Computation, Proof, Machine

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.

• 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.

'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