OpenAI’s announcement of an AI-generated solution to the Navier–Stokes problem has intensified speculation that mathematics might soon be “solved,” as many have said that chess and Go have been “solved.” In this talk, I challenge this narrative by questioning two assumptions on which it rests: that AI has genuinely solved a mathematical problem, and that mathematics is fundamentally about solving problems. In short, I will suggest that mathematical solutions require intelligible proofs that advance humanunderstanding and that mathematics itself is a human enterprise that encompasses far more than problem solving. Recent AI achievements should not be thought of as a “human defeat,” as mathematics is not an adversarial game. Rather, they invite us to reconsider what mathematics is and what norms we should endorse to foster the flourishing of human mathematics. Finally, I will consider a future in which the production and appreciation of mathematics increasingly come apart. Drawing on analogies with aesthetic appreciation, I will ask whether part of the value of human mathematical practice is connected to the activity of engaging with mathematics itself – and, in particular, in the firsthand insights that such engagement can provide.

Silvia De Toffoli is an Associate Professor of Philosophy at the University School for Advanced Studies IUSS Pavia. Her research focuses on epistemology and the philosophy of mathematics. She is President of the Association for the Philosophy of Mathematical Practice (APMP). She holds PhDs in Philosophy (Stanford University, 2019) and Mathematics (TU Berlin and BMS, 2013). She has two forthcoming books: How to Prove Things with Diagrams (Oxford University Press) and Fallibilist Epistemology of Mathematics (Cambridge University Press)

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