OpenProblemBench: Benchmarking AI on Open Problems in the Foundational Theoretical Sciences

Abstract: The next frontier for artificial general intelligence is tackling unresolved scientific problems, calling for benchmarks that assess progress beyond established knowledge. We introduce OpenProblemBench, a benchmark of 82 unresolved problems drawn from the mathematics and theoretical physics literature. Each problem supplies the research context, assumptions, and prior progress needed to investigate the question. We select problems whose proposed solutions admit comparatively clear checks of their decisive mathematical or computational claims. Four evaluator models independently assess the correctness, completeness, and degree of progress of each submission without reference solutions. Across seven evaluated configurations, GPT-6-Astra achieves the highest mean judged solve rate of 14.0%, compared with 5.5-6.7% for the evaluated full-size open models and 2.4-3.7% for Flash models. Case comparisons connect stronger outcomes to changes in problem representation, general arguments that extend beyond finite evidence, and proofs of the steps needed to complete a solution. By grounding evaluation in questions arising from the research literature, OpenProblemBench provides a setting for investigating the capabilities and limitations of AI as a contributor to foundational theoretical science.