Terence Tao says AI could trigger math's biggest crisis since Gödel
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Terence Tao, in an essay for the 2026 International Congress of Mathematicians, argues that AI could trigger a crisis for mathematics comparable to the foundational upheaval of the early 20th century, but this time centered on the field's values and practices rather than on mathematical truth. He proposes that AI tools will soon perform a reasonable fraction of research-level mathematical tasks, citing the First-Proof Project where seven out of ten unpublished problems received at least one passing grade from an AI system at low cost. Tao warns that generative AI's focus on benchmarkable outputs could distort mathematical goals, invoking Goodhart's law, and that an overabundance of AI-generated proofs may outpace human verification and comprehension. He also notes that AI-polished proofs, while easy to read, strip away useful friction and signals that help readers learn. As concrete guidance, he points to the Leiden Declaration and suggests that a result should not be published if authors cannot convincingly demonstrate they can give a clear, expert-level talk on it, making a proof no human can explain incomplete. Tao emphasizes the need to protect the irreducibly human aspect of mathematics, especially in training young mathematicians, and discloses his own use of AI for auxiliary tasks like literature search and slide preparation.
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