Computation, Proof, Machine: Mathematics Enters a New Age

Author:   Gilles Dowek (Ecole Polytechnique, Paris) ,  Pierre Guillot ,  Marion Roman
Publisher:   Cambridge University Press
Edition:   New edition
ISBN:  

9780521118019


Pages:   158
Publication Date:   05 May 2015
Format:   Hardback
Availability:   Manufactured on demand   Availability explained
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Computation, Proof, Machine: Mathematics Enters a New Age


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Author:   Gilles Dowek (Ecole Polytechnique, Paris) ,  Pierre Guillot ,  Marion Roman
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press
Edition:   New edition
Dimensions:   Width: 14.50cm , Height: 1.30cm , Length: 22.30cm
Weight:   0.300kg
ISBN:  

9780521118019


ISBN 10:   0521118018
Pages:   158
Publication Date:   05 May 2015
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand   Availability explained
We will order this item for you from a manufactured on demand supplier.
Language:   English

Table of Contents

Part I. Ancient Origins: 1. From the prehistory to the Greeks; 2. Two thousand years of computation; Part II. The Age of Reason: 3. Predicate logic; 4. The decision problem; 5. Church's thesis; 6. Lambda-calculus; 7. Constructivity; 8. Constructive proofs and algorithms; Part III. Crisis of the Axiomatic Method: 9. Intuitionistic type theory; 10. Automated proof; 11. Automated proof checking; 12. News from the field; 13. Instruments; 14. The end of axioms?; 15. Conclusion: as we near the end of this mathematical voyage.

Reviews

'In this pithy, award-winning account of the growing role of computation in mathematics, Gilles Dowek adds further evidence, if any were needed, that the Age of the Algorithm is upon us. A master storyteller, the author takes the reader on an exhilarating journey through the history of mathematics, as he explains, in engaging, vivid prose, why to prove is to compute. A delightful read brimming with big ideas.' Bernard Chazelle, Princeton University 'An engaging study of the history of computing told from a distinctive perspective. Gilles Dowek examines the traditional axiomatic conception of mathematical proof and argues that the advent of computer-assisted proofs (for example the Appel-Haken proof of the four color theorem, the proof of Hale's theorem) and the recent development of the proofs-as-programs idea together lead the way to a new conception of proof, one in which computation rather than logical reasoning plays the dominant role. The result is an illuminating challenge to one of the firmest orthodoxies in the foundations of mathematics.' Michael Detlefsen, University of Notre Dame 'Dowek's book is a superb overview of the transformation of mathematics toward becoming a computational science. It is historically rich, philosophically inquisitive and mathematically rigorous.' Andrew Arana, Metascience


An engaging study of the history of computing told from a distinctive perspective. Gilles Dowek examines the traditional axiomatic conception of mathematical proof and argues that the advent of computer-assisted proofs (for example the Appel-Haken proof of the four color theorem, the proof of Hale's theorem) and the recent development of the proofs-as-programs idea together lead the way to a new conception of proof, one in which computation rather than logical reasoning plays the dominant role. The result is an illuminating challenge to one of the firmest orthodoxies in the foundations of mathematics. Michael Detlefsen, University of Notre Dame


Author Information

Gilles Dowek is a mathematician, logician and computer scientist, and currently a researcher at the French Institute for Research in Computer Science and Automation (INRIA). He is a member of the scientific board of the Société informatique de France and of CERNA. He is also a consultant with the National Institute of Aerospace, a NASA-affiliated laboratory. He is the recipient of the French Mathematical Society's Grand Prix d'Alembert des Lycéens for his popular science work. Pierre Guillot is a lecturer in Mathematics at the University of Strasbourg's Institute of Advanced Mathematical Research (IRMA). Marion Roman is a France-based translator.

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