International effort creates curated list of 50 verifiable mathematical challenges
Mathematicians from around the world gathered in six cities to compile 50 open mathematical problems with the distinguishing feature that solutions can be automatically verified. The initiative was organized by Epoch AI, an organization that tracks artificial intelligence progress, with participating researchers submitting problems spanning knot theory, algebra, topology, and number theory. Several problems from the new list have already been solved, including some significant ones, as AI systems continue to make advances on previously intractable mathematical challenges.
The initiative emerged from Epoch AI's mission to track artificial intelligence progress by identifying mathematical problems where correctness can be automatically verified. This verification requirement distinguishes the curated list from traditional open mathematics problems, which often demand human expert review to confirm solutions. The distributed workshop model across six major cities enabled international participation, allowing mathematicians to collectively identify problems spanning multiple disciplines.
Several problems on the list have already yielded to computational and algorithmic approaches. The Sum of Three Cubes problem exemplifies the computational intensity involved—solving for one specific case previously required millions of computing hours and millions of dollars in resources. As AI systems become increasingly sophisticated at mathematical reasoning, these benchmarks may help researchers assess whether AI advances represent genuine breakthroughs or incremental improvements.
This curated list could accelerate the pace at which mathematical discoveries are made and verified, particularly as AI systems grow more capable. Researchers and institutions may benefit from prioritized targets for computational effort and funding allocation. However, the broader implications remain uncertain—establishing automatically verifiable benchmarks might shift mathematical focus toward problems with computable solutions, potentially away from areas where proof verification requires deep human insight and creativity.