Must we follow the “big data” method?

Digitalisation of our world is resulting in ever-increasing amounts of data from social networks and citizen science (data collected by citizens). Substantial information technology needs are appearing with respect to data safety and storage, but also in mathematics! In the United States, laboratories such as MIT's Human Dynamics Lab bring together mathematicians, sociologists and IT specialists in a field referred to as “Computational Social Science”, but in France there is no equivalent. Yet there is a real need to develop new theories not only in statistics and optimisation but also geometry (see Stéphane Mallat's text). These theories could also be used in fields like geophysics where the amount of data to analyse (models and observations) continues to increase.

However, “big data”, which is comparable to statistical approaches (individual-based, microscopic, multi-agent) counts for nothing without “small data”. Small data, obtained from macroscopic and deterministic approaches, is used to understand phenomena and formalise the essential. This is the important role of fundamental research.

The mathematics to be developed is also to be found between the two, in the micro-macro and deterministic-stochastic mix. The approaches adopted by physicists working on these subjects (see Mathematics in the real world) must mobilise mathematics.