The Agnostic Structure of Data Science Methods

In this paper we want to discuss the changing role of mathematics in science, as a way to discuss some methodological trends at work in big data science. More specifically, we will show how the role of mathematics has dramatically changed from its more classical approach. Classically, any application of mathematical techniques requires a previous understanding of the phenomena, and of the mutual relations among the relevant data; modern data analysis appeals, instead, to mathematics in order to identify possible invariants uniquely attached to the specific questions we may ask about the phenomena of interest. In other terms, the new paradigm for the application of mathematics does not require any understanding of the phenomenon, but rather relies on mathematics to organize data in such a way as to reveal possible invariants that may or may not provide further understanding of the phenomenon per se, but that nevertheless provide an answer to the relevant question.