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The History of Mathematical Proof in Ancient Traditions

Publisher: Cambridge : Cambridge University Press, 2012.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
Explores the nature of mathematical proof in a range of historical settings, providing the first comprehensive history of proof.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
ISBN: 9781107012219 110701221X 1283521733 9781283521734 9781139516723 1139516728 9781139518581 1139518585
OCLC Number: 804038758
Description: 1 online resource (612 pages) : illustrations
Contents: Prologue: historiography and history of mathematical proof: a research program Karine Chemla; Part I. Views on the Historiography of Mathematical Proof: 1. The Euclidean ideal of proof in The Elements and philological uncertainties of Heiberg's edition of the text Bernard Vitrac; 2. 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; 3. The texture of Archimedes' arguments: through Heiberg's veil Reviel Netz; 4. John Philoponus and the conformity of mathematical proofs to Aristotelian demonstrations Orna Harari; 5. Contextualising Playfair and Colebrooke on proof and demonstration in the Indian mathematical tradition (1780-1820) Dhruv Raina; 6. Overlooking mathematical justifications in the Sanskrit tradition: the nuanced case of G. F. Thibaut Agathe Keller; 7. The logical Greek versus the imaginative Oriental: on the historiography of 'non-Western' mathematics during the period 1820-1920 Francois Charette; Part II. History of Mathematical Proof in Ancient Traditions: The Other Evidence: 8. The pluralism of Greek 'mathematics' Geoffrey Lloyd; 9. Generalizing about polygonal numbers in ancient Greek mathematics Ian Mueller; 10. Reasoning and symbolism in Diophantus: preliminary observations Reviel Netz; 11. Mathematical justification as non-conceptualized practice: the Babylonian example Jens Hoyrup; 12. Interpretation of reverse algorithms in several Mesopotamian texts Christine Proust; 13. Reading proofs in Chinese commentaries: algebraic proofs in an algorithmic context Karine Chemla; 14. Dispelling mathematical doubts: assessing mathematical correctness of algorithms in Bhaskara's commentary on the mathematical chapter of the Aryabhatiya Agathe Keller; 15. Argumentation for state examinations: demonstration in traditional Chinese and Vietnamese mathematics Alexei Volkov; 16. 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 Chemla, Karine.

Abstract:

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

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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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