Benchmark Almanac

FrontierMath Tier 4

AI Co-Mathematician 47.9% leads since May 2026
GPT-6 Astra 97.6% leads since September 2026
Fading

Models solve research-level math problems that take experts days, submitting answers through a Python function. Each answer is verified automatically as correct or incorrect.

OpenAI funded FrontierMath and can access part of it, and a June 2026 v2 corrected 12 Tier 4 problems and removed 7.

Made by
Epoch AI
Released
July 2025
Kind
Research mathematics
Level
Research frontier
Scored
Checked automatically
Answers
Short answer
Tasks
Public, plus a private test set
Strongest model tested
GPT-6 Astra #3 on the capability index
Last in a launch post
September 2026, dropped after it saturated
Last model added
September 2026
Scores refreshed
November 12th, 2026

In the authors’ words

We introduce FrontierMath, a benchmark of hundreds of original, exceptionally challenging mathematics problems crafted and vetted by expert mathematicians. The questions cover most major branches of modern mathematics – from computationally intensive problems in number theory and real analysis to abstract questions in algebraic geometry and category theory. Solving a typical problem requires multiple hours of effort from a researcher in the relevant branch of mathematics, and for the upper end questions, multiple days. FrontierMath uses new, unpublished problems and automated verification to reliably evaluate models while minimizing risk of data contamination. Current state-of-the-art AI models solve under 2% of problems, revealing a vast gap between AI capabilities and the prowess of the mathematical community. As AI systems advance toward expert-level mathematical abilities, FrontierMath offers a rigorous testbed that quantifies their progress.

Abstract of FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI (arXiv:2411.04872, CC0)
55
Models scored in Epoch AI’s runs
6
Launch posts list it, from 1 lab

AI Co-Mathematician leads with 47.9% among models released by May 2026

Best score per model from Epoch AI’s own runs. Where a model ran with several settings or harnesses, we keep its best.

GPT-6 Astra leads with 97.6%, claims included

Best score per model from every source, including labs’ own numbers and claims Epoch AI collected from reports and papers. Labs pick their own settings, so a claim can beat an independent run of the same model.

The newest model with a score here came out in May 2026, and nobody has tested a newer one. Among the 20 highest-ranked models on the capability index, these have no score yet:

One of them reports a score in its own model card. We plot lab claims in the charts below.

  1. 1 AI Co-Mathematician 47.9%
  2. 2 GPT-5.5 Pro xhigh 39.6%
  3. 3 GPT-5.4 Pro web 37.5%
  4. 4 GPT-5.5 xhigh 35.4%
  5. 5 GPT-5.2 Pro web 31.3%
  6. 6 Claude Opus 4.8 max 31.3%
  7. 7 GPT-5.4 xhigh 27.1%
  8. 8 Claude Opus 4.7 xhigh 22.9%
  9. 9 Claude Opus 4.6 max 22.9%
  10. 10 GPT-5.2 xhigh 18.8%
  11. 11 Gemini 3 Pro 18.8%
  12. 12 Gemini 3.1 Pro 16.7%
  13. 13 GPT-5 Pro high 14.6%
  14. 14 Muse Spark 14.6%
  15. 15 Kimi K2.6 14.6%
  16. 16 Gemini 3.5 Flash high 14.6%
  17. 17 GPT-5 high 12.5%
  18. 18 GPT-5.1 high 12.5%
  19. 19 GLM-5.1 12.5%
  20. 20 Gemini 2.5 Deep Think 10.4%
  21. 21 Qwen 3.6 Plus 2026-04-02 8.33%
  22. 22 Claude Sonnet 4.6 16k thinking 8.30%
  23. 23 o4-mini high 6.25%
  24. 24 GPT-5 mini high 6.25%
  25. 25 GPT-5.4 Nano high 6.25%
  26. 26 Kimi K2.5 Fireworks 4.20%
  27. 27 o3-mini high 4.17%
  28. 28 Claude Opus 4 27K 4.17%
  29. 29 Gemini 2.5 Pro Jun 2025 4.17%
  30. 30 Gemini 2.5 Flash Jun 2025 4.17%
  31. 31 Claude Opus 4.1 27K 4.17%
  32. 32 Claude Sonnet 4.5 32k thinking 4.17%
  33. 33 Claude Opus 4.5 no thinking 4.17%
  34. 34 Gemini 3 Flash 4.17%
  35. 35 Qwen 3.6 Max (Preview) 4.17%
  36. 36 GLM-4.6 Together 2.13%
  37. 37 DeepSeek-V3.2 Thinking; Fireworks 2.10%
  38. 38 GLM-5 2.10%
  39. 39 o3 high 2.08%
  40. 40 Grok 4 2.08%
  41. 41 Grok 4 Heavy web app 2.08%
  42. 42 GPT-5 nano medium 2.08%
  43. 43 Claude Haiku 4.5 32K 2.08%
  44. 44 Qwen 3.5 Plus (hosted 397B-A17B) 2.08%
  45. 45 GPT-5.4 Mini high 2.08%
  46. 46 Claude 3.5 Sonnet Jun 2024 0%
  47. 47 Claude 3.5 Sonnet (October 2024) 0%
  48. 48 Grok 3 0%
  49. 49 GPT-4.1 0%
  50. 50 Claude Sonnet 4 0%
  51. 51 Qwen3-235B-A22B-Thinking Jul 2025 0%
  52. 52 Kimi K2 Thinking Together 0%
  53. 53 GLM-4.7 Together 0%
  54. 54 Qwen 3.5 Flash (hosted 35B-A3B) 0%
  55. 55 Qwen 3.6 Flash 2026-04-16 0%

