Mathematical Data Science
This work addresses the problem of discovering new mathematical structures for mathematicians and researchers in the field of machine learning.
The authors explored the application of machine learning to discover new mathematical structures, presenting case studies in number theory and representation theory. The results are qualitative, with no specific numbers provided.
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.