The History of mathematical proof in ancient traditions

Abstract

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.