From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier
This position paper reviews recent advances in AI for Mathematics (AI4Math), particularly LLM-driven theorem provers for formal proof generation. It argues that current systems are limited to well-defined problems and cannot handle open-ended frontier research like discovering new theorems. The authors advocate shifting from problem solvers to research agents capable of rigorous formal reasoning, and identify key limitations across datasets, relational structure, exploration, tools, and human-AI collaboration, outlining a roadmap for the future of AI4Math.
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[Submitted on 8 Jul 2026]
Title:From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier
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Abstract:Recent developments in AI for Mathematics (AI4Math), especially Large Language Model (LLM)-driven theorem provers, has achieved remarkable success in formal proof generation for well-defined mathematical problems through Interactive Theorem Proving (ITP) languages. However, current systems remain fundamentally limited in tackling frontier research mathematics, such as discovering new theorems or resolving open conjectures, which are often open-ended, under-specified, and involve multiple layers of abstraction. We argue that the next leap in AI4Math systems requires a decisive shift from predefined problem-solvers to research agents that can address frontier mathematical challenges with rigorous formal mathematical reasoning. In this position paper, we provide a systematic review of the field, covering datasets, auto-formalization, and proof synthesis. More importantly, we identify core limitations of existing systems in serving as mathematical research agents, examining issues across datasets, relational structure, mathematical exploration, tool ecosystem, and human-AI collaboration, outlining a strategic road-map for the future of AI4Math.
Subjects:
Computation and Language (cs.CL); Artificial Intelligence (cs.AI)
Cite as: arXiv:2607.07779 [cs.CL]
(or arXiv:2607.07779v1 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2607.07779
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Eric Jiang [view email] [v1] Wed, 8 Jul 2026 17:46:36 UTC (1,544 KB)
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