Did AI just crack math's hardest problems?

As of October 2026, OpenAI's AI has written 721 maths papers and solved Navier-Stokes, and AI alone has solved 5 problems mathematicians could not (Epoch AI's list).

721

maths papers written by OpenAI’s AI · Oct 2026

How good is AI at maths?

Each line is the highest AI score on one test, by the month the model came out. When AI nearly maxes a test, a harder one takes over.

0%50%100%2020202220242026Share of the test AI gets right (highest so far)Beyond the tests: problems nobody had solvedJun 2026 · AI solves its first problem mathematicians couldn'tJun 2026 · AI solves its first problem mathematicians couldn'tSep 2026 · OpenAI's AI solves Navier-Stokes, a $1 million prize problemSep 2026 · OpenAI's AI solves Navier-Stokes, a $1 million prize problemOct 2026 · 10 of 49 problems mathematicians couldn't solve are now solvedOct 2026 · 10 of 49 problems mathematicians couldn't solve are now solvedGSM8K · babbage · 0.7% · Jun 2020GSM8K · code-davinci-002 · 56.8% · Mar 2022GSM8K · text-davinci-003 · 78.2% · Nov 2022GSM8K · gpt-4-0314 · 92% · Mar 2023GSM8K · DeepSeek-Coder-V2-Instruct · 94.5% · Jun 2024MATH Level 5 · gpt-4-0613 · 23% · Jun 2023MATH Level 5 · gpt-4-1106-preview · 40% · Nov 2023MATH Level 5 · gpt-4-turbo-2024-04-09 · 46.7% · Apr 2024MATH Level 5 · gpt-4o-2024-05-13 · 51.1% · May 2024MATH Level 5 · claude-3-5-sonnet-20240620 · 51.7% · Jun 2024MATH Level 5 · gpt-4o-mini-2024-07-18 · 52.6% · Jul 2024MATH Level 5 · gpt-4o-2024-08-06 · 53.3% · Aug 2024MATH Level 5 · o1-mini-2024-09-12_high · 89.2% · Sep 2024MATH Level 5 · o1-2024-12-17_high · 94.7% · Dec 2024MATH Level 5 · o3-mini-2025-01-31_high · 96.5% · Jan 2025MATH Level 5 · o4-mini-2025-04-16_high · 97.8% · Apr 2025MATH Level 5 · gpt-5-2025-08-07_high · 98.1% · Aug 2025OTIS Mock AIME · gpt-4-0314 · 0.6% · Mar 2023OTIS Mock AIME · gpt-4-0613 · 1.1% · Jun 2023OTIS Mock AIME · claude-2.0 · 2.5% · Jul 2023OTIS Mock AIME · claude-3-opus-20240229 · 4.7% · Feb 2024OTIS Mock AIME · gpt-4-turbo-2024-04-09 · 6.7% · Apr 2024OTIS Mock AIME · gemini-1.5-pro-001 · 6.8% · May 2024OTIS Mock AIME · gpt-4o-mini-2024-07-18 · 6.9% · Jul 2024OTIS Mock AIME · Llama-3.1-405B-Instruct · 9.7% · Jul 2024OTIS Mock AIME · o1-mini-2024-09-12_high · 46.9% · Sep 2024OTIS Mock AIME · o1-2024-12-17_high · 73.3% · Dec 2024OTIS Mock AIME · o3-mini-2025-01-31_high · 76.9% · Jan 2025OTIS Mock AIME · grok-3-mini-beta_high · 77.8% · Apr 2025OTIS Mock AIME · o3-2025-04-16_medium · 84.4% · Apr 2025OTIS Mock AIME · Qwen3-235B-A22B-Thinking-2507 · 86.7% · Jul 2025OTIS Mock AIME · openai/gpt-oss-120b_high · 88.9% · Aug 2025OTIS Mock AIME · gpt-5-2025-08-07_high · 91.4% · Aug 2025OTIS Mock AIME · gpt-5.2-2025-12-11_high · 96.1% · Dec 2025OTIS Mock AIME · gpt-5.4-2026-03-05_high · 97.8% · Mar 2026OTIS Mock AIME · claude-opus-4-7_xhigh · 97.8% · Apr 2026OTIS Mock AIME · gpt-5.5-pro-pre-release_xhigh · 100% · Apr 2026FrontierMath Tier 4 · o3-mini-2025-01-31_high · 0% · Jan 2025FrontierMath Tier 4 · o4-mini-2025-04-16_high · 4.9% · Apr 2025FrontierMath Tier 4 · gpt-5-2025-08-07_high · 22% · Aug 2025FrontierMath Tier 4 · gpt-5.2-pro-2025-12-11_xhigh · 46% · Dec 2025FrontierMath Tier 4 · gpt-5.4-pro-2026-03-05_xhigh · 58.5% · Mar 2026FrontierMath Tier 4 · gpt-5.5-pro_xhigh · 78.1% · Apr 2026FrontierMath Tier 4 · claude-fable-5_max · 90.2% · Jun 2026FrontierMath Tier 4 · gpt-6-astra_high · 97.6% · Sep 2026FrontierMath Tier 4 · gpt-6.1-sol_max · 100% · Sep 202612343100%4100%298%195%0%50%100%2020202220242026Share of the test AI gets right(highest so far)Beyond the tests: problems nobody had solvedJun 2026 · AI solves its first problem mathematicians couldn'tSep 2026 · OpenAI's AI solves Navier-Stokes, a $1 million prize problemOct 2026 · 10 of 49 problems mathematicians couldn't solve are now solvedGSM8K · babbage · 0.7% · Jun 2020GSM8K · code-davinci-002 · 56.8% · Mar 2022GSM8K · text-davinci-003 · 78.2% · Nov 2022GSM8K · gpt-4-0314 · 92% · Mar 2023GSM8K · DeepSeek-Coder-V2-Instruct · 94.5% · Jun 2024MATH Level 5 · gpt-4-0613 · 23% · Jun 2023MATH Level 5 · gpt-4-1106-preview · 40% · Nov 2023MATH Level 5 · gpt-4-turbo-2024-04-09 · 46.7% · Apr 2024MATH Level 5 · gpt-4o-2024-05-13 · 51.1% · May 2024MATH Level 5 · claude-3-5-sonnet-20240620 · 51.7% · Jun 2024MATH Level 5 · gpt-4o-mini-2024-07-18 · 52.6% · Jul 2024MATH Level 5 · gpt-4o-2024-08-06 · 53.3% · Aug 2024MATH Level 5 · o1-mini-2024-09-12_high · 89.2% · Sep 2024MATH Level 5 · o1-2024-12-17_high · 94.7% · Dec 2024MATH Level 5 · o3-mini-2025-01-31_high · 96.5% · Jan 2025MATH Level 5 · o4-mini-2025-04-16_high · 97.8% · Apr 2025MATH Level 5 · gpt-5-2025-08-07_high · 98.1% · Aug 2025OTIS Mock AIME · gpt-4-0314 · 0.6% · Mar 2023OTIS Mock AIME · gpt-4-0613 · 1.1% · Jun 2023OTIS Mock AIME · claude-2.0 · 2.5% · Jul 2023OTIS Mock AIME · claude-3-opus-20240229 · 4.7% · Feb 2024OTIS Mock AIME · gpt-4-turbo-2024-04-09 · 6.7% · Apr 2024OTIS Mock AIME · gemini-1.5-pro-001 · 6.8% · May 2024OTIS Mock AIME · gpt-4o-mini-2024-07-18 · 6.9% · Jul 2024OTIS Mock AIME · Llama-3.1-405B-Instruct · 9.7% · Jul 2024OTIS Mock AIME · o1-mini-2024-09-12_high · 46.9% · Sep 2024OTIS Mock AIME · o1-2024-12-17_high · 73.3% · Dec 2024OTIS Mock AIME · o3-mini-2025-01-31_high · 76.9% · Jan 2025OTIS Mock AIME · grok-3-mini-beta_high · 77.8% · Apr 2025OTIS Mock AIME · o3-2025-04-16_medium · 84.4% · Apr 2025OTIS Mock AIME · Qwen3-235B-A22B-Thinking-2507 · 86.7% · Jul 2025OTIS Mock AIME · openai/gpt-oss-120b_high · 88.9% · Aug 2025OTIS Mock AIME · gpt-5-2025-08-07_high · 91.4% · Aug 2025OTIS Mock AIME · gpt-5.2-2025-12-11_high · 96.1% · Dec 2025OTIS Mock AIME · gpt-5.4-2026-03-05_high · 97.8% · Mar 2026OTIS Mock AIME · claude-opus-4-7_xhigh · 97.8% · Apr 2026OTIS Mock AIME · gpt-5.5-pro-pre-release_xhigh · 100% · Apr 2026FrontierMath Tier 4 · o3-mini-2025-01-31_high · 0% · Jan 2025FrontierMath Tier 4 · o4-mini-2025-04-16_high · 4.9% · Apr 2025FrontierMath Tier 4 · gpt-5-2025-08-07_high · 22% · Aug 2025FrontierMath Tier 4 · gpt-5.2-pro-2025-12-11_xhigh · 46% · Dec 2025FrontierMath Tier 4 · gpt-5.4-pro-2026-03-05_xhigh · 58.5% · Mar 2026FrontierMath Tier 4 · gpt-5.5-pro_xhigh · 78.1% · Apr 2026FrontierMath Tier 4 · claude-fable-5_max · 90.2% · Jun 2026FrontierMath Tier 4 · gpt-6-astra_high · 97.6% · Sep 2026FrontierMath Tier 4 · gpt-6.1-sol_max · 100% · Sep 20263100%4100%298%195%
  • 1School sums
  • 2Competition maths
  • 3Top high-school contest
  • 4Research-level problems

