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## Details

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:

## Reviews

*Editorial reviews*

Publisher Synopsis

'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 "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 Read more...

*User-contributed reviews*