Mathematics and Machine Creativity: A Survey on Bridging Mathematics with AI

TL;DR

This survey explores how AI, especially reinforcement learning and large language models, is transforming mathematical research through creative outputs and interdisciplinary collaboration, despite current limitations in complex reasoning.

Contribution

It provides a comprehensive overview of AI's role in mathematics, emphasizing its creative potential and addressing communication gaps between AI and mathematicians.

Findings

AI contributes to mathematics through flexible algorithms and inductive reasoning.

Large language models exhibit creative capabilities that can inspire mathematical research.

There is a need for better interdisciplinary communication between AI and mathematicians.

Abstract

This paper presents a comprehensive overview on the applications of artificial intelligence (AI) in mathematical research, highlighting the transformative role AI has begun to play in this domain. Traditionally, AI advancements have heavily relied on theoretical foundations provided by mathematics and statistics. However, recent developments in AI, particularly in reinforcement learning (RL) and large language models (LLMs), have demonstrated the potential for AI to contribute back to mathematics by offering flexible algorithmic frameworks and powerful inductive reasoning capabilities that support various aspects of mathematical research. This survey aims to establish a bridge between AI and mathematics, providing insights into the mutual benefits and fostering deeper interdisciplinary understanding. In particular, we argue that while current AI and LLMs may struggle with complex deductive reasoning, their "inherent creativity", the ability to generate outputs at high throughput based on recognition of shallow patterns, holds significant potential to support and inspire mathematical research. This creative capability, often overlooked, could be the key to unlocking new perspectives and methodologies in mathematics. Furthermore, we address the lack of cross-disciplinary communication: mathematicians may not fully comprehend the latest advances in AI, while AI researchers frequently prioritize benchmark performance over real-world applications in frontier mathematical research. This paper seeks to close that gap, offering a detailed exploration of AI fundamentals, its strengths, and its emerging applications in the mathematical sciences.