First to reach 90%

The month each maths test was first passed at 90%, and the AI that did it
LevelTestMonthAIScore
1School sumsGSM8KMar 2023GPT-492%
2Competition mathsMATH Level 5Dec 2024o195%
3Top high-school contestOTIS Mock AIMEAug 2025GPT-591%
4Research-level problemsFrontierMath Tier 4Jun 2026Claude Fable 590%

  1. Millennium Prize problems

    OpenAI Navier-Stokes paper

    Navier-Stokes solved

    OpenAI's AI, Sep 2026

  2. Problems mathematicians couldn't solve

    Epoch AI FrontierMath Open Problems

    10 of 49

    • AI alone (5)
    • AI with mathematicians (5)

    2 Erdős problems nobody had solved, solved by AI alone · GPT-6 Astra first, Sep 2026

  3. Research-level problems

    FrontierMath Tier 4

    100%

    GPT-6.1 Sol, Sep 2026

  4. High-school competition maths

    OTIS Mock AIME

    100%

    first GPT-5.5, Apr 2026

Did OpenAI solve Navier-Stokes?

Yes. OpenAI’s AI solved it in September 2026. The Clay Institute, which awards the $1 million prize, says the problem “has apparently been settled”.

  • Navier-StokesSolved by OpenAI’s AI · Sep 2026 · $1 million Millennium Prize

Every level

Maths results by level: test, model, result, date
LevelTestModelResultDate
Millennium Prize problemsOpenAI Navier-Stokes paperOpenAI’s AINavier-Stokes solvedSep 2026
Problems mathematicians couldn't solveEpoch AI FrontierMath Open ProblemsSeveral AIs10 of 49Oct 2026
Research-level problemsFrontierMath Tier 4GPT-6.1 Sol100%Sep 2026
High-school competition mathsOTIS Mock AIMEfirst GPT-5.5100%Apr 2026
Sources (10)
  1. GitHub, github.com/openai/math
  2. Epoch AI, epoch.ai/frontiermath/open-problems
  3. OpenAI, openai.com/index/navier-stokes-solution
  4. Epoch AI, epoch.ai/benchmarks/gsm8k
  5. Epoch AI, epoch.ai/benchmarks/math-level-5
  6. Epoch AI, epoch.ai/benchmarks/otis-mock-aime-2024-2025
  7. Epoch AI, epoch.ai/benchmarks/frontiermath-tier-4-v2
  8. Epoch AI, Announcing FrontierMath Erdős, Sep 2026
  9. Epoch AI, epoch.ai/benchmarks/frontiermath-tier-4
  10. Clay Mathematics Institute, claymath.org/news/navier-stokes-announcement