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View PDF HTML (experimental) Abstract:An essay, based on a public lecture delivered at the 2026 International Congress of Mathematicians, on how the mathematical community might respond to the arrival of artificial intelligence tools that are capable of performing research-level mathematical tasks. Rather than debating the capabilities of such tools, we condition on the hypothesis that these capabilities will arrive, and examine instead a question that is orthogonal to it: what the goals and values of mathematical research actually are. The problem-solving component of mathematics is used as a case study. Comments: 12 pages, four figures. Submitted to the Proceedings of the ICM 2026 Subjects: History and Overview (math.HO) MSC classes: Primary 00A30, Secondary 01A80, 68T01, 68V20, 68V35 Cite as: arXiv:2608.16753 [math.HO] (or arXiv:2608.16753v1 [math.HO] for this version) https://doi.org/10.48550/arXiv.2608.16753 arXiv-issued DOI via DataCite (pending registration) Submission history From: Terence C. Tao [view email] [v1] Mon, 17 Aug 2026 15:59:47 UTC (3,396 KB)