# Machine-Learning Number Fields

arXiv: https://arxiv.org/abs/2011.08958 · HTML: https://mlsanity.com/paper/2011.08958/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2020.

## Built on by (most cited first, 9 of 9)

- [Machine-Learning Mathematical Structures](https://mlsanity.com/paper/2101.06317/) (2021)
- [Murmurations of elliptic curves](https://mlsanity.com/paper/2204.10140/) (2022)
- [A Triumvirate of AI Driven Theoretical Discovery](https://mlsanity.com/paper/2405.19973/) (2024)
- [From Black Box to Bijection: Interpreting Machine Learning to Build a Zeta Map Algorithm](https://mlsanity.com/paper/2511.12421/) (2025)
- [Machines Learn Number Fields, But How? The Case of Galois Groups](https://mlsanity.com/paper/2508.06670/) (2025)
- [Machine Learning Mutation-Acyclicity of Quivers](https://mlsanity.com/paper/2411.04209/) (2024)
- [Learning Fricke signs from Maass form Coefficients](https://mlsanity.com/paper/2501.02105/) (2025)
- [Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspective](https://mlsanity.com/paper/2510.21999/) (2025)
- [Murmurations: a case study in AI-assisted mathematics](https://mlsanity.com/paper/2603.09680/) (2026)

## Abstract (arXiv)

We show that standard machine-learning algorithms may be trained to predict certain invariants of algebraic number fields to high accuracy. A random-forest classifier that is trained on finitely many Dedekind zeta coefficients is able to distinguish between real quadratic fields with class number 1 and 2, to 0.96 precision. Furthermore, the classifier is able to extrapolate to fields with discriminant outside the range of the training data. When trained on the coefficients of defining polynomials for Galois extensions of degrees 2, 6, and 8, a logistic regression classifier can distinguish between Galois groups and predict the ranks of unit groups with precision >0.97.