AI for Mathematics: Progress, Challenges, and Prospects

TL;DR

This paper reviews recent progress and challenges in AI for Mathematics, emphasizing the development of specialized and foundation models to enhance mathematical research and reasoning capabilities.

Contribution

It provides a systematic overview of AI4Math, categorizing research into problem-specific and general-purpose models, and discusses future prospects for AI in mathematical discovery.

Findings

AI4Math revitalizes mathematical problem solving with data-driven approaches.

Research is categorized into specialized architectures and foundation models.

Future AI systems aim to facilitate discovery and unified theories in mathematics.

Abstract

AI for Mathematics (AI4Math) has emerged as a distinct field that leverages machine learning to navigate mathematical landscapes historically intractable for early symbolic systems. While mid-20th-century symbolic approaches successfully automated formal logic, they faced severe scalability limitations due to the combinatorial explosion of the search space. The recent integration of data-driven approaches has revitalized this pursuit. In this review, we provide a systematic overview of AI4Math, highlighting its primary focus on developing AI models to support mathematical research. Crucially, we emphasize that this is not merely the application of AI to mathematical activities; it also encompasses the development of stronger AI systems where the rigorous nature of mathematics serves as a premier testbed for advancing general reasoning capabilities. We categorize existing research into two complementary directions: problem-specific modeling, involving the design of specialized architectures for distinct mathematical tasks, and general-purpose modeling, focusing on foundation models capable of broader reasoning, retrieval, and exploratory workflows. We conclude by discussing key challenges and prospects, advocating for AI systems that go beyond facilitating formal correctness to enabling the discovery of meaningful results and unified theories, recognizing that the true value of a proof lies in the insights and tools it offers to the broader mathematical landscape.