Mathematics, Statistics and Data Science

The process of extracting information from data has a long history (see, for example, [1]) stretching back over centuries. Because of the proliferation of data over the last few decades, and projections for its continued proliferation over coming decades, the term Data Science has emerged to describe the substantial current intellectual effort around research with the same overall goal, namely that of extracting information. The type of data currently available in all sorts of application domains is often massive in size, very heterogeneous and far from being collected under designed or controlled experimental conditions. Nonetheless, it contains information, often substantial information, and data science requires new interdisciplinary approaches to make maximal use of this information. Data alone is typically not that informative and (machine) learning from data needs conceptual frameworks. Mathematics and statistics are crucial for providing such conceptual frameworks. The frameworks enhance the understanding of fundamental phenomena, highlight limitations and provide a formalism for properly founded data analysis, information extraction and quantification of uncertainty, as well as for the analysis and development of algorithms that carry out these key tasks. In this personal commentary on data science and its relations to mathematics and statistics, we highlight three important aspects of the emerging field: Models, High-Dimensionality and Heterogeneity, and then conclude with a brief discussion of where the field is now and implications for the mathematical sciences