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The proof is in the pudding the changing nature of mathematical proof / Steven G. Krantz.
| Author/creator | Krantz, Steven G., 1951- |
| Format | Electronic |
| Publication Info | New York ; London : Springer, |
| Description | xvi, 264 p. : ill. ; 26 cm. |
| Supplemental Content | Full text available from Springer Books |
| Supplemental Content | Full text available from Springer Nature - Springer Mathematics and Statistics eBooks 2011 English International |
| Subjects |
| Portion of title | Changing nature of mathematical proof |
| Portion of title | Mathematical proof |
| Partial contents | What is a proof and why? -- The ancients -- The Middle Ages and an emphasis on calculation -- The dawn of the modern age -- Hilbert and the twentieth century -- The tantalizing four-color theorem -- Computer-generated proofs -- The computer as an aid to teaching and a substitute for proof -- Aspects of modern mathematical life -- Beyond computers : the sociology of mathematical proof -- A legacy of elusive proofs -- John Horgan and "the death of proof?" -- Closing thoughts. |
| Abstract | 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 some examples of mathematical proofs that were generated in ways inconceivable 100 years ago.... Many of the proofs treated in this book are described in some detail, with figures and explanatory equations.--From publisher description. |
| Bibliography note | Includes bibliographical references (p. 241-249) and index. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2011928557 |
| ISBN | 9780387489087 (acid-free paper) |
| ISBN | 0387489088 (acid-free paper) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | ✔ Available |