This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research and how a number of historical accounts can be deepened by embracing philosophical questions.
Architecture of Modern Mathematics
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Editorial Reviews
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The essays are uniformly a joy to read, and the bibliography is ample, giving interested readers an extensive springboard for further exploration. I recommend it highly. Andrew Arana the Mathmatical Intelligencer
About the Author
Jeremy Gray is Professor of the History of Mathematics and Director of the Centre for the History of the Mathematical Sciences at the Open University, and a regular Visiting Professor at the University of Warwick. He works on the history of mathematics in the 19th and 20th Centuries, and also on issues in the philosophy and social significance of mathematics. He wrote 'The Hilbert Challenge', Oxford University Press, 2000, and he was the editor of and a contributor to 'The Symbolic Universe: geometry and physics, 1890-1930', Oxford University Press, 1999. His book 'Janos Bolyai, non-Euclidean geometry, and Nature of Space', a Burndy Library publication, MIT, came out in 2004. Jose Ferreiros is 'profesor titular' for Logic and Philosophy of Science at the University of Seville. He is the author of 'Labyrinth of Thought: A history of set theory and its role in modern mathematics', Basel, Birkhauser, 1999, 'Science Networks' no. 23. He has edited in Spanish 'Riemanniana Selecta' (Madrid, CSIC, 2000, bilingual edition) and Dedekind's foundational works (Madrid, Alianza Editorial, 1997), and has published papers on the history and philosophy of logic, mathematics, and general science in journals such as 'The Bulletin of Symbolic Logic', 'Historia Mathematica', 'Archive for History of Exact Sciences', 'Science in Context', 'Theoria' and 'Critica'. Among his forthcoming papers are contributions to 'Landmarks in Western Mathematics' (Elsevier), 'The Shaping of Arithmetic' (Springer), 'Filosofia de las ciencias matematicas, naturales y sociales' (Trotta), and 'Philosophical insights into logic and mathematics' (Kluwer).
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mathematical modernism, considered empiricism, ideal divisors, finitist standpoint, finitist mathematics, categoricity results, historical elucidation, logically valid sentences, idéalités mathématiques, higher number classes, symbolic realism, semantical completeness, cyclotomic integers, domain conception, accessible domains, homotopy exact sequence, higher congruences, homomorphism theorem, fibre spaces, homotopy groups, ordinary integers, homotopy theory, axiomatic analysis, pensée mathématique, empirical space Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Riemannian Background, Crossroads of Mathematics, Riemann's Habilitationsvortrag, Frege's Philosophy, Epistemology of Mathematics, Felix Hausdorff's Considered Empiricism, Cultural Phenomenon, Emory Noether, Hilbert's Conception of Geometry, Emmy Noether, Mac Lane, Rise of Functors, Development of Dedekind's Theory of Ideals, Das Chaos, Hilbert's Grundlagen, Mathematische Annalen, Prague Theorem, Erlangen Program, Felix Klein, Hermann Weyl, Frege's Grundlagen, Presses Universitaires de France, Walter Purkert, Principia Mathematica, Logische Untersuchungen Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
mathematical modernism, considered empiricism, ideal divisors, finitist standpoint, finitist mathematics, categoricity results, historical elucidation, logically valid sentences, idéalités mathématiques, higher number classes, symbolic realism, semantical completeness, cyclotomic integers, domain conception, accessible domains, homotopy exact sequence, higher congruences, homomorphism theorem, fibre spaces, homotopy groups, ordinary integers, homotopy theory, axiomatic analysis, pensée mathématique, empirical space Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Riemannian Background, Crossroads of Mathematics, Riemann's Habilitationsvortrag, Frege's Philosophy, Epistemology of Mathematics, Felix Hausdorff's Considered Empiricism, Cultural Phenomenon, Emory Noether, Hilbert's Conception of Geometry, Emmy Noether, Mac Lane, Rise of Functors, Development of Dedekind's Theory of Ideals, Das Chaos, Hilbert's Grundlagen, Mathematische Annalen, Prague Theorem, Erlangen Program, Felix Klein, Hermann Weyl, Frege's Grundlagen, Presses Universitaires de France, Walter Purkert, Principia Mathematica, Logische Untersuchungen Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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