A collection of unsolved mathematics problems that have resisted serious attempts by professional mathematicians. AI solutions would meaningfully advance the state of human mathematical knowledge.
This work was supported by Schmidt Sciences.
Interested in purchasing access to solution verifiers? See below.
A Genus 2 Curve over the Rationals with a Rational Torsion Point of Prime Order at Least 31
Moderately interestingArithmetic geometry
Construction - Finite
Record Breaking
Solved
Short Superpermutations over 8, 9, and 10
Moderately interestingCombinatorics
Construction - Family
Improved Bound
Unsolved
A Baillie–PSW Pseudoprime
Moderately interestingNumber theory
Counterexample
Integer Solution
Unsolved
Chowla's Cosine Problem
Moderately interestingAnalysis
Construction - Finite
Improved Bound
Unsolved
Large ℓ-Rank in Class Groups of Imaginary Quadratic Fields
Moderately interestingAlgebraic number theory
Record Breaking
Unsolved
A Rational Diophantine Septuple
Moderately interestingDiophantine
Integer Solution
Unsolved
The Earth–Moon Problem
Moderately interestingGraph theory
Construction - Finite
Improved Bound
Unsolved
Existence of EFX Allocations
Moderately interestingSocial choice
Construction - Finite
Counterexample
Unsolved
Elliptic Curves over Q of Large Rank
Moderately interestingArithmetic geometry
Construction - Finite
Record Breaking
Unsolved
Euler's Sum of Powers Conjecture
Moderately interestingDiophantine
Counterexample
Integer Solution
Verifier Access
Problems in FrontierMath: Open Problems are designed so that, even though no solution is known today, potential solutions can be checked for accuracy by a bespoke computer program, which we call a verifier.
Access to the verifiers is available for purchase by any party. Proceeds help fund the expansion of the benchmark. Our main cost is compensation to mathematicians, as the problems and verifiers are labor-intensive to formulate and implement.
At present, OpenAI is the only entity to have purchased access to the verifiers. OpenAI funded the creation of the original FrontierMath: Tiers 1-4, but Open Problems is developed independently and owned solely by Epoch.
Contact us with inquiries about purchasing access to the verifiers.
We also removed the Ramsey-style hypergraph problem from the benchmark. Here we determined that, in hindsight, the problem did not meet our minimum bar for notability.
2026-06-27: We have stopped displaying failed AI attempts on the website. Problem pages will continue to be updated to reflect notable partial progress and solutions. We also modified the prompt for the problem about finding a surface with a high number of singularities. The verifier for this problem needs to be modified before it can handle what was described as Method C.
2026-03-05: We removed one problem from the benchmark, as we have determined that any solution would not meet our bar of being a publishable result in its own right. The problem page remains up: see it for more info on an AI-generated solution and subsequent human elaboration.
We also removed the Ramsey-style hypergraph problem from the benchmark. Here we determined that, in hindsight, the problem did not meet our minimum bar for notability.
2026-06-27
We have stopped displaying failed AI attempts on the website. Problem pages will continue to be updated to reflect notable partial progress and solutions. We also modified the prompt for the problem about finding a surface with a high number of singularities. The verifier for this problem needs to be modified before it can handle what was described as Method C.
2026-03-05
We removed one problem from the benchmark, as we have determined that any solution would not meet our bar of being a publishable result in its own right. The problem page remains up: see it for more info on an AI-generated solution and subsequent human elaboration.