The Institut Henri Poincaré (IHP) was inaugurated in 1928 by Émile Borel to promote exchanges between French and foreign mathematicians. Over the years, the institute has welcomed the world’s leading researchers in mathematics and theoretical physics (Einstein, for example), while developing links with the public: film club, public lectures, school activities, documentaries and exhibitions. The IHP ciné-club, “Univers Convergents”, hosted at the Grand Action cinema, offers free monthly evenings of science-themed films followed by a decoding session with researchers. In 2020, the 7th edition will be launched, after the team has contributed to the programming of the Timeworld selection of films about time shown in Paris cinemas. By 2021, the IHP will have evolved into a Maison des mathématiques, open to new missions: while still hosting leading research activities, it will promote exchanges between researchers and society. In a mediation space of over 600 m2, it will introduce non-specialists to the vast world of mathematics, to portraits of researchers and to the fascinating phenomena associated with mathematics and its interactions with computer science, physics, biology, art…