A landscape of French mathematical research

French mathematical research is being piloted by the Insmi on a national scale, with due regard to many partners, notably academic ones. It covers the whole spectrum of mathematics and pays particular attention to the interactions with the other sciences, as well as with society, industry and enterprises.

Research in France

From Pascal and Descartes to the "Bourbaki group", mathematical research is strongly rooted in France.

France, a welcoming home for mathematicians

Prestigiously awarded with 12 Fields medals, 1 Gauss prize, 4 Abel prizes, 4 Shaw Prizes, the French mathematical school enjoys a strong international recognition. French mathematical academic journals are classed among the highest publications in terms of international ranking and recognition.

International recognition

  • ​12 Fields Medals | Laurent SCHWARTZ (1950), Jean-Pierre SERRE (1954), René THOM (1958), Alexander GROTHENDIECK (1966), Alain CONNES (1982), Pierre-Louis LIONS and Jean-Christophe YOCCOZ (1994), Laurent LAFFORGUE (2002), Wendelin WERNER (2006), NGÔ Bào Châu and Cédric VILLANI (2010), Artur AVILA (2014).
  • 1 Gauss Prize | Yves MEYER (2010). 
  • 4 Abel Prizes | Jean-Pierre SERRE (2003), Jacques TITS (2008), Mikhail GROMOV (2009), Yves MEYER (2017).
  • 1 Wolf Prize in Mathematics since 2010 | Jean-François LE GALL (2019)
  • 4 Shaw Prizes | Maxime KONTSEVITCH (2012), Claire VOISIN (2017), Michel TALAGRAND (2019), Jean-Michel BISMUT (2021).

France boasts a wide range of research structures that complement each other: CNRS laboratories, host units, networks of all kinds, national programs, etc. The Insmi's mission is to structure the French mathematical community and to work towards its integration into the international community.

The mathematics laboratories are essentially university laboratories or laboratories linked to the grandes écoles. They receive financial support from the universities (or grandes écoles) and the CNRS. The French National Research Agency (ANR) participates in the financing of various projects. In addition, as part of the future investment program (PIA), the French government has launched a labeling program such as the "Laboratories of Excellence (LabEx)" action.

Finally, two foundations, the Fondation sciences mathématiques de Paris (FSMP) and the Fondation mathématique Jacques Hadamard (FMJH), provide funding from public and private sources; both host a LabEx.

Who are the actors of research?

The Insmi coordinates a myriad of actors with very different statutes and missions:

  • laboratories, located in French universities or Grandes Ecoles, which are associated with the CNRS;

  • the national support units for mathematical research, including documentation and publishing, computer and technical resources, the dissemination of mathematics and interactions with companies;

  • thematic research networks at a national level;

  • international research centres dedicated to hosting programmes and symposia;

  • international networks and joint international research units;

  • international programmes and research schools in all countries of the world.

Three international research centres for mathematicians from around the world

At the heart of Paris, the Institut Henri Poincaré (IHP) is one of the oldest international structures dedicated to mathematics and theoretical physics. It organises thematic trimesters, international conferences and regular seminars, and hosts the Poincaré Chair, created in 2013 with the Clay Institute. The IHP also offers a wide range of activities aimed at the general public and will open in 2022 a place dedicated to exhibitions and exchanges between research, education and society, the Maison Poincaré.

On the Luminy-Marseille campus, the International Centre for Mathematical Encounters (Cirm) organises conferences, colloquia, thematic sessions and small group research in residence, attracting researchers from all over the world. The Jean Morlet Chair, which lasts six months, provides an opportunity for conferences, working groups, small group work or events for the general public on a specific scientific theme.

Based in Bures-sur-Yvette, in the heart of Paris-Saclay, the Institut des Hautes Etudes Scientifiques (IHES) is a research centre and a meeting place of reference for interdisciplinary exchanges in mathematics, theoretical physics and any other science related to them. It is distinguished by a research based on people rather than on programmes.

Actions towards developing countries

Cimpa, the International Centre for Pure and Applied Mathematics, promotes research in mathematics in developing countries through three major activities:

  • The organisation of around 20 research schools per year, its historical activity;
     
  • supporting research training by funding research-level courses;
     
  • funding the participation of young mathematicians in short international thematic programmes.

