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Mathematics

Competition math, open research problems and formal proofs.

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Open research problems solved by AI (FrontierMath Erdős)

Share of 68 significant open Erdős problems a model solves with a machine-checked proof, in one attempt with a ~$300 budget.

What this measures: Unlike exam-style tests, nobody knew the answers to these problems when the test was made. A model only scores if the Lean proof checker accepts its proof or disproof.

0%5%10%15%20%

Plotted at model release dates (the benchmark launched 1 September 2026, so earlier models were evaluated retroactively). Outside the official one-attempt rules, 17 of the 68 problems have now been solved by some means, including 12 credited to OpenAI's 6 October research release. Contamination risk grows as solutions are published.

Source: Epoch AIData as of 9 Nov 2026
Show data table and sources
DateLabelValue
23 Apr 2026GPT-5.50%
3 Sept 2026GPT-6 Astra (pre-release)2.9%
29 Sept 2026GPT-6.1 Sol4.4%

Erdős problems with a computer-checked solution

Problems in the community Erdős problems database whose solution has been formalized in the Lean proof checker, at the end of each month.

What this measures: Paul Erdős left behind more than a thousand math problems. This counts how many have a solution that the Lean proof checker has verified step by step, whether the proof came from a human or an AI.

01002003004002026

Counts solutions from any source, human or AI, so this is not a count of AI solutions. Early growth partly reflects the database being built. The sources don't explain the August 2026 jump. Since 6 October 2026 erdosproblems.com no longer shows solved counts, and the 12 FrontierMath Erdős problems Epoch AI credits to OpenAI's 6 October release are not yet included. Each point is the last row of its month in the database's statistics_history.csv.

Sources: Erdős problems community database (Tao et al.), Erdős problems community databaseData as of 9 Nov 2026
Show data table and sources
DateLabelValue
30 Sept 20253 problems
31 Dec 202538 problems
31 Jan 202669 problems
28 Feb 2026110 problems
31 Mar 2026124 problems
30 Apr 2026167 problems
31 May 2026186 problems
30 Jun 2026199 problems
31 Jul 2026207 problems
31 Aug 2026292 problems
28 Sept 2026317 problems
29 Oct 2026318 problems
6 Nov 2026318 problems

Competition math (AIME-style problems)

Best independently measured score on Epoch AI's OTIS Mock AIME 2024–25 (45 problems), by model release date.

What this measures: Problems from the level of the American Invitational Mathematics Examination, the qualifier for the US Math Olympiad team. In 2023 the best AI solved almost none.

0%50%100%202420252026

Saturated · last data Apr 2026: Top models score 100% (GPT-5.5 Pro, April 2026), so this test can no longer show progress and labs stopped reporting it. Now watch: FrontierMath and FrontierMath Erdős (open problems).

Release dates for GPT-4 (0613), Claude 2.0, Claude 3 Opus and Llama 3.1 are the models' public release dates. Each problem is worth about 2.2 points. Labs stopped reporting AIME in 2026 because top models solve it all.

Sources: Epoch AI, MathArena (ETH Zurich)Data as of 9 Nov 2026
Show data table and sources
DateLabelValue
14 Mar 2023GPT-4 (0314)0.6%
13 Jun 2023GPT-4 (0613)1.1%
11 Jul 2023Claude 2.02.5%
4 Mar 2024Claude 3 Opus4.7%
9 Apr 2024GPT-4 Turbo (Apr 2024)6.7%
23 Jul 2024Llama 3.1 405B9.7%
12 Sept 2024o1-mini (high)47%
17 Dec 2024o1 (high)73%
31 Jan 2025o3-mini (high)77%
16 Apr 2025o384%
7 Aug 2025GPT-5 (high)91%
11 Dec 2025GPT-5.2 (high)96%
5 Mar 2026GPT-5.498%
23 Apr 2026GPT-5.5 Pro100%

Best AI score at the International Mathematical Olympiad

Points out of 42 on the year's IMO paper, for results graded by or reported as graded by IMO coordinators.

What this measures: The International Mathematical Olympiad is the world's top math contest for high-school students: six proof problems, 42 points in total. Gold usually needs about 29–35.

  • Best AI score
  • Reference level
01020304020252026Perfect score

Saturated: AI systems were reported to reach a perfect 42/42 in 2026, so the contest can't show further progress. The next frontier is open research problems. Now watch: FrontierMath Erdős and Erdős problems solved.

Gold-medal cutoffs: 35 (2025), 29 (2026). The 2026 results were reported by Chinese media and the companies; we found no statement published by the IMO itself.

Sources: Google DeepMind, France 24 / AFP, China DailyData as of 9 Nov 2026
Show data table and sources
DateLabelValue
25 Jul 2024AlphaProof + AlphaGeometry 228 points
21 Jul 2025Gemini Deep Think35 points
22 Jul 2026dots-note-3.0 / Huawei Celia42 points
Perfect score42 points

FrontierMath: hard math problems solved

Best score on Epoch AI's FrontierMath (corrected v2 set), plotted at each model's release date.

What this measures: Hundreds of unpublished problems written by mathematicians. Tiers 1–3 are advanced; Tier 4 is research-level. Answers are checked automatically.

Updated
  • Tiers 1–3 (advanced)
  • Tier 4 (research-level)
0%50%100%20252026

Tier 4 (research-level), Saturated: Epoch AI considers Tier 4 saturated: GPT-6 Astra solved the last problem no model had solved (September 2026), and GPT-6.1 Sol scores 100%. Now watch: FrontierMath Erdős (68 genuinely open problems).

Epoch AI re-ran older models on the corrected v2 problem set (June 2026), so early points come from those re-runs. OpenAI funded FrontierMath and has access to many problems; Epoch keeps a held-out set. Answers are checked automatically. These are not proofs of open problems.

Source: Epoch AIData as of 10 Nov 2026
Show data table and sources
SeriesDateLabelValue
Tiers 1–3 (advanced)17 Dec 2024o1 (high)15%
Tiers 1–3 (advanced)31 Jan 2025o3-mini (high)19%
Tiers 1–3 (advanced)16 Apr 2025o4-mini (high)36%
Tiers 1–3 (advanced)7 Aug 2025GPT-5 (high)55%
Tiers 1–3 (advanced)11 Dec 2025GPT-5.2 Pro74%
Tiers 1–3 (advanced)5 Mar 2026GPT-5.4 Pro83%
Tiers 1–3 (advanced)23 Apr 2026GPT-5.5 Pro88%
Tiers 1–3 (advanced)9 Jul 2026GPT-5.6 Sol89%
Tiers 1–3 (advanced)1 Sept 2026Claude Fable 5.190%
Tiers 1–3 (advanced)3 Sept 2026GPT-6 Astra94%
Tiers 1–3 (advanced)9 Nov 2026Claude Fable 5.2 (max)95%
Tier 4 (research-level)16 Apr 2025o4-mini4.9%
Tier 4 (research-level)7 Aug 2025GPT-522%
Tier 4 (research-level)11 Dec 2025GPT-5.2 Pro46%
Tier 4 (research-level)5 Mar 2026GPT-5.4 Pro59%
Tier 4 (research-level)23 Apr 2026GPT-5.5 Pro78%
Tier 4 (research-level)9 Jun 2026Claude Fable 590%
Tier 4 (research-level)3 Sept 2026GPT-6 Astra98%
Tier 4 (research-level)29 Sept 2026GPT-6.1 Sol (max)100%
Tier 4 (research-level)9 Nov 2026Claude Fable 5.2 (max)100%

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