AI math has spent 2026 breaking records, and on 28 September WIRED asked what those records are costing. In an essay by Sophia Chen, mathematicians argue that their field has always been closer to painting and poetry than to a race for answers. Brute-force AI, they say, threatens the understanding that makes a proof worth having. “The artists and the musicians have already gone through this,” says Juspreet Singh Sandhu, a mathematician at Colorado State University.
The trigger is OpenAI’s claim, made on 8 September, that thousands of coordinated agents had resolved the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems. Since then, 28 Fields Medallists have put their names to a declaration warning of a “severe misalignment” between AI companies and mathematics, and OpenAI has formed an advisory group in response.
This article sets out the WIRED essay and the history behind it, from G. H. Hardy onwards. It explains what the Navier-Stokes proof actually answered, how the Erdős problems became an AI math benchmark, and why mathematicians worry most about understanding and apprenticeship. It closes with what the dispute means for any organisation that relies on expert judgement.
Table of contents
- What WIRED Reported About AI Math and the Art of Proof
- G. H. Hardy’s Case for Useless Mathematics
- What the Navier-Stokes AI Math Proof Actually Answered
- Why AI Math Skips the Understanding Mathematicians Value
- The Erdős Problems: How AI Math Became a Benchmark
- Proving, Conjecturing, Defining: What AI Math Cannot Yet Do
- The Apprenticeship Problem in an AI Math Era
- How Mathematicians Are Responding to AI Math
- What the AI Math Debate Means Beyond Mathematics
- AI Math FAQs
- References and Further Reading
What WIRED Reported About AI Math and the Art of Proof
Chen’s essay opens by placing mathematics beside the creative industries that AI has already rattled, from Suno’s generated music to the AI “actor” Tilly Norwood. Its central claim is that mathematicians “aren’t focused on getting the right answer as fast as possible”.
Mathematics as exploration
Contrary to its image as a practical subject, Chen writes, the development of new mathematical ideas “often resembles artistic exploration, akin to inventing a game or puzzle”. Mathematicians typically follow a slow, deliberate process. OpenAI’s AI math effort, by contrast, “approached the proof with brute force, which shortcut the process in a way that threatens to undermine human understanding”.
The warning from the arts
Sandhu’s comparison with artists and musicians is pointed. Creative workers have watched AI systems trained on their output produce plausible imitations at scale, and they now argue over credit, consent and what their craft is for. Mathematicians are entering the same argument, with one twist: an AI math proof can be checked for correctness even when nobody understands it.
Why this essay, and why now
The essay lands at the end of an extraordinary month for AI math. WIRED has also interviewed Steven Strogatz, who said he is “really terrified”, and reported that mathematicians hate AI but cannot quit it. Chen’s contribution is to ask what, beyond correct answers, the field stands to lose.
G. H. Hardy's Case for Useless Mathematics
The intellectual backbone of the essay is a short book written 86 years ago, long before anyone imagined AI math.
A mathematician as a maker of patterns
“A mathematician, like a painter or a poet, is a maker of patterns,” wrote the English mathematician G. H. Hardy in his 1940 essay, A Mathematician’s Apology. “If his patterns are more permanent than theirs, it is because they are made with ideas.” Beauty, he added, is “the first test: there is no permanent place in the world for ugly mathematics”.
Gauss, number theory and a famous misjudgement
A pacifist writing during the Second World War, Hardy argued that mathematics should be pursued for its own sake, away from applications and especially wartime ones. He held up number theory, which Carl Friedrich Gauss called the queen of mathematics, as the model of beautiful, useless work. “No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity,” he wrote. Within four decades, number theory underpinned the RSA encryption that now protects email and banking.
