000			a
999			_c31935 _d31935
008			230419b xxu||||| |||| 00| 0 eng d
020			_a9780691234366
082			_a511.36 _bSTI
100			_aStillwell, John
245			_aStory of proof : logic and the history of mathematics
260			_bPrinceton University Press, _aPrinceton : _c2022
300			_axiv, 441 p. ; _bill., (b & W and col.), _c25 cm
365			_b45.00 _cUSD _d85.90
504			_aIncludes bibliographical references and index.
520			_aHow 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.
650			_aProof theory History
650			_aLogic
650			_aMathematics
942			_2ddc _cBK