Source: Epoch AI runs (CC BY 4.0)

  1. 1 GPT-6 Astra 97.6%
  2. 2 AI Co-Mathematician 47.9%
  3. 3 GPT-5.5 Pro xhigh 39.6%
  4. 4 GPT-5.5 39.6%
  5. 5 GPT-5.4 Pro 38%
  6. 6 GPT-5.2 Pro web 31.3%
  7. 7 Claude Opus 4.8 max 31.3%
  8. 8 GPT-5.4 xhigh 27.1%
  9. 9 Claude Opus 4.7 xhigh 22.9%
  10. 10 Claude Opus 4.6 max 22.9%
  11. 11 GPT-5.2 xhigh 18.8%
  12. 12 Gemini 3 Pro 18.8%
  13. 13 Gemini 3.1 Pro 16.7%
  14. 14 GPT-5 Pro high 14.6%
  15. 15 Muse Spark 14.6%
  16. 16 Kimi K2.6 14.6%
  17. 17 Gemini 3.5 Flash high 14.6%
  18. 18 GPT-5 high 12.5%
  19. 19 GPT-5.1 high 12.5%
  20. 20 GLM-5.1 12.5%
  21. 21 Gemini 2.5 Deep Think 10.4%
  22. 22 Qwen 3.6 Plus 2026-04-02 8.33%
  23. 23 Claude Sonnet 4.6 16k thinking 8.30%
  24. 24 o4-mini high 6.25%
  25. 25 GPT-5 mini high 6.25%
  26. 26 GPT-5.4 Nano high 6.25%
  27. 27 Kimi K2.5 Fireworks 4.20%
  28. 28 o3-mini high 4.17%
  29. 29 Claude Opus 4 27K 4.17%
  30. 30 Gemini 2.5 Pro Jun 2025 4.17%
  31. 31 Gemini 2.5 Flash Jun 2025 4.17%
  32. 32 Claude Opus 4.1 27K 4.17%
  33. 33 Claude Sonnet 4.5 32k thinking 4.17%
  34. 34 Claude Opus 4.5 no thinking 4.17%
  35. 35 Gemini 3 Flash 4.17%
  36. 36 Qwen 3.6 Max (Preview) 4.17%
  37. 37 GLM-4.6 Together 2.13%
  38. 38 DeepSeek-V3.2 Thinking; Fireworks 2.10%
  39. 39 GLM-5 2.10%
  40. 40 o3 high 2.08%
  41. 41 Grok 4 2.08%
  42. 42 Grok 4 Heavy web app 2.08%
  43. 43 GPT-5 nano medium 2.08%
  44. 44 Claude Haiku 4.5 32K 2.08%
  45. 45 Qwen 3.5 Plus (hosted 397B-A17B) 2.08%
  46. 46 GPT-5.4 Mini high 2.08%
  47. 47 Claude 3.5 Sonnet Jun 2024 0%
  48. 48 Claude 3.5 Sonnet (October 2024) 0%
  49. 49 Grok 3 0%
  50. 50 GPT-4.1 0%
  51. 51 Claude Sonnet 4 0%
  52. 52 Qwen3-235B-A22B-Thinking Jul 2025 0%
  53. 53 Kimi K2 Thinking Together 0%
  54. 54 GLM-4.7 Together 0%
  55. 55 Qwen 3.5 Flash (hosted 35B-A3B) 0%
  56. 56 Qwen 3.6 Flash 2026-04-16 0%

Sources: Labs’ model cards and Epoch AI runs (CC BY 4.0)

