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.
To understand the future of mathematics, this fascinating book returns to its past, tracing the hidden history that follows the thread of computation.
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.
'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
Ask a Question About this Product More... |