TY - JOUR AU - Bright, Curtis AU - Cheung, Kevin K. H. AU - Stevens, Brett AU - Kotsireas, Ilias AU - Ganesh, Vijay PY - 2021/05/18 Y2 - 2024/03/29 TI - A SAT-based Resolution of Lam's Problem JF - Proceedings of the AAAI Conference on Artificial Intelligence JA - AAAI VL - 35 IS - 5 SE - AAAI Technical Track on Constraint Satisfaction and Optimization DO - 10.1609/aaai.v35i5.16483 UR - https://ojs.aaai.org/index.php/AAAI/article/view/16483 SP - 3669-3676 AB - In 1989, computer searches by Lam, Thiel, and Swiercz experimentally resolved Lam's problem from projective geometry—the long-standing problem of determining if a projective plane of order ten exists. Both the original search and an independent verification in 2011 discovered no such projective plane. However, these searches were each performed using highly specialized custom-written code and did not produce nonexistence certificates. In this paper, we resolve Lam's problem by translating the problem into Boolean logic and use satisfiability (SAT) solvers to produce nonexistence certificates that can be verified by a third party. Our work uncovered consistency issues in both previous searches—highlighting the difficulty of relying on special-purpose search code for nonexistence results. ER -