Mathematics
AI and Machine Learning in Number Theory: Predicting Class Numbers of Real Quadratic Fields
- AI in mathematics
- machine learning in number theory
- AutoML research
- class number problem
- real quadratic fields
- Dedekind zeta function
- symbolic classification
- LightGBM
- CatBoost
- artificial intelligence research
MLJAR tools were used in the following publication.
Machine Learning Class Numbers of Real Quadratic Fields
Malik Amir, Yang-Hui He, Kyu-Hwan Lee, Thomas Oliver, Eldar Sultanow
Microsoft Research New England, USA | City, University of London, UK | Simons Foundation (Grant #712100) | EPSRC Research Grant EP/S032460/1
This research demonstrates how artificial intelligence and machine learning can be applied to fundamental problems in number theory, including the classification of real quadratic fields by their class numbers. Using LightGBM, CatBoost, symbolic classification, and automated feature engineering, the study shows how AI models can rediscover deep mathematical structures such as genus theory and the analytic class number formula. The work introduces a cost-function framework to quantify separability of arithmetic invariants and highlights the role of explainable AI in mathematical discovery. This case study illustrates how AutoML and data-driven methods can accelerate research in pure mathematics and computational number theory.
International Journal of Data Science in the Mathematical Sciences • September 19, 2022
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