Mathematicians to AI labs: stop treating our field as your benchmark

What happened

On September 11, Terence Tao and a group of research mathematicians published *A Severe Misalignment of AI in Mathematics* on Tao's WordPress and at mathandai.org. The piece argues that the current AI-industry push to have LLMs solve famous open problems — IMO golds, Millennium Prize–adjacent conjectures, long-standing lemmas — is actively harmful to mathematics as a discipline, even as the underlying models get genuinely better at proof work.

The post hit the front page of Hacker News with 831 points and produced the kind of thread where working mathematicians, ex-mathematicians, and ML researchers all showed up in the same replies. The core claim is careful: the authors are not denying that LLMs can now attack real research problems. They are saying that the *goal* of solving problems, in the AI-company sense, is not the goal mathematicians thought they shared with them.

The essay reframes famous problems as *lighthouses* — landmarks whose value was never the solution itself but the new ideas, abstractions, and pedagogy the community had to invent to reach them. Under that reading, an AI that emits a 400-page verified proof of an open conjecture and no accompanying human-legible theory has strip-mined the landmark while leaving the terrain dark.

Why it matters

The HN comment section did what HN does and immediately pattern-matched to prior art. One commenter invoked Mochizuki's Inter-universal Teichmüller theory and the abc conjecture — a proof so opaque that a decade later the community still can't agree whether it exists. Another compared Tao's argument to Baudelaire's 19th-century complaint that photography was a refuge for failed painters. A third rolled out the 1990s "computers will kill chess" analogy and noted that chess is, empirically, healthier than it has ever been.

Each analogy is doing different work, and it's worth separating them. The chess comparison is the weakest: chess is a closed game with a fixed objective, mathematics is an open-ended search for structure, and "who wins" was never the point of a proof the way it is the point of a match. The Mochizuki comparison is sharper — it's the existence proof that a correct-but-incomprehensible proof can be functionally worthless to the community that was supposed to inherit it. The Baudelaire comparison is the most interesting and the most dangerous: photography did not destroy painting, but it absolutely destroyed *portrait painting as a livelihood* for a generation, and the survivors reorganized around what cameras couldn't do. Mathematicians reading this essay are being asked whether they want to be the portrait painters.

The deeper technical point is Goodhart's Law dressed in a lab coat. Solving a famous problem was a proxy for having developed genuinely new machinery. The proxy worked for centuries because the only known route to the solution ran through the machinery. LLMs may be the first system in history that can, at least sometimes, reach the solution without the machinery — the equivalent of a student who consistently gets the right answer on the exam without being able to explain any step. In an educational setting we'd call that cheating; in a benchmark setting we call it state of the art.

Commenter *jeremysalwen* put the sharpest version of this in the thread: AI hasn't destroyed mathematicians' ability to understand and share ideas — it has destroyed the *yardstick* they used to measure contributions to that understanding. That is a more surgical claim than "AI is bad for math," and it's the one working researchers should sit with. If the currency of the field was "solved a hard problem," and the currency can now be minted by a data center, the field needs a new currency fast.

What this means for your stack

You are probably not proving the Riemann Hypothesis this quarter. You are, however, almost certainly living inside a version of the same dynamic, and the mathematicians are just the canary that talks. Every team that has watched a metric get optimized until the underlying thing it measured evaporated — DAU that doesn't correlate with revenue, code coverage that doesn't correlate with bugs caught, LeetCode scores that don't correlate with shipping — has already lived a smaller version of this essay.

Three concrete implications if you build with or evaluate LLMs:

First, treat benchmark scores as adversarial data. When a lab announces a new SOTA on a math or coding eval, the interesting question is no longer "did the model get smarter" but "did the benchmark get gamed, and by which of the three usual mechanisms" — training-set contamination, harness overfitting, or scaffolding that does the actual work off-model. The math community's complaint is the same complaint SWE-Bench maintainers have been making for a year, just with older institutions behind it.

Second, the harness is the product, not the model — and increasingly, the *evaluation* is the product too. If you're building agentic systems, the interesting artifact from this essay isn't the philosophy, it's the reminder that your eval design is the thing your model will eventually be shaped to satisfy. Pick evals whose optimization you'd actually want to live inside. "Passes the test" is not the same as "does the job," and the gap widens with capability, not shrinks.

Third, document the machinery, not just the answer. The mathematicians' real fear is a world of correct outputs and no transferable understanding. In an engineering org that translates directly: PRs that pass CI but nobody can review, incident post-mortems written by an agent that nobody reads, architecture decisions justified by "the model recommended it." If your team's institutional knowledge lives only in the artifacts an LLM produced, you are one model deprecation away from a codebase you can operate but no longer understand.

Looking ahead

The essay is not going to slow any AI lab down; "solved a famous open problem" is far too clean a marketing beat to give up. What it might do is accelerate a split the math community was heading toward anyway — between mathematicians who treat LLMs as collaborators inside a human-legible research process, and a parallel track of AI-labs-plus-formal-verification that produces correct proofs the way a compiler produces correct binaries: useful, opaque, and not really the same activity. Both can be valuable. Only one of them is what Tao and his co-authors mean by mathematics, and pretending they're the same thing is the misalignment the title is pointing at.