From Decision-Makers to Researchers: LLMs and Formal Mathematics at the Forefront

The development of large language models (LLMs) as tools for automated theorem proving has already yielded significant success in generating formal proofs for well-defined problems. However, these systems are still far from being able to handle research-level mathematics—such as discovering new theorems or resolving open conjectures.

What Are the Limitations of Current Approaches?

Modern systems based on interactive theorem proving (ITP) languages are effective primarily when the problem is well-defined in advance. Research mathematics, on the other hand, is often open-ended, unspecified, and multi-level in terms of abstraction.

The authors identify several key problems with existing solutions:

• shortcomings in datasets for training and evaluation;
• weak support for relational structures in a mathematical context;
• limited capabilities for mathematical research and search;
• an underdeveloped ecosystem of tools;
• ineffective human-AI interaction.

Proposed Shift

The main thesis of the paper is the need to transition from predefined “solvers” to research agents capable of applying rigorous formal mathematical reasoning to cutting-edge scientific problems.

The article presents a systematic review of the field, covering datasets, autoformalization, and proof synthesis, and formulates a strategic roadmap for the further development of AI4Math.

Source: cs.CL updates on arXiv.org