Computation, Proof, Machine: Mathematics Enters a New Age
Autor Gilles Dowek Traducere de Pierre Guillot, Marion RomanHardback – 4 mai 2015
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Specificații
ISBN-13: 9780521118019
ISBN-10: 0521118018
Pagini: 158
Ilustrații: 6 b/w illus.
Dimensiuni: 145 x 223 x 13 mm
Greutate: 0.3 kg
Ediția:Nouă
Editura: Cambridge University Press
Colecția Cambridge University Press
Locul publicării:New York, United States
ISBN-10: 0521118018
Pagini: 158
Ilustrații: 6 b/w illus.
Dimensiuni: 145 x 223 x 13 mm
Greutate: 0.3 kg
Ediția:Nouă
Editura: Cambridge University Press
Colecția Cambridge University Press
Locul publicării:New York, United States
Cuprins
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.
Recenzii
'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
'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
Notă biografică
Descriere
To understand the future of mathematics, this fascinating book returns to its past, tracing the hidden history that follows the thread of computation.