Professor Olivia Caramello, President of the Grothendieck Institute and Coordinator of its Centre for Topos Theory and its Applications (CTTA), and Professor Alain Connes, member of the Scientific Council of the Institute, took part, on 10 April 2026, in the framework of Horizon Maths 2026: mathematics and Music, at the Henri Poincaré Institute in Paris, in the concluding round table dedicated to creativity and co-creativity in mathematics, computer science and music, together with Gérard Assayag (STMS-Ircam/Sorbonne Université) and Indre Viskontas (Creative Brain Lab, University of San Francisco).
This round table, moderated by Moreno Andreatta (CNRS, University of Strasbourg), provided an opportunity to reflect on the links between mathematics, music, computer science and cognitive science: intuition and rigour, structure and invention, unity and variation.
Olivia Caramello spoke in particular about how toposes can help thinking, both in mathematics and in music, about the relationship between identity and transformation: how the same structure can generate different forms without ceasing to be recognisable.
Alain Connes presented a mathematical framework inspired by musical scales, where the action of integers on frequencies naturally gives rise to a Grothendieck topos. He showed that its space of points is closely connected to the Riemann zeta function, suggesting that the structure underlying musical harmony reaches into the core of number theory.
Watch the video here.
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