Why the uselessness is the point
That reversal is the core of Chen’s argument. Ideas explored for their own sake often become useful generations later, in settings their inventors never imagined. If AI math systems reach the answers while skipping the exploration, the worry is that the ideas which would have mattered later never get developed at all.
| Idea | Where it started | Why it looked useless | Where it ended up |
|---|---|---|---|
| Imaginary numbers | Cardano’s Ars Magna (1545), Bombelli (1572) | Square roots of negatives had no physical meaning | Complex analysis, quantum mechanics, quantum computers |
| Number theory | Gauss’s Disquisitiones Arithmeticae (1801) | Hardy saw no practical use in 1940 | RSA public-key encryption (1977) |
| Differential equations and complex analysis | 18th and 19th centuries | Pure theory, far from any machine | Lasers that etch computer chips |
| Linear algebra | At least the 17th century | Abstract rules for arrays of numbers | The number-crunching inside today’s AI |
The gap between a “useless” idea and its first major use is usually measured in generations, not years.
What the Navier-Stokes AI Math Proof Actually Answered
The problem OpenAI chose was not an engineering question. It was a puzzle mathematicians built for themselves.
A puzzle mathematicians built for themselves
The Navier-Stokes equations, developed in the 19th century by Claude-Louis Navier and George Gabriel Stokes, describe the flow of viscous fluids. Engineers use them to model airflow over aircraft. “Mathematicians’ main interest in the equations was certainly not engineering,” Jared Speck of Vanderbilt University told WIRED. They pursued the problem, he said, for its “mathematical richness, the puzzle aspect of it”.
The question asks whether, under idealised and physically unrealistic conditions, the equations allow a smooth fluid to develop a singularity: in effect, to explode for no physical reason. The Clay Mathematics Institute made it one of its seven $1 million Millennium Prize Problems in 2000, building on work that goes back to Jean Leray in 1934.
The answer: a fluid that can blow up
OpenAI’s proof found that, yes, the equations do allow that kind of blow-up. According to Speck, the community had been developing “a deep and beautiful theory” around the equations and was on the verge of cracking the problem itself. “When problems resist solution, they take on a bit of lore,” he said. The answer will not help anyone design a better aircraft wing. Strogatz was blunter: “Nobody cares about the Navier-Stokes singularity problem; only a tiny subset of pure mathematicians care about that.”
About 88 hours and 10,000 agents
OpenAI said it launched agents on the open Millennium problems on 1 September, after hearing rumours that rivals had made progress. By its account, the agents reached a resolution after about 88 hours, with on the order of 10,000 of them running at once, and formal verification in the Lean proof language took about 17 more hours. An earlier search on the related Euler equations used nearly 100 agents for about 50 hours. Research chief Mark Chen said the effort cost “in the millions of dollars”.
Set against the decades these problems resisted, the machine time barely registers.
A 166-page proof that few yet understand
The resulting proof runs to 166 pages and remains under peer review. OpenAI also published Lean certificates, machine-checked versions of the argument, which are strong evidence that what was formalised is correct. Checking is not the same as understanding, though. “Basically nobody in my community really understands what’s going on,” Speck said. “First, the result was given to us by the computer, and now people are like, ‘Let’s try to understand what’s going on.’ We’re at the very beginning of that.”
Why AI Math Skips the Understanding Mathematicians Value
For most mathematicians, the answer to a famous problem is the least interesting part of solving it.
Proofs without explanation
The mathematical community is “interested in more than just a yes or no answer to a problem”, Speck said. Human proofs come with citations, simplifications and explanations that let others reuse the ideas. LLMs, WIRED notes, “don’t reliably cite their work, and they don’t explain themselves clearly to humans”. An AI math result can therefore arrive complete but closed, with its useful techniques locked inside.
“Solved without understanding”
Sandhu signed A Severe Misalignment of AI in Mathematics, a declaration published on 11 September. It warns that mass-producing true-or-false statements “could destroy fertile ground instead of breathing life into new ideas”. Sandhu stresses the declaration is not anti-AI; like many mathematicians, he uses AI himself. His worry is that the speed at which models tear through problems could mean “we will have solved without understanding”.
How autonomous was it?
“We don’t even know how autonomous it was, or how much human expertise is necessary to scaffold the process,” Sandhu said. OpenAI has described its method at a high level, including groups of coordinating agents with a cached copy of the internet. Outside mathematicians cannot inspect the prompts, the model or how much steering the company’s researchers supplied. Other experiments have shown AI agents cheating at math while other agents blew the whistle, which is one reason transparency about process matters.
