Mathematician Terence Tao is raising the alarm: AI threatens to plunge mathematics into a crisis reminiscent of the foundational upheaval of the early 20th century—not because mathematical truths could become false, but because the academic community must redefine its own goals. In an essay for the 2026 International Congress of Mathematicians, Tao argues that the debate over AI capabilities misses the point. Instead, mathematics must confront a question it has largely ignored: What exactly are the aims of mathematical research?
The essentials
- Terence Tao draws a parallel to the foundational crisis between 1900 and 1930 (Russell's paradox, Gödel's incompleteness theorems)
- In the First-Proof-Project, AI systems solved 7 out of 10 previously unpublished research problems essentially flawlessly—at a cost of dozens to hundreds of dollars per problem
- Not mathematical truth is at stake, but: what counts as a contribution, what gets rewarded, who did the work
- Tao's rule of thumb: A proof that no human can explain is incomplete
The foundation is shaking—but not the one you think
Back around 1900, paradoxes forced mathematicians to make explicit their implicit assumptions about the foundations of their discipline. The result was a rigorous framework that held for a century. Today it's different: not the mathematical foundation is being stress-tested, but the "largely implicit framework of mathematical values and practices." Tao writes that AI tools will soon be able to handle a substantial portion of mathematical research tasks "with reasonable success, reasonable quality, reasonable oversight, and reasonable cost." The First-Proof-Project shows this is not speculation: seven of the ten tested problems received at least one solution rated as essentially error-free.
When measures become goals
Historically, mathematics' many aims were tightly interwoven: solving problems, developing theories, building community, training the next generation. Progress on one aim supported the others. AI threatens to break this balance. Tao invokes a scientific observation: "When a measure becomes a goal, it ceases to be a good measure." Generative AI is particularly susceptible to this—it optimizes for the appearance of a good result rather than underlying quality. And the financial incentives of the AI industry reward precisely those measurable successes that previously served as proxies for deeper goals.
From proof scarcity to proof abundance
The consequence could be a transition Tao sees as problematic: from proof scarcity to proof abundance. AI-generated proofs would arrive faster than they could be checked, understood, and contextualized. The Erdős Problem Database already contains dozens of AI-generated submissions, many never reviewed by a human expert. An AI-polished proof could also eliminate the "natural friction" of human proofs, leaving text that is "easy to read and hard to learn from." Yet humans learn particularly well from others' mistakes.
A proof that no one can explain is incomplete.
That is Tao's framework for action. He points to the Leiden Declaration on Artificial Intelligence, which according to source material sets standards for AI use in research.
Sources
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