FrontierMath Tiers 1-3 leaderboard

What FrontierMath Tiers 1-3 measures

FrontierMath is a set of original, unpublished math problems written and vetted by expert mathematicians and maintained by Epoch AI. The problems range across most major branches of modern mathematics, from computation-heavy number theory and real analysis to abstract questions in algebraic geometry and category theory. Epoch describes a typical problem as needing several hours of work from a researcher in the relevant field, and the hardest as needing days. Tiers 1-3 is the base set of 295 problems, running from advanced undergraduate material up to early-career research level. A harder 43-problem expansion is tracked separately as Tier 4.

Every problem has a single exact answer that can be checked automatically, so grading needs no judge model. For each question the model submits a Python function that returns its answer, and the score is the share of problems solved. Because the questions are unpublished, the numbers on this page come from Epoch's private set, which makes memorizing answers from training data much harder than on a public benchmark.

How to read this page

The chart plots each model's score against its output price per 1M tokens. Output price is the sensible proxy here because a solve usually comes from a long reasoning trace, while the problem statement is short. Epoch reports each model at its best-performing reasoning effort, so the leaderboard shows what a model can do when it is allowed to think at length, and the bill for that is larger than the list price of a quick reply suggests.

Limitations

Epoch revised the dataset on 2026-06-12 after finding errors in 42% of the earlier problems, so scores before and after that update are not comparable and this page uses only the revised set. The top models now solve most of the Tiers 1-3 problems, so differences of a point or two among the leaders are within the noise of a 295-question test; the harder Tier 4 page does more to separate them. Epoch also discloses that FrontierMath was developed with funding from OpenAI, which has exclusive access to a subset of the problems. Only twelve problems are public, so outsiders cannot audit the rest. Finally, exact-answer grading rewards getting the number right, not producing a sound proof.