Machine Learning Class Numbers of Real Quadratic Fields
This work addresses a specific mathematical problem in number theory, but it is incremental as it applies existing ML methods to a new dataset.
The paper tackled the problem of classifying real quadratic fields by their class numbers (1, 2, and 3) using machine learning, resulting in developed formulas for these class numbers that apply to their dataset.
We implement and interpret various supervised learning experiments involving real quadratic fields with class numbers 1, 2 and 3. We quantify the relative difficulties in separating class numbers of matching/different parity from a data-scientific perspective, apply the methodology of feature analysis and principal component analysis, and use symbolic classification to develop machine-learned formulas for class numbers 1, 2 and 3 that apply to our dataset.