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020 _a9780691234373
024 7 _a10.1515/9780691234373
_2doi
035 _a(DE-B1597)BR1273419
035 _z(OCoLC)1347381552
040 _aDE-B1597
_beng
_cDE-B1597
_erda
041 0 _aeng
044 _anju
_cUS-NJ
072 7 _aSCI
_x034000
_2bisacsh
072 7 _aMAT
_x015000
_2bisacsh
072 7 _aMAT
_x018000
_2bisacsh
100 1 _aStillwell, John,
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 0 0 _aThe Story of Proof :
_bLogic and the History of Mathematics /
_cJohn Stillwell, John Stillwell.
264 1 _aPrinceton, NJ
_bPrinceton University Press,
_c[2022]
264 4 _c©2022
300 _a1 online resource
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 0 _tFrontmatter --
_tContents --
_tPreface --
_tCHAPTER 1 Before Euclid --
_tCHAPTER 2 Euclid --
_tCHAPTER 3 After Euclid --
_tCHAPTER 4 Algebra --
_tCHAPTER 5 Algebraic Geometry --
_tCHAPTER 6 Calculus --
_tCHAPTER 7 Number Theory --
_tCHAPTER 8 The Fundamental Theorem of Algebra --
_tCHAPTER 9 Non-Euclidean Geometry --
_tCHAPTER 10 Topology --
_tCHAPTER 11 Arithmetization --
_tCHAPTER 12 Set Theory --
_tCHAPTER 13 Axioms for Numbers, Geometry, and Sets --
_tCHAPTER 14 The Axiom of Choice --
_tCHAPTER 15 Logic and Computation --
_tCHAPTER 16 Incompleteness --
_tBibliography --
_tIndex
506 0 _arestricted access
_uhttp://purl.org/coar/access_right/c_16ec
_fonline access with authorization
_2star
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.
538 _aMode of access: Internet via World Wide Web.
545 _aJohn Stillwell is emeritus professor of mathematics at the University of San Francisco. His many books include Elements of Mathematics and Reverse Mathematics (both Princeton).
546 _aIn English.
588 0 _aDescription based on online resource; title from PDF title page (publisher's Web site, viewed March 03 2026)
650 7 _aSCIENCE / History.
_2bisacsh
650 7 _aMATHEMATICS / History & Philosophy.
_2bisacsh
650 7 _aMATHEMATICS / Logic.
_2bisacsh
653 0 _aTheorem
653 0 _aAxiom
653 0 _aNatural number
653 0 _aComputation
653 0 _aGeometry
653 0 _aReal number
653 0 _aMathematics
653 0 _aPeano axioms
653 0 _aPredicate logic
653 0 _aSummation
653 0 _aEquation
653 0 _aRule of inference
653 0 _aWell-order
653 0 _aPythagorean theorem
653 0 _aProof theory
653 0 _aSubset
653 0 _aContinuous function (set theory)
653 0 _aGentzen's consistency proof
653 0 _aZorn's lemma
653 0 _aTruth value
653 0 _aComputable function
653 0 _aDirect proof
653 0 _aAlgorithm
653 0 _aAxiom of choice
653 0 _aSet theory
653 0 _aTuring machine
653 0 _aDeterminant
653 0 _aMathematical induction
653 0 _aPrime number
653 0 _aSpecial case
653 0 _aPlayfair's axiom
653 0 _aCountable set
653 0 _aExtreme value theorem
653 0 _aRational number
653 0 _aCredential
653 0 _aAddition
653 0 _aMathematician
653 0 _aFundamental theorem
653 0 _aQuaternion
653 0 _aDesargues's theorem
653 0 _aPermutation
653 0 _aNumber theory
653 0 _aCommutative property
653 0 _aIntuitionism
653 0 _aInference
653 0 _aInfimum and supremum
653 0 _aSelf-reference
653 0 _aPrime factor
653 0 _aCalculation
653 0 _aAnalogy
653 0 _aAnalysis
653 0 _aAssociative property
653 0 _aRecursively enumerable set
653 0 _aDedekind cut
653 0 _aHypothesis
653 0 _aPrediction
653 0 _aLogical connective
653 0 _aIntermediate value theorem
653 0 _aAleph number
653 0 _aTotal order
653 0 _aConstructive analysis
653 0 _aReason
653 0 _aInfinitesimal
653 0 _aIdentifiability
653 0 _aPower set
653 0 _aHypotenuse
653 0 _aLogic
653 0 _aProof by infinite descent
653 0 _aSatisfiability
653 0 _aQuantity
653 0 _aTheorem
653 0 _aAxiom
653 0 _aNatural number
653 0 _aComputation
653 0 _aGeometry
653 0 _aReal number
653 0 _aMathematics
653 0 _aPeano axioms
653 0 _aPredicate logic
653 0 _aSummation
653 0 _aEquation
653 0 _aRule of inference
653 0 _aWell-order
653 0 _aPythagorean theorem
653 0 _aProof theory
653 0 _aSubset
653 0 _aContinuous function (set theory)
653 0 _aGentzen's consistency proof
653 0 _aZorn's lemma
653 0 _aTruth value
653 0 _aComputable function
653 0 _aDirect proof
653 0 _aAlgorithm
653 0 _aAxiom of choice
653 0 _aSet theory
653 0 _aTuring machine
653 0 _aDeterminant
653 0 _aMathematical induction
653 0 _aPrime number
653 0 _aSpecial case
653 0 _aPlayfair's axiom
653 0 _aCountable set
653 0 _aExtreme value theorem
653 0 _aRational number
653 0 _aCredential
653 0 _aAddition
653 0 _aMathematician
653 0 _aFundamental theorem
653 0 _aQuaternion
653 0 _aDesargues's theorem
653 0 _aPermutation
653 0 _aNumber theory
653 0 _aCommutative property
653 0 _aIntuitionism
653 0 _aInference
653 0 _aInfimum and supremum
653 0 _aSelf-reference
653 0 _aPrime factor
653 0 _aCalculation
653 0 _aAnalogy
653 0 _aAnalysis
653 0 _aAssociative property
653 0 _aRecursively enumerable set
653 0 _aDedekind cut
653 0 _aHypothesis
653 0 _aPrediction
653 0 _aLogical connective
653 0 _aIntermediate value theorem
653 0 _aAleph number
653 0 _aTotal order
653 0 _aConstructive analysis
653 0 _aReason
653 0 _aInfinitesimal
653 0 _aIdentifiability
653 0 _aPower set
653 0 _aHypotenuse
653 0 _aLogic
653 0 _aProof by infinite descent
653 0 _aSatisfiability
653 0 _aQuantity
700 1 _aStillwell, John,
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
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