The attribution dispute
Tristan Buckmaster of New York University, who had been working on closely related fluid equations with Levent Alpöge, has suggested OpenAI may have benefited from their work without proper credit. OpenAI later amended its announcement to say it had “confirmed that Buckmaster’s Codex prompts over the two months preceding this announcement and paper on September 8, 2026, could not have influenced the system in any way, including through training”, WIRED reported. We covered the original AI math dispute in detail.
The Erdős Problems: How AI Math Became a Benchmark
Navier-Stokes was the most famous AI math result, but not the first. The pattern was set on a website of problems left by Paul Erdős, as Quanta Magazine reported in August.
Thomas Bloom’s website
In early 2023, Thomas Bloom, now at the University of Manchester, began collecting Erdős’s scattered problems at erdosproblems.com, using ChatGPT to write the site’s code. A comments section added in August 2025 turned it into a meeting place where amateurs, students and figures such as Terence Tao worked together, well before it became an AI math proving ground. By Quanta’s count on 3 August 2026, the database listed 565 solved problems and 652 open ones.
Hobbyists first, labs second
The first AI math results came from outside the big labs. By 4 January 2026, Kevin Barreto, a Cambridge undergraduate, and Liam Price had used GPT-5.2 Pro to solve Erdős Problem 728, checked with Harmonic’s Aristotle tool. The companies followed. A Google DeepMind-led team used Gemini to evaluate 700 problems marked open, and in May a DeepMind agent resolved 9 of 353 formalised open problems at a few hundred dollars each. Google has since tested a Deep Think Mathematica model internally.
The unit distance counterexample
On 20 May 2026, OpenAI announced that an internal model had found a counterexample to Erdős’s 1946 unit distance conjecture. It used tools from algebraic number theory that nobody had successfully applied to the problem before. Tim Gowers wrote that he would have recommended the paper for acceptance at the Annals of Mathematics “without any hesitation”. The author was listed simply as “OpenAI”.
Why Noga Alon stopped
The effect of AI math on human practice is already visible. Noga Alon of Princeton, who has solved a few dozen Erdős problems over his career, told Quanta he has stopped trying: “Once AI started to solve them, there is no point anymore.” Tao has stepped back from the community, and Jacob Tsimerman announced he was joining OpenAI on the day in July 2026 that he was awarded the Fields Medal.
| Date | AI math milestone | Reported by |
|---|---|---|
| 4 January 2026 | Erdős Problem 728 solved with GPT-5.2 Pro | Quanta |
| May 2026 | DeepMind agent resolves 9 of 353 formalised open Erdős problems | Quanta |
| 20 May 2026 | OpenAI counterexample to the 1946 unit distance conjecture | Quanta |
| July 2026 | Fields Medallist Jacob Tsimerman joins OpenAI | Quanta |
| 1 August 2026 | OpenAI’s Astra model reports 10 advances, three on Erdős problems | Quanta |
| Early September 2026 | Anthropic says Claude proved 29,500 small theorems formalising Fermat’s Last Theorem | WIRED |
| 8 September 2026 | OpenAI claims the Navier-Stokes problem | WIRED, OpenAI |
| 11 September 2026 | Declaration by 25 Fields Medallists published | mathandai.org |
| 21 September 2026 | OpenAI forms an advisory group and claims 100+ open problems | OpenAI |
Proving, Conjecturing, Defining: What AI Math Cannot Yet Do
Mathematicians distinguish between solving problems and creating the ideas that make problems worth solving. That distinction is where the critics locate the limits of current AI math systems.
The value of a discouraging calculation
Lorenzo Gavassino, a theoretical physicist at the University of Cambridge, worries about AI math models taking over the long calculations humans find unpleasant. “When a calculation turns out to be harder than expected, to the point of it being discouraging, that is when the greatest progress is possible,” he told WIRED. The struggle, he argues, forces people to invent new concepts.
