Mathematics · Benchmark profile
Epoch AI's corrected v2 Tier 4 expansion, a separate set of exceptionally difficult research-level mathematics problems evaluated with Python-enabled iterative reasoning.
Data verified 27 Jul 2026 · Methodology 1.8.0
Benchmark score on FrontierMath v2 Tier 4
GPT-5.6 Sol leads at 83%, followed by GPT-5.6 Terra (68.3%) and GPT-5.6 Luna (58.5%).
10 ranked models · higher is better · labels show rank and score
| Model | Rank | Provider | Score |
|---|---|---|---|
| GPT-5.6 Sol | #1 | OpenAI | 83% |
| GPT-5.6 Terra | #2 | OpenAI | 68.3% |
| GPT-5.6 Luna | #3 | OpenAI | 58.5% |
| GPT-5.5 Pro | #4 | OpenAI | 39.6% |
| GPT-5.4 Pro | #5 | OpenAI | 37.5% |
| GPT-5.5 | #6 | OpenAI | 35.4% |
| Claude Opus 4.8 | #7 | Anthropic | 31.3% |
| GPT-5.4 | #8 | OpenAI | 27.1% |
| Claude Opus 4.7 | #9 | Anthropic | 22.9% |
| Claude Opus 4.6 | #10 | Anthropic | 22.9% |
One best score per model · higher is better
| Rank | Model | Provider | License | Evidence use | Score |
|---|---|---|---|---|---|
| #1 | GPT-5.6 Sol gpt-5.6-sol | OpenAI | closed | Reference only | 83% |
| #2 | GPT-5.6 Terra gpt-5.6-terra | OpenAI | closed | Estimated reference | 68.3% |
| #3 | GPT-5.6 Luna gpt-5.6-luna | OpenAI | closed | Estimated reference | 58.5% |
| #4 | GPT-5.5 Pro gpt.5.5.pro | OpenAI | closed | Estimated reference | 39.6% |
| #5 | GPT-5.4 Pro gpt-5-4-pro | OpenAI | closed | Estimated reference | 37.5% |
| #6 | GPT-5.5 gpt-5.5 | OpenAI | closed | Estimated reference | 35.4% |
| #7 | Claude Opus 4.8 claude-opus-4-8 | Anthropic | closed | Reference only | 31.3% |
| #8 | GPT-5.4 gpt-5.4 | OpenAI | closed | Reference only | 27.1% |
| #9 | Claude Opus 4.7 claude-opus-4-7 | Anthropic | closed | Reference only | 22.9% |
| #10 | Claude Opus 4.6 claude-opus-4-6 | Anthropic | closed | Reference only | 22.9% |
| #11 | GPT-5.2 gpt-5.2 | OpenAI | closed | Estimated reference | 18.8% |
| #12 | Gemini 3 Pro gemini-3-pro | closed | Reference only | 18.8% | |
| #13 | Gemini 3.1 Pro gemini-3-1-pro | closed | Estimated reference | 16.7% | |
| #14 | Muse Spark muse-spark | Meta | closed | Reference only | 14.6% |
| #15 | Gemini 3.5 Flash gemini-3.5-flash | closed | Estimated reference | 14.6% | |
| #16 | Kimi K2.6 kimi-k2.6 | Moonshot AI | open | Estimated reference | 14.6% |
| #17 | GLM-5.1 glm-5-1 | Z.AI | open | Reference only | 12.5% |
| #18 | GPT-5.1 gpt.5.1 | OpenAI | closed | Estimated reference | 12.5% |
| #19 | Qwen3.6 Plus qwen3-6-plus | Alibaba Cloud | closed | Reference only | 8.3% |
| #20 | Claude Sonnet 4.6 claude-sonnet-4-6 | Anthropic | closed | Reference only | 8.3% |
| #21 | GPT-5.4 nano gpt.5.4.nano | OpenAI | closed | Reference only | 6.3% |
| #22 | o4-mini (high) o4-mini-high | OpenAI | closed | Estimated reference | 6.3% |
| #23 | Kimi K2.5 kimi-k2.5 | Moonshot AI | open | Reference only | 4.2% |
| #24 | Claude Opus 4.5 claude-opus-4-5 | Anthropic | closed | Reference only | 4.2% |
| #25 | Claude Sonnet 4.5 claude-sonnet-4-5 | Anthropic | closed | Estimated reference | 4.2% |
| #26 | Gemini 2.5 Flash gemini-2.5-flash | closed | Reference only | 4.2% | |
| #27 | Gemini 2.5 Pro gemini-2.5-pro | closed | Reference only | 4.2% | |
| #28 | Gemini 3 Flash gemini-3-flash | closed | Reference only | 4.2% | |
| #29 | Qwen 3.6 Max (preview) qwen3-6-max-preview | Alibaba Cloud | closed | Reference only | 4.2% |
| #30 | GLM-4.6 glm-4.6 | Z.AI | open | Reference only | 2.1% |
| #31 | DeepSeek V3.2 deepseek-v3.2 | DeepSeek | open | Reference only | 2.1% |
| #32 | GLM-5 glm-5 | Z.AI | open | Reference only | 2.1% |
| #33 | Claude Haiku 4.5 claude-haiku-4-5-20251001 | Anthropic | closed | Estimated reference | 2.1% |
| #34 | Grok 4 grok-4 | xAI | closed | Reference only | 2.1% |
| #35 | o3 o3 | OpenAI | closed | Reference only | 2.1% |
| #36 | Qwen3.5 Plus qwen3-5-plus | Alibaba Cloud | closed | Estimated reference | 2.1% |
| #37 | GPT-5.4 mini gpt-5.4-mini | OpenAI | closed | Estimated reference | 2.1% |
| #38 | Claude 3.5 Sonnet claude-3-5-sonnet | Anthropic | closed | Estimated reference | 0% |
| #39 | GLM-4.7 glm-4.7 | Z.AI | open | Reference only | 0% |
| #40 | GPT-4.1 gpt-4-1 | OpenAI | closed | Reference only | 0% |
| #41 | Grok 3 [Beta] grok-3-beta | xAI | closed | Reference only | 0% |
| #42 | Kimi K2 kimi-k2 | Moonshot AI | closed | Reference only | 0% |
| #43 | Qwen3 235B 2507 (Reasoning) qwen3-235b-2507-reasoning | Alibaba Cloud | open | Estimated reference | 0% |
| #44 | Qwen3.5 Flash qwen3-5-flash | Alibaba Cloud | closed | Reference only | 0% |
The top of this snapshot is led by GPT-5.6 Sol at 83%; third place is 24.5 points behind. The top-10 spread is 60.1 points.
About FrontierMath v2 Tier 4
Epoch AI's corrected v2 Tier 4 expansion, a separate set of exceptionally difficult research-level mathematics problems evaluated with Python-enabled iterative reasoning. Results stay tied to the exact model variant and evaluation system. Multiple systems for the same model use the best published score on this page; overall Lumina scoring uses the median of ranking-eligible rows.
Open benchmark source ↗FAQ
Epoch AI's corrected v2 Tier 4 expansion, a separate set of exceptionally difficult research-level mathematics problems evaluated with Python-enabled iterative reasoning.
GPT-5.6 Sol by OpenAI currently leads with 83%.
44 models in the LuminaBench cohort have a qualifying score on this benchmark.
No. This benchmark is display-only and does not enter the overall Lumina composite.
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