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This paper critiques the current capabilities of Large Language Model (LLM)-driven theorem provers in formal mathematics, highlighting their inability to tackle open-ended and abstract mathematical research challenges. It emphasizes the necessity for a paradigm shift from mere problem-solving to developing research agents capable of engaging with frontier mathematical inquiries. The authors provide a comprehensive review of existing systems, pinpointing their limitations and proposing a strategic roadmap for advancing AI4Math towards effective mathematical research agents.
Current LLM-driven theorem provers fall short in addressing the complexities of frontier mathematics, necessitating a shift towards research agents that can engage in rigorous mathematical exploration.
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.
