This volume explores how mathematical propositions are discovered, how they are demonstrated in various mathematical cultures - ancient Greece, classical Islam, medieval and modern Europe, India, China, and pre-modern Japan - and how they are shaped in texts and stylistic traditions.The geographic range is not restricted simply to Europe and the method of demonstration is not limited to the axiomatic method, which is thought to have emerged in ancient Greece. Topics of the discussions include the visual and axiomatic modes of reasoning in ancient Greece, algebraic demonstrations in classical Islam, algorithmic procedures in India and China, demonstrations and counter-arguments in mathematical analysis in modern Europe, and reasoning by induction in ancient Greece and pre-modern Japanese mathematics (Wasan). The studies also extend to arguments and demonstrations beyond 'pure mathematics' in the field of mathematical sciences, e.g., hydrostatics, optics, etc.; and include discussions of philosophical and methodological views on demonstration and the nature of mathematical objects, as well as comparative approaches to proof and demonstration in Eastern and Western mathematics.This unique volume is an up-to-date essential resource for historians and philosophers of mathematics. It is also suitable reading for specialists in mathematics education and comparative East-West studies, and dedicated to the topics of discoveries and proofs in a range of historical and cultural settings.
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
ISBN-13
978-981-4689-36-6 (9789814689366)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Herausgeber*in
The Hellenic Open Univ, Greece
Chinese Academy Of Sciences, China
Mathematical Sciences and Philosophy in Ancient Greece and Byzantium: Pre-Euclidean Greek Mathematics; The Rise of Mathematics in Ancient Greece; On the Sphericity of the Surface of Water at Rest; The Treatise On the Section of a Cone of Serenos of Antinoeia; Interpretations of Greek Logic in Polish School; Platonic and Aristotelian Mathematics in Georgius Trapezuntius; Mathematical Sciences in the Arabic World: Rewriting the History of Classical Mathematics from al-Khayyaem to Descartes; Ibn al-Haytham's Geometrization of Place, and the Affirmation of the Visibility of Space in Optics; On Postulates in the Ashkal al-Ta'sis by al-Samarqandi; Abd Al-Rahman Al-Sufi: Study of the Lunar and Solar Eclipses with the Astrolabe; Mathematical Sciences and Philosophy in the European Tradition: Objects and Demonstrations in the Philosophy of Mathematics of Alessandro Piccolomini (1508-1579); Descartes, van Schooten and the Third Degree Equation; A la recherche d'une methode: le traite des coniques de John Wallis; Leibniz's Parisian Studies on Infinitesimal Mathematics; Ampere's 'Theorem' and Weierstrass's Counter-examples; Gauss's Disquistiones Arithmeticae and the 12th Problem of Hilbert; Mathematical Sciences and Philosophy in the Orient: Ramanujan, His Lost Notebook, its Importance; Mathematics in China during the 20th Century; Yamataization: The World's Oldest Example of Structuralism; A Narrative of the YBZ: From Suan Shu Shu to the Western Mirror of European Learning; Pre-modern Japanese Mathematics (Wasan) and Demonstration; Dutch Algebra and Arithmetic in Japan before the Meiji Restoration; Comparative, Methodological and Philosophical Studies: Two Archetypes of Mathematical Thought: Ancient Greece and Ancient China; Symmetry and Form: East and West; Epic Geometry: Proof Structures in Ancient Greek and Early Chinese Literature; History of Mathematics from the View of the Working Mathematician; Distributed Cognition in Mathematical Reasoning;
