Sylvie Benzoni © Marco Perez for the Poincaré Institute

French Touch: La Maison Poincaré opened on a historic site. Could you introduce us to this place?
Sylvie Benzoni: A stone's throw from the Pantheon, it is a campus built from the beginning of the 20th century on the site of a former convent bought by the University of Paris in order to establish several institutes there. Housed in the former physical chemistry laboratory of physicist Jean Perrin, Nobel Prize winner in 1926, the Maison Poincaré is therefore next to the Marie Curie Radium Institute, built just before the war of 1914, the Institute of Oceanography, the Laboratory of Physicochemical Biology and the Henry Poincaré Institute of which the museum is a part.

FT: A mecca for maths where numbers dominate?
SB: It is reductive to say that maths is the science of numbers. The discipline is much broader. In the first room of the museum, a metro map has been created that aims to display all the variety and breadth of mathematics as well as all the interconnections between their different fields. For example, you can see a numbers district in which there is a "number theory" station on a line called "arithmetic". There is also the forms district since, with numbers, this is how children enter maths. There is also the variations district, where we deal with what varies according to time or position, a randomness district that concerns all phenomena linked to chance, and then two more mysterious districts for the public: the structures district, extremely important in mathematics, and the foundations district, which is what maths is based on.

FT: One of the reasons for this museum is to combine mathematics with the arts. Where does this momentum come from?
SB: The Henri Poincaré Institute holds a collection of about 600 mathematical objects. Most of these objects date back to the 19th century. They were designed for educational purposes so that students, particularly those at the nearby École Normale Supérieure, could practice on these geometric shapes that illustrated mathematical equations. These objects then fell into disuse as other types of geometry emerged. These objects as we see them induced misconceptions. So mathematicians gradually forgot about them. Until artists like Man Ray and Max Ernst rediscovered them. Their discovery by Man Ray in a forgotten cupboard at the Sorbonne was the subject of a 2019 film, “Man Ray and the Shakespearean Equations,” in which we see an archive of the artist explaining the inspiration he found in these “equation objects.” We hear him say, in somewhat clumsy French, that he likes mysteries and not so much solutions... Ultimately he didn't care about trying to understand what these objects meant. It was their shapes that interested him.

Gallery | MODELING space ©Institut Henri Poincaré, Paris / Atelier Novembre, du&ma, Thibaut Voisin

FT: However, the link between art and mathematics is not obvious. How do you illustrate this link?
SB: In the museum, an entire room is dedicated to the arts. We try to show the common approaches that there can be. For example, the theory of knots is illustrated here by a table of mathematical knots. Usually, this theory is illustrated by knots made of string. Here, we wanted to make pearl necklaces, as a nod to the artist Jean-Michel Othoniel. While working on the museum project, I discovered that in his exhibition at the Petit Palais in 2021, Jean-Michel Othoniel exhibited “wild knots” made with the help of the Mexican mathematician Aubin Arroyo and from which he drew inspiration to make works of art in steel balls. “Wild knots” are a concept in mathematics. Here we can clearly see how art and mathematics can intertwine. The museum also exhibits contemporary art, such as the sculptures of Ulysse Lacoste.

FT: Why do you think it is essential to know mathematics to launch an artistic career?
SB: As soon as there are shapes, we need mathematics to understand. Some artists can quite easily design works without being at all aware of their mathematical representation. I am thinking, for example, of Japanese artists, represented in France by the Mingei gallery, who weave bamboo. They create mathematical objects without knowing it since these shapes must take into account the elasticity of the fiber. The theory of elasticity is very mathematical. Mathematics is also very close to music or even digital art. In this field I am thinking, for example, of Marie-Paule Cani, an associate professor and professor at Polytechnique, who has always been drawn to art. She is a pioneer in visual modeling of animated natural scenes. Her motivation to contribute to mathematics therefore comes from artistic considerations. Finally, starting in May, the museum will present two art exhibitions: on the one hand, “Intuitive Generations. When artists are inspired by mathematics", in partnership with the Wagner gallery specializing in geometric abstraction, and on the other hand "Infra-terre. Incursion chromatique", designed by the Mineral Collection of Sorbonne University with the artist Caroline Besse and the Henri Poincaré Institute. The connections are innumerable in fact!

FT: Maison Poincaré also aims to restore the image of maths even though we observe a lack of interest in French schools. What is mathematics for in life and why is it a problem to drop out of college?
SB: The visit allows many teachers to get the message across that maths is used to learn to think, to reason. Because we hold reasonings, if possible logical, and we avoid contradictions, or at least if not we use them to demonstrate things… So learning to think through maths is really important, especially to avoid being fooled by “fake news” and other current scourges. There is also the fact of being more comfortable with certain calculations, but we should not reduce maths to calculation. The museum presents a series of fun devices that encourage us to think and realize that there is not necessarily a single solution to a problem.

FT: Math is most often seen as a chore at school. Why is it important in 2024 to change this image?
SB: I think one of the reasons is that we lack scientists in general. We can't do science without mathematics. So we often think mainly of physics. But current biology, what we call quantitative biology, uses mathematics. There is a shortage of scientists everywhere, in the digital world, and to do computer science, you also need to have skills in mathematics. So it's really to bring more young people to have a scientific culture in the broad sense, and in particular mathematics. That's the challenge: to bring more young people towards this culture.

Inauguration ©Institut Henri Poincaré, Paris / November Workshop, du&ma, Laurent Ardhuin

FT: We see a lot of female faces throughout the visit. One of your wishes was that maths would be represented by women despite the lack of parity. How can young schoolgirls who visit this museum project themselves?
SB: We asked ourselves what image we wanted to give of maths. We could have chosen a very historical image, based on well-known characters, therefore men, white and old often… This image was not retained, in favor of a more balanced and lively image. Some historical characters are of course presented, but we also gave a lot of space to contemporary portraits, like that of Adam Ouorou, who spent a large part of his career at Orange or Eugenia Cheng, a British mathematician who chose to teach in an art school, while being a pianist. They tell in a varied setting their journey, their way of arriving at maths, their ways of practicing it, so that young people in particular can tell themselves that it is possible.

FT: Today we see that confidence in science can sometimes falter in favor of ideologies. How can an institution like this help restore confidence?
SB: I tend to be optimistic and believe in youth. By welcoming as many young people as possible here, the museum helps to promote this openness since here we show quite different maths and in a world that these young people do not necessarily suspect. Giving a taste for maths also helps to avoid sinking into conspiracy theories. The enthusiasm is there. I wanted to see sparks light up in the eyes of visitors. After almost five months of opening the museum, we can say that the result is there. There is a strong expectation on the part of maths teachers and school slots are full until the end of the year.

The Rulpidon, work of Ulysse Lacoste, in the Jacqueline Ferrand Garden | BREATHE space at Maison Poincaré ©Institut Henri Poincaré, Paris - Ulysse Lacoste