Mathematical Data Science

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. Broadly speaking, the field of data science is concerned with assembling, curating and analyzing large datasets, and developing methods which enable its users to not just answer predetermined questions about the data but to explore it, make simple descriptions and pictures, and arrive at novel insights. This certainly sounds promising as a tool for mathematical discovery! Mathematical data science is not new and has historically led to very important results. A famous example is the work of Birch and Swinnerton-Dyer leading to their conjecture [BSD65], based on computer generation of elliptic curves and linear regression analysis of the resulting data. However, the field really started to take off with the deep learning revolution and with the easy access to ML models provided by platforms such as Py-Torch and TensorFlow, and built into computer algebra systems such as Mathematica, Magma and SageMath.