Terence Tao says AI could push mathematics from proof scarcity to proof abundance

量子位 · wechat · 2026-07-27

Tao warns that AI may push mathematics from proof scarcity into proof overproduction

At ICM, Fields Medalist Terence Tao argued that mathematics is entering a new crisis—not of logic, but of values and practice—as AI starts to reshape how research is done.

He started from an external benchmark: FirstProof reportedly solved 7 of 10 new research-level math problems under controlled evaluation, with per-problem compute costs ranging from $10 to $1,000.
Tao’s working assumption is that AI will soon be able to handle a substantial share of research-grade math at reasonable cost.
That breaks the old math pipeline, which depends on a chain of distinct steps: generate, verify, write clearly, publish, and canonize.
He warned that AI could flood the system with proofs that are correct but too long, poorly digested, or impossible for humans to absorb, creating a bottleneck in verification, exposition, peer review, and textbook-level consolidation.
His key thesis: math is likely moving from an era of proof scarcity to one of proof abundance, and the profession’s reward system is not ready for that shift.

Tao endorsed norms from the Leiden AI and Mathematics Declaration: disclose AI use, keep human responsibility for correctness, and do not publish results that the author cannot explain clearly and correctly at expert level. He also argued that education, hiring, grant applications, and public outreach need especially strict human-centered rules. The final message: mathematicians should define the rules themselves rather than letting AI product incentives do it for them.

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Terence Tao says AI could push mathematics from proof scarcity to proof abundance

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