On 21 May 2026, EDF Lab Paris-Saclay hosted the Aristote association’s seminar “Quelles mathématiques pour une IA fiable, frugale, moins artificielle ?”, bringing together mathematicians, researchers and industry representatives to explore new mathematical foundations for artificial intelligence. The programme highlighted the potential of topos theory to support approaches to AI centred on structure, reasoning and abstraction, rather than statistical learning alone.
Olivia Caramello, President of the Grothendieck Institute, presented Topos et ‘ponts’ pour l’intelligence artificielle générale, exploring how topos-theoretic bridges and relative toposes can help organise knowledge across different levels of abstraction, connect complementary perspectives and support explainable, formally verifiable reasoning, with Raven’s matrices as a concrete example. Laurent Lafforgue, a member of the Institute’s Scientific Council, delivered Calculer avec les sous-espaces, examining how the correspondence between geometric and logical descriptions of subtoposes opens the way to new forms of computation and the construction of topos-theoretic deep neural networks.
Video recordings of the morning and afternoon sessions are available on the conference website. Readers can also discover Olivia Caramello’s perspective in the accompanying interview “Des topos et des ponts”, which discusses her mathematical journey, the unifying power of toposes and their prospects for artificial intelligence.
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