Computation, proof, machine : mathematics enters a new age / Gilles Dowek; translated from the French by Pierre Guillot and Marion Roman.
Material type: TextPublication details: New York : Cambridge University Press, 2015.Description: viii, 152 pages : illustrations ; 22 cmISBN:- 9780521133777
- Mathematics enters a new age
- 510.9 23 D746
Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
---|---|---|---|---|---|---|---|
Books | ISI Library, Kolkata | 510.9 D746 (Browse shelf(Opens below)) | Available | 137446 |
Includes bibliographical references
Part one: Ancient origins.
1. The prehistory of mathematics and the Greek resolution --
2. Two thousand years of computation --
Part two: The age of reason.
3. Predicate logic --
4. From the decision problem to Church's theorem --
5. Church's thesis --
6. Lambda calculus, or an attempt to reinstate computation in the realm of mathematics --
7. Constructivity --
8. Constructive proofs and algorithms --
Part three: Crisis of the axiomatic method.
9. Intuitionistic type theory --
10. Automatic theorem proving --
11. Proof checking --
12. News from the field --
13. Instruments --
14. The end of axioms?.
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.
Text in English.
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