Interpreters of the Oracle:

Scott Aaronson on Mathematics After the Machine Proofs

Nov 2, 2026 · @Thomas Abshier

The taunt

In early October, a nine-year-old boy in Austin told his mother that a robot had solved the problem she had worked on for her whole career. His mother is Dana Moshkovitz, a complexity theorist at the University of Texas. The problem was the Unique Games Conjecture. The robot was an unreleased OpenAI model, and the claimed proof was one of several hundred results the company posted in a single day. The boy’s father, Scott Aaronson, told the story on his blog, and Curt Jaimungal opened his late-October Theories of Everything interview with Aaronson by reading it back to him.

Aaronson directs the Quantum Information Center at UT Austin. He is one of the most widely read theoretical computer scientists alive, and he spent the last four years working on AI safety. He is neither a promoter of the AI companies nor an opponent of them. That makes him an unusually useful witness to what has just happened to mathematics.

His central claim fits in one sentence. Machines now reach the answers to precisely stated problems faster and more reliably than the people who posed them, and the task left to mathematicians is to build a culture that keeps human understanding at the center anyway. I think he is right on the facts and right on the duty. Where I part from him is what “understanding” is, and that difference turns out to matter more for physics than for mathematics. This essay walks through his argument, notes where the record differs from what was said in conversation, and ends with what I think the episode means for those of us who work on the foundations of physics.

What happened in October

Three events frame the conversation, and it helps to have them straight before following Aaronson’s reasoning.

The OpenAI release. On October 6, 2026, OpenAI posted a public repository of 722 manuscripts, grouped into 372 “families” of results, produced by an internal model not released to the public (Let’s Data Science). The company said it put roughly 4,000 open problems to the model, spending about three hours of computing time on average on each result it kept. Among the claims: a proof of Subhash Khot’s Unique Games Conjecture, a case of the Hodge conjecture, a “quasi-Riemann” result on the zeros of L-functions, and a resolution of the unitary synthesis problem that Aaronson himself posed with Greg Kuperberg (ThePrint). A substantial fraction of the results came with machine-checked proofs in the Lean proof assistant; OpenAI warned that the rest “could have issues,” and it withdrew three manuscripts and revised fourteen within a day (Implicator). This followed OpenAI’s September 8 claim that it had solved the Navier–Stokes Millennium Problem, which had not been independently verified at the time of the release.

Before releasing, OpenAI consulted an independent advisory group hosted at the Institute for Advanced Study, whose members include Timothy Gowers and Edward Witten. Aaronson summarizes that group’s verdict as: release it, without endorsing or condemning it, and let the mathematical community sort it out.

The Anthropic paper. A day earlier, on October 5, Josh Alman and Virginia Vassilevska Williams posted a 76-page preprint giving the first polynomial improvements over the textbook algorithms for two of the oldest problems in fine-grained complexity, 3SUM and all-pairs shortest paths. The improvements in the exponents are tiny (n^1.9992 instead of n^2), but they overturn hypotheses that a decade of conditional lower bounds had rested on. The paper states that Anthropic’s Claude found the core algorithm and that the two human authors checked, simplified, extended, and took responsibility for it (MathWorld).

The protest. On October 7, the Association for Human Mathematics, a newly formed group of several hundred mathematicians whose members pledge not to use AI in their research, issued a statement calling the OpenAI release “a demonstration of power” rather than scholarship and urging mathematicians to stop working with the company. Its most quoted line was that mathematicians “did not ask for this work to be done” (Pillitteri; Mezha).

Proofs nobody can read yet

The first thing Aaronson wants people to understand is that a solved problem is not yet an understood one. Since the release, his wife has spent nearly all her working time trying to follow the machine’s proof of the conjecture she had pursued since before they met. Many of the manuscripts, he says, would be returned by any journal on sight. They spend pages on points every expert already knows, then skip the crucial step in a sentence.

His diagnosis is that the models lack a picture of their reader: what the reader already knows, and what he needs explained. He notes that brilliant first-year graduate students fail the same way. The irony is that the remedy is also a machine. Moshkovitz has been reading the proof with an AI assistant at her elbow, asking it about one step at a time, and Aaronson suggests this may simply be how papers are read from now on. But he still wants the important results rewritten into linear, human expositions and talks, and he expects that work from human experts in the coming months, because “we do only work at human speed.”

Jaimungal asked whether the future mathematician becomes a hierophant, an interpreter of sacred mysteries. Aaronson did not flinch from the comparison. Literary scholars, he observed, are not hired to write a new Iliad; they interpret the great works handed down to them. An astronomer looks through a telescope and writes about what he sees. A biologist who studies bears does not list the bear as a co-author. Mathematicians imagined their role was larger than that: finding solutions that only a trained biological intelligence could find. As of this past summer, he says, machines do that part better, and that “does permanently change the nature of what it is that we do.”

