The History of Mathematical Proof in Ancient Traditions
Cambridge University Press, Jul 5, 2012 - Philosophy
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.
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abbreviations algebraic proof algorithm al≠Hajj‚j analysis ancient ancient Greece angles appears Arabic Arabo≠Latin Archimedes argument Aristotelian demonstrations Aristotle’s arithmetical astronomy Babylonian Book Busard Cantor century Chemla Chinese Chinese mathematical circle codex Colebrooke Colebrooke’s commentary computations conclusion context correctness critical edition cylinder deductive developed Diophantus discussion Doric equal establish Euclid’s Elements Eutocius evidence example fact Figure geometrical Gerard of Cremona Greek manuscripts Greek mathematics Greek text Heiberg historiography history of mathematical HÝyrup Indian astronomy Indian mathematics indirect tradition interpretation introduced Ish‚q–Th‚bit Klamroth Knorr lines Liu Hui manuscript diagrams mathematical proof mathematical texts mathematicians medieval method modern multiplied Netz Nicomachus Nine Chapters objects operations Philoponus polygonal numbers Porisms Posterior Analytics practice of proof problem procedure Proclus proposition question reasoning reciprocal relation result Saito Sanskrit sequence sources square statement structure symbols tablets textual Thibaut transformation translation transmission treatise triangle Vitrac writing