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Mathematical Data Science

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arxiv 2502.08620 v1 pith:GZAN5SWC submitted 2025-02-12 math.HO cs.LGmath.COmath.NTmath.RT

Michael R. Douglas , Kyu-Hwan Lee This is my paper · ORCID
classification math.HOcs.LGmath.COmath.NTmath.RT
keywords mathematicaldatadoinglearningmachinesciencestudiestheory
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Can machine learning help discover new mathematical structures? In this article we discuss an approach to doing this which one can call "mathematical data science". In this paradigm, one studies mathematical objects collectively rather than individually, by creating datasets and doing machine learning experiments and interpretations. After an overview, we present two case studies: murmurations in number theory and loadings of partitions related to Kronecker coefficients in representation theory and combinatorics.

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  1. Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning

    math.NT 2025-09 conditional novelty 4.0 of 10

    A large empirical study of congruent number elliptic curves up to D < 3×10^6 confirms several Selmer-rank heuristics but does not support the paper's headline claim that Goldfeld's conjecture is rigorously verified.

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