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9781107012219

The History of Mathematical Proof in Ancient Traditions

by
  • ISBN13:

    9781107012219

  • ISBN10:

    110701221X

  • Format: Hardcover
  • Copyright: 2012-08-27
  • Publisher: Cambridge Univ Pr

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Summary

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.

Table of Contents

Prologue: historiography and history of mathematical proof: a research program
Views on the Historiography of Mathematical Proof
The Euclidean ideal of proof in The Elements and philological uncertainties of Heiberg's edition of the text
Diagrams and arguments in ancient Greek mathematics: lessons drawn from comparisons of the manuscript diagrams with those in modern critical editions
The texture of Archimedes' arguments: through Heiberg's veil
John Philoponus and the conformity of mathematical proofs to Aristotelian demonstrations
Contextualising Playfair and Colebrooke on proof and demonstration in the Indian mathematical tradition (1780-1820)
Overlooking mathematical justifications in the Sanskrit tradition: the nuanced case of G. F. Thibaut
The logical Greek versus the imaginative Oriental: on the historiography of 'non-Western' mathematics during the period 1820-1920
History of Mathematical Proof in Ancient Traditions: The Other Evidence
The pluralism of Greek 'mathematics'
Generalizing about polygonal numbers in ancient Greek mathematics
Reasoning and symbolism in Diophantus: preliminary observations
Mathematical justification as non-conceptualized practice: the Babylonian example
Interpretation of reverse algorithms in several Mesopotamian texts
Reading proofs in Chinese commentaries: algebraic proofs in an algorithmic context
Dispelling mathematical doubts: assessing mathematical correctness of algorithms in Bhaskara's commentary on the mathematical chapter of the Aryabhatiya
Argumentation for state examinations: demonstration in traditional Chinese and Vietnamese mathematics
A formal system of the Gougu method - a study on Li Rui's detailed outline of mathematical procedures for the right-angled triangle
Table of Contents provided by Publisher. All Rights Reserved.

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