# The History of Mathematical Proof in Ancient Traditions

Cambridge University Press, 7/5/2012

EAN 9781107012219, ISBN10: 110701221X

Hardcover, 614 pages, 24.7 x 17.4 x 3.6 cm

Language: English

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.

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 (1780Ã¢â‚¬â€œ1820) 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 1820Ã¢â‚¬â€œ1920 FranÃƒÂ§ois 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 HÃƒÂ¸yrup

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 AryabhatÃ„Â±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.

Advance praise: '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 19th-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.' Jeremy Gray, Open University