Math
FrontierMath Tier 4 Leaderboard
FrontierMath Tier 4 is the hardest tier of Epoch AI's research-level mathematics benchmark, holding problems that working mathematicians consider genuinely difficult research questions. Scores here stay low even for frontier models, making it the sharpest available read on mathematical ability.
Source: epoch15 open models ranked+64 proprietaryData through Oct 2026
All models ranked on FrontierMath Tier 4
Proprietary / closed models are shown dimmed — you can't run them locally, but they show where the open field stands.
| # | Model | Score | VRAM @ Q4 |
|---|---|---|---|
| 1 | GPT 6.1 Sol Max · proprietary | 100.0% | API only |
| 2 | GPT 6 Astra (high) · proprietary | 97.6% | API only |
| 3 | GPT 6 Astra (xhigh) · proprietary | 97.6% | API only |
| 4 | GPT 6 Astra Max · proprietary | 97.6% | API only |
| 5 | GPT 6 Astra (medium) · proprietary | 97.6% | API only |
| 6 | Claude Opus 5.5 Max · proprietary | 95.0% | API only |
| 7 | GPT 6.1 Terra Max · proprietary | 92.7% | API only |
| 8 | Claude Fable 5 Max · proprietary | 90.2% | API only |
| 9 | GPT 6 Sol Max · proprietary | 90.0% | API only |
| 10 | Claude Fable 5.1 Max · proprietary | 87.8% | API only |
| 11 | GPT 6 Astra (low) · proprietary | 87.8% | API only |
| 12 | GPT 5.6 Sol Max · proprietary | 82.9% | API only |
| 13 | GPT 6 Astra None · proprietary | 82.9% | API only |
| 14 | Claude Sonnet 5.5 Max · proprietary | 80.5% | API only |
| 15 | GPT 5.6 Sol Promax · proprietary | 80.5% | API only |
| 16 | Gemini 4 Argon (high) · proprietary | 78.0% | API only |
| 17 | GPT 5.5 Pro (xhigh) · proprietary | 78.0% | API only |
| 18 | Gdm Ai Co Mathematician · proprietary | 75.6% | API only |
| 19 | Claude Opus 5 Max · proprietary | 73.2% | API only |
| 20 | GPT 5.5 (xhigh) · proprietary | 72.5% | API only |
| 21 | GPT 5.6 Terra Max · proprietary | 70.7% | API only |
| 22 | Muse Wonder 1.0 Max · proprietary | 70.7% | API only |
| 23 | Kimi K3.1 Pro Together Max · proprietary | 65.8% | API only |
| 24 | GPT 5.6 Luna Max · proprietary | 61.0% | API only |
| 25 | GPT 5.4 Pro (Mar 05, 2026, xhigh) · proprietary | 58.5% | API only |
| 26 | Claude Opus 4.8 Max · proprietary | 56.1% | API only |
| 27 | GPT 6 Luna Max · proprietary | 56.1% | API only |
| 28 | GPT 5.4 (Mar 05, 2026, xhigh) · proprietary | 49.0% | API only |
| 29 | Claude Haiku 5.5 Max · proprietary | 46.3% | API only |
| 30 | DeepSeek V4.1 Flash 1017 · 763.2B | 46.3% | ~458 GB |
| 31 | Muse Spark 1.3 Max · proprietary | 46.3% | API only |
| 32 | Qwen3.8 Max (xhigh) · proprietary | 46.3% | API only |
| 33 | GPT 5.2 Pro (Dec 11, 2025, xhigh) · proprietary | 46.0% | API only |
| 34 | Muse Spark 1.3 (xhigh) · proprietary | 41.5% | API only |
| 35 | Kimi K3 · 2779.9B | 39.0% | ~1674 GB |
| 36 | Gemini 3.7 Flash (high) · proprietary | 36.6% | API only |
| 37 | Qwen3.7 Max · proprietary | 34.2% | API only |
| 38 | Qwen3.8 Max (Sep 02, xhigh) · proprietary | 34.2% | API only |
| 39 | Claude Opus 4.7 Max · proprietary | 31.7% | API only |
| 40 | Grok 4.6 (xhigh) · proprietary | 31.7% | API only |
| 41 | Muse Spark Open 816B A42B · 822.0B | 31.7% | ~543 GB |
| 42 | GPT 5.2 (Dec 11, 2025, xhigh) · proprietary | 31.7% | API only |
| 43 | Claude Sonnet 5 Max · proprietary | 29.3% | API only |
| 44 | GLM 5.2 · 753.3B | 29.3% | ~456 GB |
| 45 | GLM 5.3 · 753.3B | 29.3% | ~456 GB |
