The History of Mathematical Proof in Ancient Traditions

Karine Chemla, Centre National de la Recherche Scientifique (CNRS)

Cambridge University Press | 2012 | 614 páginas | PDF | 7,52 Mb

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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 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

Table of 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 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 Aryabhatıya 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.

Outro livro de Karine Chemla , disponível no blog:

- K. Chemla (éd.) (2004). History of science, history of text, Springer, Collection « Boston studies in the philosophy of science 

Capítulos em livros de Karine Chemla , disponíveis no blog:

- Karine Chemla et Agathe Keller. (2002). The Sanskrit karanis, and the Chinese mian , Yvonne Dold-Samplonius, Joseph W. Dauben, Menso Folkerts, Benno van Dalen (éds.), From China to Paris: 2000 Years of Mathematical Transmission (Actes du Colloque de Bellagio, 5-2000) (pp. 87-132). Steiner Verlag, Stuttgart .

- K. Chemla (2005). The interplay between proof and algorithm in 3rd century China : The operation as prescription of computation and the operation as argument, in Paolo Mancosu, Klaus F. Jorgensen & Stig Andur Pedersen (éds.), Visualization, Explanation and Reasoning styles in mathematics,(pp. 123-145).  Synthese Library Series, volume 327, Springer, 

- K. Chemla (2009). Proof in the Wording : Two modalities from Ancient Chinese , in G. Hanna, H. N. Jahnke, H. Pulte (éds.), Explanation and Proof in Mathematics : Philosophical and Educational Perspectives, (pp. 253—285), Springer.

-  K. Chemla (2012). Using documents from ancient China to teach mathematical proof in G. Hanna and M. de Villiers (eds.), Proof and Proving in Mathematics Education (pp. 423 -). New ICMI Study Series 15

Capítulos em livros de Karine Chemla , disponíveis online (link externo ao blog):

- K. Chemla  (2010). A Chinese Canon in Mathematics and its two Layers of Commentaries : Reading a collection of texts as shaped by actors, in F. Bretelle-Establet (éd.), Looking at it from Asia : the processes that shaped the sources of history of science (pp 169—210), Springer, Boston Studies in the Philosophy of Science 265