Mathematics in the Presidential Science Council

My catalyst was a computer science course at the École Normale Supérieure de jeunes filles (ENSJF). I particularly remember a question in a programming project, asking for a simulation calculation of the average depth of 2-3 trees, which plunged me into a perplexity abyss because the notion of 'average' depended on the studied distribution, which was not specified: either the tree is obtained through a sequence of random insertions (easy to simulate), or we consider the uniform distribution over all 2-3 trees containing n elements. This second possibility seemed more natural to me, but I didn't know how to simulate it efficiently. I also remember a class showing the lower bound n log n for the worst-case complexity of any comparison-based sorting algorithm. The idea that it was possible to show a lower bound on all imaginable comparison sorting algorithms was magical.

From the study subject's perspective, there is continuity between mathematics and algorithmics. The break is at the level of the scientific community: we don't publish in the same journals, don't attend the same conferences and symposiums, and therefore form bonds and collaborate with different people.

• Where mathematicians and algorithmists share the same workspace, it positively influences algorithmic research, through a (potential) opening towards more advanced and perhaps deeper mathematical methods.
• Where algorithmists and other computer scientists share the same workspace, it positively influences algorithmic research, opening researchers to new problems or models from other computer science domains.

These two types of opening are difficult to reconcile as they stem from quite different research attitudes. One is focused on usable mathematical methods, while the other focuses on algorithm applications. But both have their place in the algorithmic research landscape.

It is impossible to study algorithms without a good foundation in mathematics. Furthermore, the mathematical knowledge an algorithmic researcher possesses is a valuable asset in itself. In machine learning, it's even more important.

Mathematics is the foundation of the sciences. But job prospects outside a career as a mathematician or in mathematics education require a certain openness to other attitudes, other criteria. Perhaps bi-disciplinary training could be considered to foster this openness.

I hope to bridge the gap between scientists and politicians, so that on one hand science can inform political decisions, and on the other hand, political decisions, sometimes motivated by other non-scientific but important criteria, are not met with distrust and misunderstanding by scientists.