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.

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.

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.