| 46 | Claude Opus 4.6 Max · proprietary | 26.8% | API only |
| 47 | DeepSeek V4 Pro 0813 · 1650.5B | 26.8% | ~991 GB |
| 48 | DeepSeek V4.1 Flash · 763.2B | 26.8% | ~458 GB |
| 49 | Gemini 3.1 Pro Preview · proprietary | 26.8% | API only |
| 50 | Gemini 3.5 Flash (high) · proprietary | 26.8% | API only |
| 51 | Mistral Large 4 1T A52B · 1000B | 26.8% | ~604 GB |
| 52 | Kimi K2.6 · 1026.9B | 25.6% | ~620 GB |
| 53 | DeepSeek V4 Flash 0731 · 304.2B | 24.4% | ~183 GB |
| 54 | Grok 4.5 (high) · proprietary | 24.4% | API only |
| 55 | Gemini 3.6 Flash (high) · proprietary | 21.9% | API only |
| 56 | Gemini 3.8 Flash (high) · proprietary | 21.9% | API only |
| 57 | GPT 5 (Aug 07, 2025, high) · proprietary | 21.9% | API only |
| 58 | GPT 5 Pro (Oct 06, 2025, high) · proprietary | 19.5% | API only |
| 59 | Gemini 3 Flash Preview · proprietary | 17.1% | API only |
| 60 | GLM 5.3 Flash · 321.3B | 17.1% | ~195 GB |
| 61 | Grok 4.20 0309 Reasoning · proprietary | 17.1% | API only |
| 62 | Grok 4.7 (xhigh) · proprietary | 17.1% | API only |
| 63 | Inkling Small · 266.0B | 17.1% | ~160 GB |
| 64 | Grok 4.3 (high) · proprietary | 14.6% | API only |
| 65 | GPT 5 Mini (Aug 07, 2025, high) · proprietary | 12.2% | API only |
| 66 | GPT 5.4 Nano (Mar 17, 2026, high) · proprietary | 12.2% | API only |
| 67 | Kimi K2.7 Code · 1026.9B | 12.2% | ~620 GB |
| 68 | GPT 5.4 Mini (Mar 17, 2026, xhigh) · proprietary | 9.8% | API only |
| 69 | Claude Opus 4.5 (Nov 01, 2025, 32K) · proprietary | 4.9% | API only |
| 70 | Inkling · 952.4B | 4.9% | ~572 GB |
| 71 | O4 Mini (Apr 16, 2025, high) · proprietary | 4.9% | API only |
| 72 | Claude Opus 4.1 (Aug 05, 2025, 32K) · proprietary | 2.4% | API only |
| 73 | Claude Sonnet 4.5 (Sep 29, 2025, 32K) · proprietary | 2.4% | API only |
| 74 | DeepSeek V4 Pro · 1598.8B | 2.4% | ~960 GB |
| 75 | GPT 5 Nano (Aug 07, 2025, high) · proprietary | 2.4% | API only |
| 76 | GPT 5.5 Instant · proprietary | 2.4% | API only |
| 77 | Gemini 2.5 Pro · proprietary | 0.0% | API only |
| 78 | Gemini 3.5 Flash Lite (high) · proprietary | 0.0% | API only |
| 79 | O3 Mini (Jan 31, 2025, high) · proprietary | 0.0% | API only |
Score vs model size
Which models give the most quality for their size — the ones worth running locally.
- Inkling Small, 266B, score 17.1% — on the efficiency frontier (best score at its size or smaller).
- DeepSeek V4 Flash 0731, 304B, score 24.4% — on the efficiency frontier (best score at its size or smaller).
- GLM 5.2, 753B, score 29.3% — on the efficiency frontier (best score at its size or smaller).
- DeepSeek V4.1 Flash 1017, 763B, score 46.3% — on the efficiency frontier (best score at its size or smaller).
FrontierMath Tier 4: frequently asked questions
- What is the best open LLM on FrontierMath Tier 4?
- DeepSeek V4.1 Flash 1017 is the top open model on FrontierMath Tier 4, scoring 46.3%. Among all models tested — including proprietary ones — it ranks #29. The top model overall is GPT 6.1 Sol Max (OpenAI) at 100.0%.
- Can open models match proprietary models on FrontierMath Tier 4?
- Not quite on FrontierMath Tier 4: the strongest proprietary model (GPT 6.1 Sol Max) scores 100.0%, ahead of the best open model (DeepSeek V4.1 Flash 1017) at 46.3% — but you can run the open one yourself.
Scores aggregated from epoch. llmrun does not run this benchmark — see the source for methodology, or the about benchmarks for what it measures.