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

**Authors:** Shizhe Liang, Wei Zhang, Tianyang Zhong, Tianming Liu  
**arXiv:** [2412.16543](https://arxiv.org/abs/2412.16543)  
**Date:** 2024-12-21  
**Summary page:** https://www.summarizepaper.com/en/paper/2412.16543v2/

## Key points

- Authors provide a comprehensive overview of AI applications in mathematical research
- Recent developments in reinforcement learning and large language models show potential for AI to contribute to mathematics
- AI systems and LLMs may struggle with complex deductive reasoning but excel at generating outputs based on recognition of shallow patterns
- Creative capability of AI can support and inspire mathematical research by unlocking new perspectives and methodologies
- Addressing the lack of cross-disciplinary communication between mathematicians and AI researchers

## Summary

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In their paper titled "Mathematics and Machine Creativity: A Survey on Bridging Mathematics with AI," authors Shizhe Liang, Wei Zhang, Tianyang Zhong, and Tianming Liu provide a comprehensive overview of the applications of artificial intelligence (AI) in mathematical research. The authors highlight the transformative role that AI is beginning to play in the field, emphasizing how recent developments in AI, particularly in reinforcement learning (RL) and large language models (LLMs), have shown the potential for AI to contribute back to mathematics by offering flexible algorithmic frameworks and powerful inductive reasoning capabilities. The survey aims to establish a bridge between AI and mathematics, providing insights into the mutual benefits of these disciplines and fostering deeper interdisciplinary understanding. The authors argue that while current AI systems and LLMs may struggle with complex deductive reasoning, their "inherent creativity" allows them to generate outputs at high throughput based on recognition of shallow patterns. This creative capability, often overlooked, holds significant potential to support and inspire mathematical research by unlocking new perspectives and methodologies. Furthermore, the paper addresses the lack of cross-disciplinary communication between mathematicians and AI researchers. It points out that mathematicians may not fully comprehend the latest advances in AI, while AI researchers often prioritize benchmark performance over real-world applications in frontier mathematical research. By offering a detailed exploration of AI fundamentals, strengths, and emerging applications in the mathematical sciences, this paper seeks to close that gap and promote a more collaborative approach towards leveraging AI for advancements in mathematics.