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010			_a 2022932472
015			_aGBC2G2349 _2bnb
016	7		_a020744270 _2Uk
020			_a9780691234366 _q(hardcover)
020			_a0691234361 _q(hardcover)
035			_a22415675
035			_a(OCoLC)1295806706
040			_aYDX _beng _erda _cIISERB
042			_alccopycat
050	0	0	_aQA9.54 _b.S74 2022
082	0	4	_a511.36 St54S _223
100	1		_aStillwell, John. _932694
245	1	4	_aThe story of proof : _blogic and the history of mathematics / _cJohn Stillwell.
246	1	0	_aLogic and the history of mathematics
260			_aPrinceton: _bPrinceton University Press, _c2022.
300			_axiv, 441 pages : _billustrations (black and white, and colour) ; _c24 cm
504			_aIncludes bibliographical references (pages [405]-418) and index.
505	0		_aBefore Euclid -- Euclid -- After Euclid -- Algebra -- Algebraic Geometry -- Calculus -- Number Theory -- The Fundamental Theorem of Algebra -- Non-Euclidean Geometry -- Topology -- Arithmetization -- Set Theory -- Axioms for Numbers, Geometry, and Sets -- The Axiom of Choice -- Logic and Computation -- Incompleteness.
520			_a"How the concept of proof has enabled the creation of mathematical knowledge. The 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		0	_aProof theory _xHistory. _932695
650		7	_aSCIENCE / History. _2bisacsh _932696
650		7	_aProof theory. _2fast _932697
655		7	_aHistory. _2fast _932698
776	0	8	_iebook version : _z9780691234373
906			_a7 _bcbc _ccopycat _d2 _encip _f20 _gy-gencatlg
942			_2ddc _cBK
999			_c10995 _d10995