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The history of mathematical proof in ancient traditions

Author: Karine Chemla
Publisher: Cambridge : Cambridge University Press, 2012.
Edition/Format:   Print book : EnglishView all editions and formats

This volume explores the nature of mathematical proof in a range of historical settings, providing the first comprehensive history of proof.

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Karine Chemla
ISBN: 9781107012219 110701221X
OCLC Number: 779264820
Description: xv, 596 pages : illustrations ; 25 cm
Contents: Prologue: Historiography and history of mathematical proof: a research programme / Karine Chemla --
Part I: Views on the historiography of mathematical proof: --
Shaping ancient Greek mathematics: the critical editions of Greek texts in the nineteenth century --
The Euclidean ideal of proof in The Elements and philological uncertainties of Heiberg's edition of the text / Bernard Vitrac --
Diagrams and arguments in ancient Greek mathematics: lessons drawn from comparisons of the manuscript diagrams with those in modern critical editions / Ken Saito and Nathan Sidoli --
The texture of Archimedes' writings: through Heiberg's veil / Reviel Netz --
John Philoponus and the conformity of mathematical proofs to Aristotelian demonstrations / Orna Harari --
Contextualizing Playfair and Colebrooke on proof and demonstration in the Indian mathematical tradition (1780-1820) / Dhruv Raina --
Overlooking mathematical justification in the Sanskrit tradition: the nuanced case of G.E.W. Thibaut / Agathe Keller --
The logical Greek versus the imaginative Oriental: on the historiography of 'non-Western' mathematics during the period 1820-1920 / François Charette. Part II: History of mathematical proof in ancient traditions: the other evidence: critical approaches to Greek practices of proof --
The pluralism of Greek 'mathematics' / G.E.R. Lloyd --
Proving with numbers in Greece --
Generalizing about polygonal numbers in ancient Greek mathematics / Ian Mueller --
Reasoning and symbolism in Diophantus preliminary observations / Reviel Netz --
Proving with numbers: establishing the correctness of algorithms --
Mathematical justification as non-conceptualized practice: the Babylonian example / Jens Hoyrup --
Interpretation of reverse algorithms in several Mesopotamian texts / Christine Proust --
Reading proofs in Chinese commentaries: algebraic proofs in an algorithmic context / Karine Chemla --
Dispelling mathematical doubts: assessing mathematical correctness of algorithms in Bhāskara's commentary on the mathematical chapter of the Āryabhaṭīya / Agathe Keller --
The later persistence of traditions of proving in Asia: late evidence of traditions of proof --
Argumentation for state examinations: demonstrations in traditional Chinese and Vietnamese mathematics / Alexei Volkov --
The later persistence of traditions of proving in Asia: interactions of various traditions --
A formal system of the Gougu method: a study on Li Rui's: detailed outline of mathematical procedures for the right-angled triangle / Tian Miao.
Responsibility: edited by Karine Chemla.
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'This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry Read more...

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