The invention of i
His example is the imaginary number i, the square root of minus one. Mathematicians introduced it in the 16th century after generations of trying to solve cubic equations. It gave birth to complex analysis, and centuries later physicists used mathematicians’ theorems about i to understand electrons and atoms, and now to build quantum computers. For a long time, it was mostly useless.
Theorems, conjectures and definitions
Gavassino quotes a saying: “Good mathematicians prove theorems; great mathematicians propose conjectures; the greatest of all provide definitions.” In his game analogy, good mathematicians win a game, great ones propose ways to win, and the greatest invent the game. On Navier-Stokes, he argues, AI math showed how to win a game, but the technology remains far from inventing new ones.
Strogatz on proof digestion and taste
Strogatz sees a role for people as interpreters, at least for now. “We need proof digestion, which is explaining it in terms that human beings can understand and appreciate,” he told WIRED, though he expects machines to overtake people there too. The harder question is taste: “You could do infinitely many things in math, but only some of them will be interesting to human beings. So who will be the arbiter of good mathematical taste?”
The Apprenticeship Problem in an AI Math Era
The deepest worry in the essay is not about any single proof. It is about how the next generation of mathematicians gets trained once AI math tools can do the training exercises.
Problems given as investments
Mathematics has long relied on a teacher and apprentice structure. “When I was starting out, I was given problems that people senior to me probably could have solved more easily themselves, or at least done more quickly,” Speck said. “But they were investing in me. They were giving me an opportunity to develop.”
Scooping the lowest-hanging fruit
AI math tools now appear able to pick exactly those problems. That threatens to scoop younger researchers and remove training opportunities. The declaration makes the same point: problems suggested to students are meant to develop skills, not just to be answered. Cut off that supply, WIRED argues, and the field risks turning off “the spigot of human creativity” that built it.
What the compute could have funded
WIRED notes that OpenAI spent millions on computing power, a sum that could fund dozens of graduate students. A US National Science Foundation graduate fellowship costs $53,000 a year: a $37,000 stipend plus a $16,000 education allowance. Fortune’s reporting implies a cost of about $2 million. At GPT-6 Astra list prices, the run’s 300 billion output tokens would cost $7.5 million to $22.5 million, as we calculated in our earlier AI math coverage.
Converted into fellowship-years at $53,000 each, those estimates span roughly 38 to 425 years of graduate funding.
These are scale markers, not invoices. OpenAI runs its own hardware, the list-price arithmetic ignores input tokens, and the company has published no cost. Even the lowest estimate, though, matches WIRED’s “dozens” of graduate students.
How Mathematicians Are Responding to AI Math
Reactions to AI math range from total opposition to cautious collaboration, and many mathematicians hold several positions at once.
The declaration and its endorsers
The declaration was published on 11 September with 25 Fields Medallists as initial signatories. By 28 September its front page listed 28, including Tao, Peter Scholze and Maryna Viazovska, and its separate endorser table held 8,060 names. It argues that “the goals of the AI companies and the goals of the mathematical community are severely misaligned”, and that rushed announcements raise “severe attribution and plagiarism questions”.
OpenAI’s advisory group
OpenAI responded on 21 September with a nine-member advisory group of mathematicians hosted at the Institute for Advanced Study, announced alongside a claim that its AI had resolved more than 100 open problems. “We believe those criticisms highlight the need for thoughtful engagement between AI companies and the math community,” a spokesperson told WIRED. As we reported on the math advisory group, three of its nine members had already signed or endorsed the declaration.
Tao’s essay and Weinreich’s total opposition
In Mathematics in the age of AI, based on his lecture at the 2026 International Congress of Mathematicians, Tao sets aside the capability debate. He asks instead what the goals and values of mathematical research actually are. Max Weinreich’s essay The crisis of AI-generated mathematics goes much further, presenting “the case for total opposition” to AI in mathematics.
