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The Story of Proof: Logic and the History of Mathematics
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About The Story Of Proof: Logic And The History Of
Review “I am a great admirer of Stillwell’s writing, and this book does not disappoint. Ranging broadly and authoritatively over the history of mathematics, he takes the reader into those places where proofs have been innovative and have played a critical role.”―David M. Bressoud, author of Calculus Reordered: A History of the Big Ideas"This is a lively story of the way that mathematics develops new concepts and ideas in order to solve hard problems. It is, at the same time, a story of the way that logic and the theory of computability emerged organically from reflection on mathematical method and thought. This book will be highly valuable to anyone interested in contemporary mathematics and how it came to be."―Jeremy Avigad, Carnegie Mellon University“The Story of Proof―a book about mathematics as proof, and proof as mathematics, through the ages―is unique and enjoyable."―Anil Nerode, Cornell University Product Description How the concept of proof has enabled the creation of mathematical knowledgeThe Story of Proof investigates the evolution of the concept of proof―one of the most significant and defining features of mathematical thought―through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge.Stillwell begins with Euclid and his influence on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as “infinitesimal algebra,” and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid. Stillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and logic, and peers into the deep chasm between natural number arithmetic and the real numbers. In its depths, Cantor, Gödel, Turing, and others found that the concept of proof is ultimately part of arithmetic. This startling fact imposes fundamental limits on what theorems can be proved and what problems can be solved.Shedding light on the workings of mathematics at its most fundamental levels, The Story of Proof offers a compelling new perspective on the field’s power and progress. About the Author John Stillwell is emeritus professor of mathematics at the University of San Francisco. His many books include Elements of Mathematics and Reverse Mathematics (both Princeton).
