# A Triumvirate of AI Driven Theoretical Discovery

arXiv: https://arxiv.org/abs/2405.19973 · HTML: https://mlsanity.com/paper/2405.19973/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 137 references that are in the map.
- First posted on arXiv 30 May 2024.

## Builds on (most cited first, 30 of 61)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solving](https://mlsanity.com/paper/2405.12205/) (2024)
- [Rediscovering orbital mechanics with machine learning](https://mlsanity.com/paper/2202.02306/) (2022)
- [Scientific Machine Learning Benchmarks](https://mlsanity.com/paper/2110.12773/) (2021)
- [Learning to Unknot](https://mlsanity.com/paper/2010.16263/) (2020)
- [Detecting Symmetries with Neural Networks](https://mlsanity.com/paper/2003.13679/) (2020)
- [Learning the greatest common divisor: explaining transformer predictions](https://mlsanity.com/paper/2308.15594/) (2023)
- [Neural Network Approximations for Calabi-Yau Metrics](https://mlsanity.com/paper/2012.15821/) (2020)
- [Machine-Learning Mathematical Structures](https://mlsanity.com/paper/2101.06317/) (2021)
- [Nonperturbative renormalization for the neural network-QFT correspondence](https://mlsanity.com/paper/2108.01403/) (2021)
- [Machine learning Calabi-Yau metrics](https://mlsanity.com/paper/1910.08605/) (2019)
- [Machine Learning CICY Threefolds](https://mlsanity.com/paper/1806.03121/) (2018)
- [Machine Learning and Computational Mathematics](https://mlsanity.com/paper/2009.14596/) (2020)
- [Deep-Learning the Landscape](https://mlsanity.com/paper/1706.02714/) (2017)
- [Learning selection strategies in Buchberger's algorithm](https://mlsanity.com/paper/2005.01917/) (2020)
- [Machine learning and information theory concepts towards an AI Mathematician](https://mlsanity.com/paper/2403.04571/) (2024)
- [The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning](https://mlsanity.com/paper/1812.02893/) (2018)
- [Quiver Mutations, Seiberg Duality and Machine Learning](https://mlsanity.com/paper/2006.10783/) (2020)
- [Machine learning for complete intersection Calabi-Yau manifolds: a methodological study](https://mlsanity.com/paper/2007.15706/) (2020)
- [Machine Learning and Big Scientific Data](https://mlsanity.com/paper/1910.07631/) (2019)
- [Learning Algebraic Structures: Preliminary Investigations](https://mlsanity.com/paper/1905.02263/) (2019)
- [Machine Learning Calabi-Yau Hypersurfaces](https://mlsanity.com/paper/2112.06350/) (2021)
- [Machine-Learning the Sato--Tate Conjecture](https://mlsanity.com/paper/2010.01213/) (2020)
- [Murmurations of elliptic curves](https://mlsanity.com/paper/2204.10140/) (2022)
- [Is deep learning a useful tool for the pure mathematician?](https://mlsanity.com/paper/2304.12602/) (2023)

## Built on by (most cited first, 5 of 5)

- [A Multi-Task Evaluation of LLMs' Processing of Academic Text Input](https://mlsanity.com/paper/2508.11779/) (2025)
- [Flow-based Extremal Mathematical Structure Discovery](https://mlsanity.com/paper/2601.18005/) (2026)
- [CayleyPy Growth: Efficient growth computations and hundreds of new conjectures on Cayley graphs (Brief version)](https://mlsanity.com/paper/2509.19162/) (2025)
- [Deep Reinforcement Learning for Fano Hypersurfaces](https://mlsanity.com/paper/2603.15437/) (2026)
- [AI and Human Approaches to Mathematical Problem Solving](https://mlsanity.com/paper/2609.17779/) (2026)

## Abstract (arXiv)

Recent years have seen the dramatic rise of the usage of AI algorithms in pure mathematics and fundamental sciences such as theoretical physics. This is perhaps counter-intuitive since mathematical sciences require the rigorous definitions, derivations, and proofs, in contrast to the experimental sciences which rely on the modelling of data with error-bars. In this Perspective, we categorize the approaches to mathematical discovery as "top-down", "bottom-up" and "meta-mathematics", as inspired by historical examples. We review some of the progress over the last few years, comparing and contrasting both the advances and the short-comings in each approach. We argue that while the theorist is in no way in danger of being replaced by AI in the near future, the hybrid of human expertise and AI algorithms will become an integral part of theoretical discovery.