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The History of Mathematical Proof in Ancient Traditions

Chemla, Karine [Hrsg.]
The History of Mathematical Proof in Ancient Traditions / ed. by Karine Chemla. - Cambridge [u.a.] : Cambridge University Press, 2012. - xv, 596 S. : graph. Darst.
ISBN 978-1-107-01221-9
£ 100,00
DDC: 511.3601

Beschreibung
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. [Verlagsinformation]

Inhalt
List of figures. ix
List of contributors. xii
Note on references. xiv
Acknowledgements. xv
KARINE CHEMLA:
Prologue. Historiography and history of mathematical proof: a research programme. 1
PART 1: VIEWS ON THE HISTORIOGRAPHY OF MATHEMATICAL PROOF
Shaping ancient Greek mathematics: the critical editions of Greek texts in the nineteenth century
1. BERNARD VITRAC:
The Euclidean ideal of proof in the Elements and philological uncertainties of Heiberg's edition of the text. 69
2. KEN SAITO AND NATHAN SIDOLI:
Diagrams and arguments in ancient Greek mathematics: lessons drawn from comparisons of the manuscript diagrams with those in modern critical editions. 135
3. REVIEL NETZ:
The texture of Archimedes' writings: through Heiberg's veil. 163
Shaping ancient Greek mathematics: the philosophers' contribution
4. ORNA HARARI:
John Philoponus and the conformity of mathematical proofs to Aristotelian demonstrations. 206
Forming views on the 'Others' on the basis of mathematical proof
5. DHRUV RAINA:
Contextualizing Playfair and Colebrooke on proof and demonstration in the Indian mathematical tradition (1780-1820). 228
6. AGATHE KELLER:
Overlooking mathematical justifications in the Sanskrit tradition: the nuanced case of G. F. W. Thibaut. 260
7. FRANÇOIS CHARETTE:
The logical Greek versus the imaginative Oriental: on the historiography of 'non- Western' mathematics during the period 1820-1920. 274
PART 2: HISTORY OF MATHEMATICAL PROOF IN ANCIENT TRADITIONS: THE OTHER EVIDENCE
Critical approaches to Greek practices of proof
8. G. E. R. LLOYD:
The pluralism of Greek 'mathematics'. 294
Proving with numbers: in Greece
9. IAN MUELLER:
Generalizing about polygonal numbers in ancient Greek mathematics. 311
10. REVIEL NETZ:
Reasoning and symbolism in Diophantus: preliminary observations. 327
Proving with numbers: establishing the correctness of algorithms
11. JENS HØYRUP:
Mathematical justification as non-conceptualized practice: the Babylonian example. 362
12. CHRISTINE PROUST:
Interpretation of reverse algorithms in several Mesopotamian texts. 384
13. KARINE CHEMLA:
Reading proofs in Chinese commentaries: algebraic proofs in an algorithmic context. 423
14. AGATHE KELLER:
Dispelling mathematical doubts: assessing mathematical correctness of algorithms in Bhāskaras commentary on the mathematical chapter of the Aryabhaṭīya. 487
The later persistence of traditions of proving in Asia: late evidence of traditions of proof
15. ALEXEI VOLKOV:
Argumentation for state examinations: demonstration in traditional Chinese and Vietnamese mathematics. 509
The later persistence of traditions of proving in Asia: interactions of various traditions
16. TIAN MIAO:
A formal system of the Gougu method: a study on Li Rui's Detailed Outline of Mathematical Procedures for the Right-Angled Triangle. 552
Index. 574

Herausgeberin
Karine Chemla, is Senior Researcher at the CNRS (Research Unit SPHERE, France) and a Senior Fellow at the Institute for the Study of the Ancient World at New York University. She is also Professor on a Guest Chair at Northwestern University, Xi'an, as well as at Shanghai Jiaotong University and Hebei Normal University, China. She was awarded a 'Chinese Academy of Sciences Visiting Professorship for Senior Foreign Scientists' in 2009. Profile page (CNRS).

Quellen: Cambridge University Press; WorldCat; Amazon (UK); Lehmanns Media
Bildquelle: Cambridge University Press
Bibliographie: [1]


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