Computation, Proof, Machine: Mathematics Enters a New Age

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.

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