The history of mathematical proof in ancient traditions
著者
書誌事項
The history of mathematical proof in ancient traditions
Cambridge University Press, 2012
- : hardback
大学図書館所蔵 全9件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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.
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