Krantz, Steven G. 1951-
The proof is in the pudding : the changing nature of mathematical proof / Changing nature of mathematical proof Mathematical proof Steven G. Krantz. - New York ; London : Springer, c2011. - xvi, 264 p. : ill. ; 26 cm.
Includes bibliographical references (p. 241-249) and index.
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.
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.
9780387489087 (acidfree paper) 0387489088 (acidfree paper)
2011928557
GBB060120 bnb
015550513 Uk
Proof theory.
Proof theory--History.
Mathematics--Philosophy.
Théorie de la démonstration.
Symbolic logic.
Mathematics--Philosophy.
QA9.54 / .K73 2011
51 KRA
The proof is in the pudding : the changing nature of mathematical proof / Changing nature of mathematical proof Mathematical proof Steven G. Krantz. - New York ; London : Springer, c2011. - xvi, 264 p. : ill. ; 26 cm.
Includes bibliographical references (p. 241-249) and index.
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.
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.
9780387489087 (acidfree paper) 0387489088 (acidfree paper)
2011928557
GBB060120 bnb
015550513 Uk
Proof theory.
Proof theory--History.
Mathematics--Philosophy.
Théorie de la démonstration.
Symbolic logic.
Mathematics--Philosophy.
QA9.54 / .K73 2011
51 KRA