Machines Learn Number Fields, But How? The Case of Galois Groups
This work addresses a specific problem in pure mathematics for researchers in number theory, representing an incremental advance by building on previous results.
The authors tackled the problem of classifying Galois groups of number field extensions using machine learning, specifically applying interpretable methods like decision trees to Dedekind zeta coefficients, and proved new classification criteria as a result.
By applying interpretable machine learning methods such as decision trees, we study how simple models can classify the Galois groups of Galois extensions over $\mathbb{Q}$ of degrees 4, 6, 8, 9, and 10, using Dedekind zeta coefficients. Our interpretation of the machine learning results allows us to understand how the distribution of zeta coefficients depends on the Galois group, and to prove new criteria for classifying the Galois groups of these extensions. Combined with previous results, this work provides another example of a new paradigm in mathematical research driven by machine learning.