# Mathematics in the Presidential Science Council

On Thursday, December 7, 2023, the President of the Republic announced the creation of a new National Science Council. The goal? To reconcile the scientific world with the political realm.

Claire Mathieu, a computer scientist and member of the Academy of Sciences, and Hugo Duminil-Copin, a mathematician and 2022 Fields Medalist, join this presidential science council at the Élysée. CNRS Mathematics (Insmi) and CNRS Computer Sciences are pleased that the challenges of research in their fields are being brought to the highest level of the political sphere, in light of tomorrow's public policies.

In disagreement with the "immigration" bill passed by Parliament, Claire Mathieu tendered her resignation from the Presidential Science Council on December 21, 2023.

Claire Mathieu reflects with us on the intrinsic link between algorithms and mathematics.

As a CNRS Research Director at the Institute for Fundamental Computer Science Research (IRIF - CNRS/Université Paris Cité), Claire Mathieu is a French computer scientist. She has devoted her career to the design and analysis of algorithms, particularly focusing on approximation algorithms, online algorithms, and auction theory. She held a chair at the Collège de France for the 2017-2018 year, and was elected to the Academy of Sciences in 2019. That same year, she received the CNRS Silver Medal.

### What was your catalyst for pursuing a career in algorithms?

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.

**Do you see a break or continuity with mathematics in this field?**** **

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.

**What role do mathematics play in the future of algorithms and artificial intelligence?**

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.

**Can mathematics be given more meaning by broadening its applications? **** **

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.

**What would be your goal within the National Science Council?**** **

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.

### Further information

- Read the profile of Claire Mathieu, CNRS Research Director at IRI
__F__(CNRS/Université Paris Cité)1 - Read the profile of Hugo Duminil-Copin, mathematician and Fields Medalist 2022
- Read the CNRS Info news The new Presidential Council for Science

- 1CNRS/Université Paris-Cité