744-1 _2doi
050		4	_aQA21-27
072		7	_aPBX _2bicssc
072		7	_aMAT015000 _2bisacsh
082	0	4	_a510.9 _223
100	1		_aKrantz, Steven G. _eauthor.
245	1	4	_aThe Proof is in the Pudding _h[electronic resource] : _bThe Changing Nature of Mathematical Proof / _cby Steven G. Krantz.
264		1	_aNew York, NY : _bSpringer New York, _c2011.
300			_aXVII, 264 p. 88 illus., 5 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_a1. 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.
520			_aKrantz’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.
650		0	_aMathematics.
650		0	_aNumerical analysis.
650		0	_aHistory.
650		0	_aMathematical logic.
650		0	_aPopular works.
650	1	4	_aMathematics.
650	2	4	_aHistory of Mathematical Sciences.
650	2	4	_aPopular Science, general.
650	2	4	_aMathematical Logic and Foundations.
650	2	4	_aNumerical Analysis.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387489087
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-48744-1
912			_aZDB-2-SMA
999			_c369514 _d369514