Position paper proposes shifting AI for formal mathematics from solvers to research agents

A new position paper on arXiv argues that current large language model (LLM)-driven theorem provers in AI for Mathematics (AI4Math) are fundamentally limited to well-defined problems and cannot address frontier research mathematics. The authors, led by Eric Jiang and including 18 co-authors, contend that the field must transition from predefined problem-solvers to research agents capable of rigorous formal reasoning for open-ended challenges such as discovering new theorems or resolving open conjectures.

The paper provides a systematic review of AI4Math, covering datasets, auto-formalization, and proof synthesis. It highlights that existing systems struggle with the open-ended, under-specified, and multi-layered nature of frontier mathematical research. The authors identify core limitations across datasets, relational structure, mathematical exploration, tool ecosystems, and human-AI collaboration, framing these as barriers to building effective research agents.

The authors propose a strategic roadmap to guide future work, emphasizing the need for systems that integrate rigorous formal reasoning with the exploratory and creative aspects of mathematical research. They argue that such agents would require advances in auto-formalization, proof synthesis, and tool integration to operate effectively at the research frontier.