IMProofBench
Agents with web search and SageMath write proofs for private PhD-level problems written by mathematicians. Experts grade the proofs, and final-answer subquestions are graded automatically.
NeurIPS 2025. The July 2026 paper v2 grew the set from 39 to 77 problems and 14 models, so scores from the two versions do not compare.
In the authors’ words
As the mathematical capabilities of large language models (LLMs) improve, it becomes increasingly important to evaluate their performance on research-level tasks at the frontier of mathematical knowledge. However, existing benchmarks are limited, as they focus solely on final-answer questions or high-school competition problems. To address this gap, we introduce IMProofBench, a private benchmark consisting of 77 peer-reviewed problems developed by expert mathematicians. Each problem requires a detailed proof and is paired with subproblems that have final answers, supporting both an evaluation by human experts and a large-scale quantitative analysis through automated grading. Furthermore, unlike prior benchmarks, the evaluation setup simulates a realistic research environment: models operate in an agentic framework with tools like web search for literature review and mathematical software such as SageMath. Our results show that current LLMs can already solve a significant percentage of research-level questions. IMProofBench will continue to evolve as a dynamic benchmark in collaboration with the mathematical community, ensuring its relevance for evaluating the next generation of LLMs.
- Level
- Research frontier Researchers, on open problems or tasks that take days
- Scored
- Graded by people Human experts grade or compare the outputs.
- Answers
- Written proof
GPT-5.4 leads with 49.3% among models released by Mar 2026
Best score per model from the benchmark's own leaderboard, read on 2 Nov 2026. Where a model ran with several settings or harnesses, we keep its best.
The newest model with a score here came out in Mar 2026, and nobody has tested a newer one. Among the 20 highest-ranked models on the capability index, these have no score yet:
- GPT-6 Astra
- Claude Opus 5.5
- GPT-6.1 Terra
- GPT-6.1 Sol
- and 16 more
- 1 GPT-5.4 49.3%
- 2
Gemini 3.1 Pro 45.7%
- 3 GPT-5.2 Pro web search 36.9%
- 4 GPT-5.2 32.4%
- 5 Claude Opus 4.6 31.7%
- 6 GPT-5 20.4%
- 7 Grok 4 11.1%
- 8 o4-mini 6.45%
- 9
Gemini 2.5 Pro Jun 2025 6.08%
- 10 Claude Opus 4.1 3.38%
| # | Model | Score | Setting | Date | Source |
|---|---|---|---|---|---|
| 1 | GPT-5.4 | 49.3% | Mar 2026 | Official leaderboard | |
| 2 | | 45.7% | Feb 2026 | Official leaderboard | |
| 3 | GPT-5.2 Pro | 36.9% | web search | Dec 2025 | Official leaderboard |
| 4 | GPT-5.2 | 32.4% | Dec 2025 | Official leaderboard | |
| 5 | Claude Opus 4.6 | 31.7% | Feb 2026 | Official leaderboard | |
| 6 | GPT-5 | 20.4% | Aug 2025 | Official leaderboard | |
| 7 | Grok 4 | 11.1% | Jul 2025 | Official leaderboard | |
| 8 | o4-mini | 6.45% | Apr 2025 | Official leaderboard | |
| 9 | | 6.08% | Jun 2025 | Official leaderboard | |
| 10 | Claude Opus 4.1 | 3.38% | Aug 2025 | Official leaderboard |
4 models have held number one since its release in Sep 2025
Lab claims count from the day the card came out, independent runs from the model’s release.
Scores over time
All the scores we have, one dot each, so a model tested at several settings appears more than once.
No lab model card reports it yet
We read the headline results of 479 launch posts from 51 labs, and none of them list this benchmark.
More in Math
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- AIME 2026 In use Models solve the 30 integer-answer problems from the 2026 AIME I and II math competitions. Scored by exact answer match. GPT-5.5 100%
- 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%
- MathArena (Apex, IMO, USAMO) In use Evaluates models on newly released math competitions after release. Final-answer or human/LLM-judged proof scores. Claude Opus 4.8 81.3%
- 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%
- USAMO 2026 In use Models write full proofs for the six problems of the 2026 USA Mathematical Olympiad. Judges grade each proof from 0 to 7 against rubrics. GPT-5.5 98.2%