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Computation, proof, machine : mathematics enters a new age

Author: Gilles Dowek; Pierre Guillot; Marion Roman
Publisher: New York, NY : Cambridge University Press, 2015.
Edition/Format:   Print book : English : First English editionView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: History
Document Type: Book
All Authors / Contributors: Gilles Dowek; Pierre Guillot; Marion Roman
ISBN: 9780521118019 0521118018 9780521133777 0521133777
OCLC Number: 903763239
Language Note: Text in English.
Description: viii, 152 pages : illustrations ; 22 cm
Contents: Part one: Ancient origins. The prehistory of mathematics and the Greek resolution --
Two thousand years of computation --
Part two: The age of reason. Predicate logic --
From the decision problem to Church's theorem --
Church's thesis --
Lambda calculus, or an attempt to reinstate computation in the realm of mathematics --
Constructivity --
Constructive proofs and algorithms --
Part three: Crisis of the axiomatic method. Intuitionistic type theory --
Automatic theorem proving --
Proof checking --
News from the field --
Instruments --
The end of axioms? --
Conclusion: As we near the end of this mathematical voyage.
Other Titles: Mathematics enters a new age
Responsibility: Gilles Dowek, French Institute for Research in Computer Science and Automation (INRIA) ; translated from the French by Pierre Guillot and Marion Roman.

Abstract:

To understand the future of mathematics, this fascinating book returns to its past, tracing the hidden history that follows the thread of computation.  Read more...

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'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 Read more...

 
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