Evaluating SageMath-Augmented LLM Agents for Computational and Experimental Mathematics
Recent advances in AI for Mathematics have focused largely on autoformalization and theorem proving. This paper proposes a ReAct-style agentic setup combining LLM reasoning with verifiable feedback from SageMath and Context7 documentation. Evaluated on research-level problems from RealMath, the setup shows substantial performance gains averaging 9.7 pp, with GPT-5.5 achieving 75.2% solve rate. Accepted to ICML 2026 3rd AI for Math Workshop.
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[Submitted on 7 Jul 2026]
Title:Evaluating SageMath-Augmented LLM Agents for Computational and Experimental Mathematics
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Abstract:Recent advances in AI for Mathematics have focused largely on autoformalization and theorem proving, leaving the role of Computer Algebra Systems (CAS) in agentic LLM workflows underexplored. We propose a ReAct-style agentic setup that combines LLM reasoning with verifiable feedback from SageMath, together with Context7 for the up-to-date documentation. We evaluate this agentic setup across frontier models for solving research-level mathematical problems from the RealMath benchmark in a setting that emulates a computational-mathematics research loop. We also propose a refinement to the RealMath benchmark by introducing a multi-step post-processing procedure and a multi-stage validation pipeline, both of which improve the quality and reliability of the extracted problem set. Our experiments reveal substantial performance gains from SageMath access across all evaluated models on +9.7~pp on average, the gains range from 1.5~pp to 27.8~pp and narrow the gap between open-weight and closed models. Qwen~3.7-Max benefits from SageMath the most, while GPT-5.5 achieves the highest solve rate of $75.2\%$ and the lowest token usage among tool-enabled configurations. Our findings suggest that CAS-augmented agents represent a promising direction for assisting mathematicians in computational exploration, and we believe that this work is a step towards automated conjecture discovery. The project repository is available online.
Comments: 37 pages, 16 figures, accepted to 3rd AI for Math Workshop at ICML 2026
Subjects:
Artificial Intelligence (cs.AI)
Cite as: arXiv:2607.06820 [cs.AI]
(or arXiv:2607.06820v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2607.06820
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Pavel Snopov [view email] [v1] Tue, 7 Jul 2026 21:29:59 UTC (6,560 KB)
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