#ModelScoreSettingDateSource
1 AI Co-Mathematician 47.9% May 2026 Epoch AI run
2 GPT-5.5 Pro 39.6% xhigh Apr 2026 Epoch AI run
3 GPT-5.4 Pro 37.5% web Mar 2026 Epoch AI run
4 GPT-5.5 35.4% xhigh Apr 2026 Epoch AI run
5 GPT-5.2 Pro 31.3% web Dec 2025 Epoch AI run
6 Claude Opus 4.8 31.3% max May 2026 Epoch AI run
7 GPT-5.4 27.1% xhigh Mar 2026 Epoch AI run
8 Claude Opus 4.7 22.9% xhigh Apr 2026 Epoch AI run
9 Claude Opus 4.6 22.9% max Feb 2026 Epoch AI run
10 GPT-5.2 18.8% xhigh Dec 2025 Epoch AI run
11 Gemini 3 Pro 18.8% Nov 2025 Epoch AI run
12 Gemini 3.1 Pro 16.7% Feb 2026 Epoch AI run
13 GPT-5 Pro 14.6% high Oct 2025 Epoch AI run
14 Muse Spark 14.6% Apr 2026 Epoch AI run
15 Kimi K2.6 14.6% Apr 2026 Epoch AI run
16 Gemini 3.5 Flash 14.6% high May 2026 Epoch AI run
17 GPT-5 12.5% high Aug 2025 Epoch AI run
18 GPT-5.1 12.5% high Nov 2025 Epoch AI run
19 GLM-5.1 12.5% Apr 2026 Epoch AI run
20 Gemini 2.5 Deep Think 10.4% Aug 2025 Epoch AI run
21 Qwen 3.6 Plus 8.33% 2026-04-02 Mar 2026 Epoch AI run
22 Claude Sonnet 4.6 8.30% 16k thinking Feb 2026 Epoch AI run
23 o4-mini 6.25% high Apr 2025 Epoch AI run
24 GPT-5 mini 6.25% high Aug 2025 Epoch AI run
25 GPT-5.4 Nano 6.25% high Mar 2026 Epoch AI run
26 Kimi K2.5 4.20% Fireworks Jan 2026 Epoch AI run
27 o3-mini 4.17% high Jan 2025 Epoch AI run
28 Claude Opus 4 4.17% 27K May 2025 Epoch AI run
29 Gemini 2.5 Pro Jun 2025 4.17% Jun 2025 Epoch AI run
30 Gemini 2.5 Flash Jun 2025 4.17% Jun 2025 Epoch AI run
31 Claude Opus 4.1 4.17% 27K Aug 2025 Epoch AI run
32 Claude Sonnet 4.5 4.17% 32k thinking Sep 2025 Epoch AI run
33 Claude Opus 4.5 4.17% no thinking Nov 2025 Epoch AI run
34 Gemini 3 Flash 4.17% Dec 2025 Epoch AI run
35 Qwen 3.6 Max (Preview) 4.17% Apr 2026 Epoch AI run
36 GLM-4.6 2.13% Together Sep 2025 Epoch AI run
37 DeepSeek-V3.2 2.10% Thinking; Fireworks Dec 2025 Epoch AI run
38 GLM-5 2.10% Feb 2026 Epoch AI run
39 o3 2.08% high Apr 2025 Epoch AI run
40 Grok 4 2.08% Jul 2025 Epoch AI run
41 Grok 4 Heavy 2.08% web app Jul 2025 Epoch AI run
42 GPT-5 nano 2.08% medium Aug 2025 Epoch AI run
43 Claude Haiku 4.5 2.08% 32K Oct 2025 Epoch AI run
44 Qwen 3.5 Plus (hosted 397B-A17B) 2.08% Feb 2026 Epoch AI run
45 GPT-5.4 Mini 2.08% high Mar 2026 Epoch AI run
46 Claude 3.5 Sonnet 0% Jun 2024 Jun 2024 Epoch AI run
47 Claude 3.5 Sonnet (October 2024) 0% Oct 2024 Epoch AI run
48 Grok 3 0% Apr 2025 Epoch AI run
49 GPT-4.1 0% Apr 2025 Epoch AI run
50 Claude Sonnet 4 0% May 2025 Epoch AI run
51 Qwen3-235B-A22B-Thinking Jul 2025 0% Jul 2025 Epoch AI run
52 Kimi K2 Thinking 0% Together Nov 2025 Epoch AI run
53 GLM-4.7 0% Together Dec 2025 Epoch AI run
54 Qwen 3.5 Flash (hosted 35B-A3B) 0% Feb 2026 Epoch AI run
55 Qwen 3.6 Flash 0% 2026-04-16 Apr 2026 Epoch AI run
#ModelScoreSettingDateSource
