Gilles Dowek

Computation, Proof, Machine (eBook, ePUB)

Mathematics Enters a New Age

• Format: ePub

Produktbeschreibung

Computation is revolutionizing our world, even the inner world of the 'pure' mathematician. Mathematical methods - especially the notion of proof - that have their roots in classical antiquity have seen a radical transformation since the 1970s, as successive advances have challenged the priority of reason over computation. Like many revolutions, this one comes from within. Computation, calculation, algorithms - all have played an important role in mathematical progress from the beginning - but behind the scenes, their contribution was obscured in the enduring mathematical literature. To understand the future of mathematics, this fascinating book returns to its past, tracing the hidden history that follows the thread of computation. Along the way it invites us to reconsider the dialog between mathematics and the natural sciences, as well as the relationship between mathematics and computer science. It also sheds new light on philosophical concepts, such as the notions of analytic and synthetic judgment. Finally, it brings us to the brink of the new age, in which machine intelligence offers new ways of solving mathematical problems previously inaccessible. This book is the 2007 winner of the Grand Prix de Philosophie de l'Academie Francaise.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 5. Mai 2015
• Englisch
• ISBN-13: 9781316379127
• Artikelnr.: 42890009

Autorenporträt

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.

Inhaltsangabe

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.

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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.

Rezensionen

'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