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IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation
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IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation
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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.
Forward citations
Cited by 6 Pith papers
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Soohak: A Mathematician-Curated Benchmark for Evaluating Research-level Math Capabilities of LLMs
Soohak is a new 439-problem mathematician-authored benchmark showing frontier LLMs reach only 30% on research math and fail to exceed 50% on refusing ill-posed questions.
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Soohak: A Mathematician-Curated Benchmark for Evaluating Research-level Math Capabilities of LLMs
Soohak is a 439-problem mathematician-curated benchmark where frontier LLMs reach at most 30.4% on research math challenges and no model exceeds 50% on refusal for ill-posed problems.
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Failure Modes of Large Language Models on Research-Level Mathematics: A Taxonomy and an Empirical Characterisation
This paper introduces a taxonomy of four LLM failure modes on research math proofs and empirically shows premise smuggling in all eight audited Gemini outputs, with a new audit instrument achieving 100% precision.
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Not All Proofs Are Equal: Evaluating LLM Proof Quality Beyond Correctness
LLM proofs for hard math problems show large differences in quality metrics like conciseness and cognitive simplicity that correctness-only tests miss, along with trade-offs between quality and correctness.
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Not All Proofs Are Equal: Evaluating LLM Proof Quality Beyond Correctness
ProofRank benchmark shows substantial differences in LLM proof quality not captured by correctness, with trade-offs between quality metrics and accuracy.
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Evaluating SageMath-Augmented LLM Agents for Computational and Experimental Mathematics
SageMath-augmented ReAct agents raise solve rates by +9.7 pp on average on a curated 133-problem RealMath subset, with GPT-5.5 reaching 75.2%.
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