Three involved mathematical societies

Three mathematical societies - which are linked to international mathematical societies - watch over the interests of French mathematics: the Société Mathématique de France (SMF), the Société de Mathématiques Appliquées et Industrielles (SMAI), the Société Française de Statistique (SFdS). They have an important editorial action and are also involved in joint actions towards society as well as towards business and industry (in particular the SFdS and the SMAI regarding this last point).

FRENCH MATHEMATICS IN FIGURES

  • 16 Fields Medals
  • 1 Gauss Prize
  • 4 Abel prizes
  • 6 CNRS gold medals

 

  • 3 mathematical societies
  • 3 international research centres
  • 20 annual research schools in developing countries
  • some 40 mathematical journals

The Study on the Socio-Economic Impact of Mathematics in France (EISEM, 2015) found that 9% of GDP and 15% of jobs in France are impacted by mathematics.

Research laboratories

The CNRS structures mathematical research in France in close partnership with the universities. It thus creates a fine network of the territory.

Research structures: UMR and FR

The Insmi's action is based on a national network that structures almost all academic research in mathematics in France. This base is made up of 43 mixed research units (UMR). The supervision of these units is carried out in a 'mixed' way in partnership between the CNRS and various higher education institutions.

In addition, there are 12 research federations (FR), which are regional associations of mathematics laboratories, UMRs or host teams. These federations are the natural interlocutor of the regions, chambers of commerce and industry or rectorates as far as mathematics is concerned.

These units are regularly evaluated on their work and organisation by the Haut Conseil de l'évaluation de la recherche et de l'enseignement supérieur (Hcéres), a national evaluation body external to the CNRS, as well as by the Comité national du CNRS. Insmi researchers are evaluated by the sections of the CNRS National Committee, mainly by section 41, dedicated to mathematics.

Consult the list of UMRs

Consult the list of ENs

Research groups (GDR)

Alongside the geographical network of UMRs, there is a thematic network of 29 research groups (GDRs), which bring together mathematicians working on a given research theme at national level.

These GDRs play an important role in scientific animation in their field by organising conferences of national or international scope, depending on the case, and summer schools for young researchers, and by supporting individual collaborations. They also play an important role with doctoral and post-doctoral students by supporting their integration into their professional environment.

Consult the list of RDGs

The Calcul Group

This GDR brings together members of the French computing community, engineers and mathematicians. It runs communication and exchange groups during scientific and technical events, hosts the CNRS network of computing engineers and participates in the pooling of computing resources throughout France.

Calcul group website

Support and research units and thematic networks

The French mathematical community has set up national instruments that the Insmi pilots or co-pilots: the support and research units (UAR), which are geographically based, have the possibility of hosting staff and for which the Insmi shares the supervision with partners (universities or learned societies); and the thematic networks (RT) within the CNRS.

Support & research units and thematic networks fulfil, at national level and in a spirit of mutualisation, the various support functions necessary for the proper development of mathematical research. They provide :

  • shared IT resources provided by the Mathrice thematic network, which is also the business network for people in charge of system and network administration;

  • documentary resources, coordinated by the Réseau national des bibliothèques de mathématiques (RNBM), a network of documentalists and librarians from the Insmi's laboratories, as well as by the Orsay Jacques Hadamard library, a national reference library; support for the publication of French mathematical journals in open access via the UAR Mathdoc, which is developing, in particular, an open-access scientific publishing platform (the Mersenne centre) and a digital library (Numdam);

  • conference centres where one can organise or participate in scientific events and meet mathematicians from all walks of life, the Institut Henri Poincaré (IHP) and the Centre international de rencontres mathématiques (CIRM);

  • a network for exchanging and sharing experiences on the dissemination of mathematics, the AuDiMath thematic network;

  • assistance in developing relations with companies, provided by the Agency for Mathematics in Interaction with Enterprise and Society (AMIES);

  • finally, the Insmi administratively manages a support and research unit linked to the CNRS's computing and data mission (MiCaDo): the Gricad unit, which pools computing skills and expertise at the regional level on the Grenoble site.

The Math Portal, a privileged access to tools and services useful to the mathematical community

The Math Portal is an entry point to digital resources useful to researchers in mathematics. Developed by Mathdoc, the RNBM and Mathrice, it offers the mathematical community a single access point:

  • scientific documentation and associated services, in free or controlled access, with
  • advanced search functions;
  • services facilitating mobile and collaborative work;
  • institutional and professional information.

portail.math.cnrs.fr/