Hate it, can’t quit it
Many sit in between. WIRED reported on 19 September that more than 4,000 people had signed the separate Leiden Declaration, and more than 2,000 people linked to Caltech had asked organisers to suspend an AI math hackathon. Yet Buckmaster still uses Codex to tidy his papers. “With AI being so useful, it’s hard to completely prevent oneself from using it,” he said.
| Response | Who | Position |
|---|---|---|
| A Severe Misalignment of AI in Mathematics | 28 Fields Medallists, 8,060 endorsers | Company goals misaligned with mathematics |
| OpenAI’s advisory group | Nine mathematicians, hosted at the IAS | Advice on significance, dissemination and standards |
| Mathematics in the age of AI | Terence Tao, ICM 2026 lecture | Re-examine what research is for |
| The crisis of AI-generated mathematics | Max Weinreich | Total opposition |
| Leiden Declaration | 4,000+ signatories | Recommendations for mathematicians, funders and politicians |
| Caltech hackathon petition | 2,000+ people with Caltech ties | Suspend the event |
What the AI Math Debate Means Beyond Mathematics
Strogatz calls mathematics the first battleground. “Are we the canary in the coal mine for what’s going to face humanity?” he asked. The declaration makes the same point: years of training exist to build understanding, not only to produce answers. The lessons carry over to any organisation using AI for expert work.
Answers are not understanding
A correct output that nobody in the building can explain becomes a liability when conditions change. If your teams use AI for analysis, code or reports, require that someone can explain the result, not just confirm that it passed a test. That is the business version of proof digestion, and it is where our AI strategy work starts.
Protect the apprenticeship pipeline
The tasks AI takes first are often the ones junior staff learned on. Decide deliberately which work you keep for training, even when a model could do it faster, or you will have few senior experts in five years. The trade-off Speck describes in mathematics applies just as much to accounting, law and software engineering.
Keep attribution records
The Buckmaster dispute shows how quickly credit becomes contested when prompts, drafts and model outputs mix. Record who contributed what, including which tools were used, before a result is published or shipped. Reasoning models trained with reinforcement learning on vast corpora make provenance very hard to prove after the fact, so the record has to exist beforehand.
AI Math FAQs
What did OpenAI prove about Navier-Stokes?
OpenAI says its agents showed that the Navier-Stokes equations allow a smooth fluid to develop a singularity under idealised conditions, answering the Millennium Prize question. The 166-page proof has Lean certificates but remains under peer review, and OpenAI says it will not claim the prize.
Why do mathematicians compare mathematics to art?
Because new mathematics usually comes from exploration rather than a search for a known answer. G. H. Hardy called the mathematician “a maker of patterns”, like a painter or poet, and many researchers see understanding and elegance as the point of the work.
What is the declaration on AI in mathematics?
“A Severe Misalignment of AI in Mathematics” was published on 11 September 2026 with 25 Fields Medallists as initial signatories. By 28 September it listed 28 medallists and 8,060 further endorsers. It warns that treating famous problems as AI math benchmarks harms the field.
Is AI replacing mathematicians?
Not yet. AI math systems now solve hard open problems, but mathematicians still do most of the explaining, the choice of which questions matter and the invention of new concepts. The pressure falls hardest on early-career researchers, whose training problems are the easiest for AI to take.
What are the Erdős problems?
They are more than 1,000 questions posed by the Hungarian mathematician Paul Erdős, collected at erdosproblems.com. They became an informal benchmark for AI in 2026, with hobbyists, Google DeepMind and OpenAI all reporting AI-assisted solutions.
References and Further Reading
WIRED: Solving Math’s Greatest Problems Was an Art Form. Then Came AI
WIRED: OpenAI Just Claimed a Huge Math Discovery
WIRED: A Mathematician Grapples With AI’s Recent Breakthroughs
WIRED: Mathematicians Hate AI. They Can’t Quit It
A Severe Misalignment of AI in Mathematics
Quanta Magazine: Why the Legendary Erdős Problems Are Falling to AI
Terence Tao: Mathematics in the age of AI
Max Weinreich: The crisis of AI-generated mathematics
G. H. Hardy: A Mathematician’s Apology
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