Maths and Cinema: The Marguerite Theorem | Interview with Ariane Mézard
Ariane Mézard is a mathematician and a professor at ENS Paris. From writing to filming, she contributed to the making of the film Le théorème de Marguerite, serving as a scientific advisor to director Anna Novion.
Q1. Ariane Mézard, can you introduce yourself?
I am 51 years old and a university professor at Sorbonne University (Institute of Mathematics of Jussieu Paris Rive Gauche). I'm on a 10-year detachment at the Department of Mathematics and Applications (DMA) of ENS PSL, and a senior member of the French University Institute (IUF). My research area is arithmetic geometry. I am particularly interested in the deformations of p-adic Galois representations.
Q2. Directed by Anna Novion, Le théorème de Marguerite released in theaters on Wednesday, November 1st. Can you tell us a bit about the story? Who is Marguerite, the film’s heroine?
Marguerite is 25 years old, in her final year of a doctoral thesis at ENS. Her research area is analytic number theory. She studies arithmetic progressions in finite sets of integers.
Marguerite, remarkably played by Ella Rumpf, is a very introverted character, with unkempt hair, focused on her thesis, which she is about to present at a seminar at the Henri Poincaré Institute. The presentation goes very poorly, leading her to abandon mathematics.
Le théorème de Marguerite is the story of a young woman who built herself up with mathematics, whose shell shatters following a failure.
Q3. Professeure en mathématiques à l’ENS, vous avez ainsi été conseillère scientifique auprès de la réalisatrice. Comment le projet vous est-il parvenu, et en quoi a consisté votre mission ?
Anna Novion, réalisatrice et scénariste, cherchait un sujet de thèse pour le personnage principal du scénario qu’elle était en train d’écrire en 2017. C’est Jean Mairesse, alors directeur adjoint de CNRS Sciences informatiques (INS2I), qui lui a conseillé de me contacter. Ni Anna ni moi-même ne savions à quoi nous attendre. Anna était bienveillante et curieuse de tout, comme un grand chef qui collecte ses ingrédients et qui est avide d’en découvrir de nouveaux. Rétrospectivement, je dirais que ma mission était d’alimenter le film d’Anna en mathématiques.
During filming, mathematics had its own team. Along with Romain Branchereau and Anthony Gauvan, who were real doctoral students at DMA at the time, we actively worked with the set design team. While Ella Rumpf, Julien Frison, and Jean-Pierre Darroussin wanted to write some of their own formulas, we preceded and accompanied them throughout the shooting. It must be said that the chalk tended to migrate onto the backs of the film crew members.
When we found our formulas wandering onto black t-shirts, we knew that touch-ups were needed on the walls of Marguerite's apartment. At ENS, my office served as a dressing room for the actors, and Romain's office became that of Laurent Werner, Marguerite's thesis director.
Q4. Could you share some feedback from this experience? Did you encounter any difficulties or surprises?
For me, it was a succession of happy and intense surprises. I had no idea of the journey required to go from a screenplay to the release of a film.
The greatest shock was to see the transition from text to its interpretation and staging, to discover the attention paid by each team member - image, sound, lighting, makeup, costume, set design, etc., during the filming of the scenes. Time stood still, everyone was telling the story in their own language, all together, directed by Anna. It was a magnificent collaborative effort. The work of the actors was also astonishing. Ella Rumpf, Jean-Pierre Darroussin, and Julien Frison are one of us.
Q5. In the film, Marguerite is a brilliant ENS mathematics student and the only girl in her class - does this situation reflect reality? As a woman, does Marguerite face more obstacles than her male peers?
Of course, there are brilliant female students in mathematics at ENS! That's the reality! But it's true that young women are in the minority. In 2017, not a single girl joined the DMA. Loneliness is inherent in research. Marguerite is probably lonelier than others due to her uniqueness. She tries to blend in, to be like others. This hinders her personal and scientific freedom.
Q6. More broadly, what perspective does the film offer on mathematical research?
Mathematical research is presented as a deeply human activity, very demanding but a source of intense emotions. The film also highlights the necessity of confrontation with others to make progress.
Q7. On the day Marguerite presents her thesis, an error shakes all her certainties, and her structure collapses. Does error often slip into mathematicians' work? What consequences can it have?
There are no errors in mathematics. If there is an error, it is no longer mathematics, "it's empty," says Laurent Werner. Work that contains an error has no value regardless of the time put into it. It's not the intention that counts, just the end. However, discovering an error in one's own work is extremely positive, it means that one has understood something that was previously elusive. Finding an error is progress. Correct it, and everything becomes mathematics again.
Q8. The Marguerite Theorem released in theaters on Wednesday, November 1st. 2023. Why is it a must-see film?
Because Marguerite is a deeply human character, a unique heroine, a mathematician.