Computer-aided Mathematics: Successes, Advances, and Trust
Thursday, November 2, 2023, 11 AM
Bahen Centre for Information Technology, BA 3200
This lecture is open to the public.
No registration is required but space is limited.
Abstract:
Progress in satisfiability (SAT) solving has made it possible to determine the correctness of complex systems and answer long-standing open questions in mathematics. The SAT-solving approach is completely automatic and can produce clever though potentially gigantic proofs. We can have confidence in the correctness of the answers because highly trustworthy systems can validate the underlying proofs regardless of their size.
We demonstrate the effectiveness of the SAT approach by presenting some recent successes, including the solution of the Boolean Pythagorean Triples problem, computing the fifth Schur number, and resolving the remaining case of Keller’s conjecture. Moreover, we constructed and validated proofs for each of these results. The second part of the talk focuses on notorious math challenges for which automated reasoning may well be suitable. In particular, we discuss advances in applying SAT-solving techniques to the Hadwiger-Nelson problem (chromatic number of the plane), optimal schemes for matrix multiplication, and the Collatz conjecture.
Bio:
Marijn Heule is an Associate Professor of Computer Science at Carnegie Mellon University. His contributions to automated reasoning have enabled him and others to solve hard problems in formal verification and mathematics. He has developed award-winning satisfiability (SAT) solvers. His preprocessing and proof-producing techniques are used in many state-of-the-art automated reasoning tools. Marijn won multiple best paper awards at international conferences, including at SAT, CADE, IJCAR, TACAS, HVC, LPAR, and IJCAI-JAIR. He is one of the editors of the Handbook of Satisfiability. This 1500+ page handbook (second edition) has become the reference for SAT research.