Galois groups of polynomials and neurosymbolic networks
This work addresses a foundational problem in algebra for mathematicians and computer scientists, but it appears incremental as it applies existing neurosymbolic methods to a new domain.
The paper tackles the problem of determining solvability by radicals in Galois theory by using a neurosymbolic network to classify Galois groups, showing it is more efficient than usual neural networks and discovering interesting distributions for non-symmetric and non-alternating groups.
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.