Computation, proof, machine: mathematics enters a new age
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English French |
| Veröffentlicht: |
New York, NY
Cambridge Univ. Press
2015
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Literaturverz. S. 149 - 152 |
| Beschreibung: | VIII, 152 S. graph. Darst. |
| ISBN: | 9780521118019 9780521133777 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804174864872898560 |
|---|---|
| adam_text | Contents
Introduction: In Which Mathematics Sets Out to
Conquer New Territories page 1
Part One: Ancient Origins
1 The Prehistory of Mathematics and the Greek
Resolution 5
2 Two Thousand Years of Computation 15
Part Two: The Age of Reason
3 Predicate Logic 31
4 From the Decision Problem to Church’s Theorem 44
5 Church’s Thesis 55
6 Lambda Calculus, or an Attempt to Reinstate
Computation in the Realm of Mathematics 69
7 Constructivity 73
8 Constructive Proofs and Algorithms 82
Part Three: Crisis of the Axiomatic Method
9 Intuitionistic Type Theory 89
10 Automated Theorem Proving 96
11 Proof Checking 105
12 News from the Field 111
13 Instruments 124
vii
Contents
14 The End of Axioms? 134
Conclusion: As We Near the End of This
Mathematical Voyage... 136
Biographical Landmarks 139
Bibliography 149
COMPUTATION, PROOF, MACHINE
Mathematics Enters a New Age
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 math-
ematical progress from the beginning - but behind the scenes, their
contribution 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 compu-
tation. Along the way it invites us to reconsider the dialogue 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 prob-
lems previously inaccessible.
This book is the 2007 Winner of the Grand Prix de Philosophie de
l Académie Française.
Mathematician, logician, and computer scientist Gilles Dowek is cur-
rently a researcher at the French Institute for Research in Computer Sci-
ence and Automation (INRIA). He is a member of the scientific board of
the Société informatique de France and of CERNA. He has also been a
consultant with the National Institute of Aerospace, a NASA-affiliated
lab. 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 translator based in France.
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| spelling | Dowek, Gilles 1966- Verfasser (DE-588)11433191X aut Les métamorphoses du calcul Computation, proof, machine mathematics enters a new age Gilles Dowek 1. publ. New York, NY Cambridge Univ. Press 2015 VIII, 152 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 149 - 152 Geschichte 1900-2000 Geschichte Mathematik Mathematik (DE-588)4037944-9 gnd rswk-swf Geschichte (DE-588)4020517-4 gnd rswk-swf Mathematics History 20th century Mathematics History Mathematics, Ancient (DE-588)1071861417 Konferenzschrift 2005 Rauischholzhausen gnd-content Mathematik (DE-588)4037944-9 s Geschichte (DE-588)4020517-4 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028105636&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028105636&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Dowek, Gilles 1966- Computation, proof, machine mathematics enters a new age Geschichte Mathematik Mathematik (DE-588)4037944-9 gnd Geschichte (DE-588)4020517-4 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4020517-4 (DE-588)1071861417 |
| title | Computation, proof, machine mathematics enters a new age |
| title_alt | Les métamorphoses du calcul |
| title_auth | Computation, proof, machine mathematics enters a new age |
| title_exact_search | Computation, proof, machine mathematics enters a new age |
| title_full | Computation, proof, machine mathematics enters a new age Gilles Dowek |
| title_fullStr | Computation, proof, machine mathematics enters a new age Gilles Dowek |
| title_full_unstemmed | Computation, proof, machine mathematics enters a new age Gilles Dowek |
| title_short | Computation, proof, machine |
| title_sort | computation proof machine mathematics enters a new age |
| title_sub | mathematics enters a new age |
| topic | Geschichte Mathematik Mathematik (DE-588)4037944-9 gnd Geschichte (DE-588)4020517-4 gnd |
| topic_facet | Geschichte Mathematik Konferenzschrift 2005 Rauischholzhausen |
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