1 GPT-6 Astra 97.6% Sep 2026 Lab model card
2 AI Co-Mathematician 47.9% May 2026 Epoch AI run
3 GPT-5.5 Pro 39.6% xhigh Apr 2026 Epoch AI run
4 GPT-5.5 39.6% Apr 2026 Lab model card
5 GPT-5.4 Pro 38% Mar 2026 Lab model card
6 GPT-5.2 Pro 31.3% web Dec 2025 Epoch AI run
7 Claude Opus 4.8 31.3% max May 2026 Epoch AI run
8 GPT-5.4 27.1% xhigh Mar 2026 Epoch AI run
9 Claude Opus 4.7 22.9% xhigh Apr 2026 Epoch AI run
10 Claude Opus 4.6 22.9% max Feb 2026 Epoch AI run
11 GPT-5.2 18.8% xhigh Dec 2025 Epoch AI run
12 Gemini 3 Pro 18.8% Nov 2025 Epoch AI run
13 Gemini 3.1 Pro 16.7% Feb 2026 Epoch AI run
14 GPT-5 Pro 14.6% high Oct 2025 Epoch AI run
15 Muse Spark 14.6% Apr 2026 Epoch AI run
16 Kimi K2.6 14.6% Apr 2026 Epoch AI run
17 Gemini 3.5 Flash 14.6% high May 2026 Epoch AI run
18 GPT-5 12.5% high Aug 2025 Epoch AI run
19 GPT-5.1 12.5% high Nov 2025 Epoch AI run
20 GLM-5.1 12.5% Apr 2026 Epoch AI run
21 Gemini 2.5 Deep Think 10.4% Aug 2025 Epoch AI run
22 Qwen 3.6 Plus 8.33% 2026-04-02 Mar 2026 Epoch AI run
23 Claude Sonnet 4.6 8.30% 16k thinking Feb 2026 Epoch AI run
24 o4-mini 6.25% high Apr 2025 Epoch AI run
25 GPT-5 mini 6.25% high Aug 2025 Epoch AI run
26 GPT-5.4 Nano 6.25% high Mar 2026 Epoch AI run
27 Kimi K2.5 4.20% Fireworks Jan 2026 Epoch AI run
28 o3-mini 4.17% high Jan 2025 Epoch AI run
29 Claude Opus 4 4.17% 27K May 2025 Epoch AI run
30 Gemini 2.5 Pro Jun 2025 4.17% Jun 2025 Epoch AI run
31 Gemini 2.5 Flash Jun 2025 4.17% Jun 2025 Epoch AI run
32 Claude Opus 4.1 4.17% 27K Aug 2025 Epoch AI run
33 Claude Sonnet 4.5 4.17% 32k thinking Sep 2025 Epoch AI run
34 Claude Opus 4.5 4.17% no thinking Nov 2025 Epoch AI run
35 Gemini 3 Flash 4.17% Dec 2025 Epoch AI run
36 Qwen 3.6 Max (Preview) 4.17% Apr 2026 Epoch AI run
37 GLM-4.6 2.13% Together Sep 2025 Epoch AI run
38 DeepSeek-V3.2 2.10% Thinking; Fireworks Dec 2025 Epoch AI run
39 GLM-5 2.10% Feb 2026 Epoch AI run
40 o3 2.08% high Apr 2025 Epoch AI run
41 Grok 4 2.08% Jul 2025 Epoch AI run
42 Grok 4 Heavy 2.08% web app Jul 2025 Epoch AI run
43 GPT-5 nano 2.08% medium Aug 2025 Epoch AI run
44 Claude Haiku 4.5 2.08% 32K Oct 2025 Epoch AI run
45 Qwen 3.5 Plus (hosted 397B-A17B) 2.08% Feb 2026 Epoch AI run
46 GPT-5.4 Mini 2.08% high Mar 2026 Epoch AI run
47 Claude 3.5 Sonnet 0% Jun 2024 Jun 2024 Epoch AI run
48 Claude 3.5 Sonnet (October 2024) 0% Oct 2024 Epoch AI run
49 Grok 3 0% Apr 2025 Epoch AI run
50 GPT-4.1 0% Apr 2025 Epoch AI run
51 Claude Sonnet 4 0% May 2025 Epoch AI run
52 Qwen3-235B-A22B-Thinking Jul 2025 0% Jul 2025 Epoch AI run
53 Kimi K2 Thinking 0% Together Nov 2025 Epoch AI run
54 GLM-4.7 0% Together Dec 2025 Epoch AI run
55 Qwen 3.5 Flash (hosted 35B-A3B) 0% Feb 2026 Epoch AI run
56 Qwen 3.6 Flash 0% 2026-04-16 Apr 2026 Epoch AI run

