History of Mathematical Proof in Ancient Traditions (eBook, PDF)

Redaktion: Chemla, Karine

• Format: PDF

Produktbeschreibung

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 and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 5. Juli 2012
• Englisch
• ISBN-13: 9781139512275
• Artikelnr.: 38277947

Inhaltsangabe

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 François 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
Høyrup; 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 Aryabhat¿ya 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.