Abstract
Recent developments in AI for Mathematics (AI4Math), especially Large Language Model (LLM)-driven theorem provers, have 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.
Blogger's Review: This paper delves into the potential applications of large language models in mathematical research, highlighting the shortcomings of existing systems and providing a clear direction for future research. The advancement of AI4Math relies not only on technological improvements but also on systematic thinking and interdisciplinary collaboration.