# Galois groups of polynomials and neurosymbolic networks

arXiv: https://arxiv.org/abs/2501.12978 · HTML: https://mlsanity.com/paper/2501.12978/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jan 2025.

## Built on by (most cited first, 3 of 3)

- [Internalizing Tools as Morphisms in Graded Transformers](https://mlsanity.com/paper/2511.17840/) (2025)
- [A Neurosymbolic Framework for Geometric Reduction of Binary Forms](https://mlsanity.com/paper/2501.15404/) (2025)
- [From Polynomials to Databases: Arithmetic Structures in Galois Theory](https://mlsanity.com/paper/2511.16622/) (2025)

## Abstract (arXiv)

This paper introduces a novel approach to understanding Galois theory, one of the foundational areas of algebra, through the lens of machine learning. By analyzing polynomial equations with machine learning techniques, we aim to streamline the process of determining solvability by radicals and explore broader applications within Galois theory. This summary encapsulates the background, methodology, potential applications, and challenges of using data science in Galois theory. More specifically, we design a neurosymbolic network to classify Galois groups and show how this is more efficient than usual neural networks. We discover some very interesting distribution of polynomials for groups not isomorphic to the symmetric groups and alternating groups.