Labs report scores for 6 models in their cards. Switch the scores above to rank them together.

9 models have held number one in Epoch AI’s runs since its release in July 2025 10 models have held number one with claims included since its release in July 2025

Lab claims count from the day the card came out, independent runs from the model’s release. We draw one row each for Epoch AI’s runs and what labs claim in their cards.

OpenAI Google DeepMind
Epoch AI runs Replaced by v2, Jun 2026
AI Co-Mathematician 47.9%
Lab claims Passed 85% in Sep 2026, by GPT-6 Astra
GPT-6 Astra 97.6%

Sources: Epoch AI runs (CC BY 4.0) and labs’ model cards

OpenAI’s own number for GPT-6 Astra passed 85% in September 2026

All the scores we have, one dot each, so a model tested at several settings appears more than once.

Run by Epoch AI Reported by the lab in its model card Best so far
0% 20% 40% 60% 80% 100% 2024 2025 2026 Near the ceiling (85%) Highest possible score GPT-6 Astra AI Co-Mathematician GPT-5.5 Pro GPT-5.2 Pro Gemini 3 Pro GPT-5 Pro Gemini 2.5 Deep Think 0% 20% 40% 60% 80% 100% 2024 2025 2026 Near the ceiling (85%) Highest possible score GPT-6 Astra AI Co-Mathematician

Sources: Epoch AI runs (CC BY 4.0) and labs’ model cards

Labs headline it less often now, last in September 2026

Launch posts from every lab that has listed it, one tick per post. Tall colored ticks include it, and short gray ones leave it out.

OpenAI
DateLaunch postScoreAs the post writes it
Sep 3, 2026 GPT-6 Astra 97.6 FrontierMath Tier 4 (v2)
Apr 23, 2026 GPT-5.5 Pro 39.6 FrontierMath Tier 4
Apr 23, 2026 GPT-5.5 39.6 FrontierMath Tier 4 (GPT-5.5 Pro)
Mar 5, 2026 GPT-5.4 Pro 38 FrontierMath Tier 4
Mar 5, 2026 GPT-5.4 27.1 FrontierMath Tier 4 (GPT-5.4)
Dec 11, 2025 GPT-5.2 14.6 FrontierMath (Tier 4) Advanced mathematics

The lab's number comes out ahead in 2 of 3 pairs that differ

Each score a lab reported for its own model, beside the same model's best score from Epoch AI. Gaps mostly come from different harnesses, effort levels and task subsets. 2 of them match, which usually means one side copied the other. Every benchmark.

Model Lab says Board says Gap
GPT-5.5 39.6% FrontierMath Tier 4 (GPT-5.5 Pro) 35.4% Epoch AI run, xhigh +4.2 pts
GPT-5.2 14.6% FrontierMath (Tier 4) Advanced mathematics 18.8% Epoch AI run, xhigh −4.2 pts
GPT-5.4 Pro 38% FrontierMath Tier 4 37.5% Epoch AI run, web +0.5 pts
GPT-5.4 27.1% FrontierMath Tier 4 (GPT-5.4) 27.1% Epoch AI run, xhigh Same
GPT-5.5 Pro 39.6% FrontierMath Tier 4 39.6% Epoch AI run, xhigh Same

Versions

We switch the top row to each new version when it comes out. Open it for one row per version. An old version stays in play while people still test it, so whoever first takes it past 85% gets credit for closing it out.

OpenAI Google DeepMind Anthropic
FrontierMath Tier 4 v2 Passed 85% in Jun 2026, by Claude Fable 5
FrontierMath Tier 4 Replaced by v2, Jun 2026
AI Co-Mathematician 47.9%
FrontierMath Tier 4 v2 Passed 85% in Jun 2026, by Claude Fable 5

Sources: Official leaderboards and Epoch AI runs (CC BY 4.0)

More in Math

All 113 in Math
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  • HMMT 2026 In use Models solve the 33 final-answer problems from the February 2026 Harvard-MIT Mathematics Tournament. Scored by exact answer match. GPT-5.5 98.5%
  • PolyMath In use Models solve 9,000 parallel math problems in 18 languages across four difficulty levels, from school math to frontier math. Final answers are checked. Qwen3.7-Max 86.5%
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  • MathArena Apex Shortlist In use Models solve 47 hard final-answer problems that MathArena selected from 2025 competitions, where the best models scored about 50% at selection. Scored by accuracy over repeated attempts. GPT-5.5 98.4%