He also grants the uncomfortable corollary. If next year’s models explain as well as they prove, the interpreter’s role shrinks again, leaving mainly the choice of where to point the telescope.

Does the machine understand?

Some mathematicians have answered the release by saying the true job was never proof but understanding, and that the machines prove without understanding. Aaronson accepts the first half and rejects the second.

He accepts that open problems are posed mainly for the understanding gained along the way. A proof that P is not equal to NP would only confirm what nearly everyone already believes; its value would lie in the new ideas needed to reach it. So the fear that an oracle “teleporting us to the answers” will short-circuit the growth of ideas is reasonable. But he is blunt that the oracle cannot be wished away. Models as strong as the one OpenAI used will soon be available to anyone. The only way to stop the flood would be to stop AI itself.

On whether the machine understands, he takes a practical stance. Nothing solves hundreds of open problems without some internal representation of what is going on, a representation that in a human being we would call understanding. Consciousness and sentience are separate questions, and he wants them kept separate. If a system satisfies every operational test for understanding a piece of mathematics, then for him it understands it. That it explains poorly proves little; so do many brilliant people.

He is sharpest against what he calls the denialist stance. People name a task AI will never do, hold it up as proof of AI’s weakness, and then, when AI does it, find reasons it doesn’t count: it was not truly creative, it only applied known techniques, the problem was not that hard. The capacity for such rationalizations, he says, is staggering. Jaimungal read back Aaronson’s own blog estimate: something like a first-year student who knows every published technique, can apply them anywhere, and can work thousands of problems in a few weeks without tiring. If a human did that even a hundred times more slowly, his name would be spoken alongside Euler’s and Erdős’s. Jaimungal suggested that the endless objections often hide a fear of becoming superfluous. Aaronson allowed that it might be a psychological defense, and added that if the real objection is metaphysical (“it is not conscious of what it is doing”), people should say so plainly and argue that question on its own terms.

I take his challenge as fair and accept it. The denialism he describes is real, and it is bad reasoning: moving the goalposts is not an argument. On the operational question, what these systems will do in the observable world, he is simply right, and anyone who plans a career or an institution on the opposite assumption will be overtaken.

But his own rule cuts both ways. If the metaphysical question is to be argued explicitly, it should not be settled implicitly by a definition. The word “understanding,” as mathematicians used it for centuries, named two things at once: a capacity (to prove, apply, extend) and an experience (the moment a structure becomes clear to a mind). The operational definition keeps the first and drops the second by stipulation. That is a legitimate choice for engineering, but it is a choice, not a discovery. Whether the second thing exists in a machine, and whether it matters, is exactly the question the definition was built to set aside. I return to it at the end, because it is where physics and mathematics part company.

Two ways to release a result

Aaronson contrasts the two companies’ October releases, and the contrast is the most practical part of the interview.

OpenAI’s Navier–Stokes announcement drew backlash. Two human mathematicians, Tristan Buckmaster and Levent Alpöge, were reportedly closing in on the problem with some AI help, and OpenAI, using far greater computing resources, got there first. Wary of a second backlash, the company sought the advisory group’s counsel, then posted the hundreds of manuscripts under its own name, mostly without human review. The work of understanding them fell on the experts in each field touched.

Anthropic did something different. Instead of publishing what its model found, it brought in two human specialists who understood the result fully and wrote it up in their own words, under their own names. Aaronson names the advantage plainly: there are “point people.” Someone has understood the result, answers for it, can give talks on it, and can answer questions. The research community has a stake in it. He names the disadvantage just as plainly: the company chose which humans would be its model’s emissaries. He thinks it chose well, but many others would have liked the job.

From this, he sees a norm forming. Nearly every research paper of the past few months carries an “AI usage statement” saying which parts were done with which models and affirming that the human authors take responsibility. (He would move it from the back of the paper to the front, since it is often the first thing he wants to know.) The emerging rule is this: if you used AI even to find the main idea, but you then understand it fully, write it in your own words, take responsibility for it, and can defend it in a talk, it is your work. The biologist’s paper about bears is still the biologist’s paper.

What will not be rewarded is the opposite: feeding thousands of problems to a model and posting whatever comes back under one’s own name, leaving others to do the understanding. That, he says, is pulling the lever on a slot machine, and anyone can pull it. He passes on a joke from his friend Boaz Barak, now a safety researcher at OpenAI: in that case the paper’s author should be the model, with a line in the acknowledgments thanking the human for suggesting the problem.

This norm deserves endorsement without qualification. It ties credit to the one thing that cannot be outsourced: a person who stands behind a claim and can be questioned about it. Authorship has always meant answerability; the machines have only made that visible.