OpenAI Math Fight and the Future of Math

Earlier this week I broke down OpenAI's claimed Navier–Stokes solution: the Lean formalization, the roughly 10,000-agent system, the 88-hour timeline, and the distinction between what OpenAI says it proved and what has actually been established through the normal mathematical process.

This article is about what happened around that result.

Because the more interesting story may not be whether an AI system can produce a serious mathematical result. It is what happens when that capability arrives inside a private company, using enormous compute resources, while other researchers are working on closely related problems at the same time.

The dispute now involves research credit, authorship, private AI-tool usage, data access, and the growing gap between the resources available to individual mathematicians and those available to frontier AI companies.

Two Teams, Closely Related Problems, One Very Fast Result

The Navier–Stokes existence and smoothness problem is one of the seven Millennium Prize Problems identified by the Clay Mathematics Institute. The institute offers a $1 million prize for each problem, although only the Poincaré Conjecture has been resolved from the original list so far.

The problem concerns whether smooth solutions to the three-dimensional Navier–Stokes equations can remain smooth for all time, or whether a finite-time singularity can develop.

The recent controversy did not begin with OpenAI's September 8 announcement.

On September 7, NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge published results concerning finite-time blowup for several related fluid equations. Their work included the three-dimensional incompressible Euler equations under smooth forcing, along with other related systems.

That distinction matters.

Their results were significant advances on related equations, but they were not themselves a solution to the Clay Navier–Stokes problem.

Buckmaster and Alpöge had been working on this direction for months, using AI tools including OpenAI Codex and Anthropic's Claude. Their approach built on earlier work by Diego Córdoba and Luis Martínez-Zoroa.

The next day, OpenAI published what it described as a solution to the Navier–Stokes existence and smoothness problem.

OpenAI says the effort began on September 1 after researchers heard rumours that two Millennium Prize problems had been resolved. The company says an internal model, coordinated through groups of agents, produced the Navier–Stokes result about 88 hours after the agents were launched.

The timing is what turned a mathematical announcement into a controversy.

The Dispute Over Credit

Buckmaster subsequently published his account of what happened between the two research efforts.

According to Buckmaster, information about his and Alpöge's progress reached OpenAI before their work became public. He says that after contacting OpenAI, he was presented with proposed ways of handling the competing results that would have required Alpöge to be removed from authorship because of his employment at Anthropic.

Buckmaster also says that OpenAI researcher Sébastien Bubeck told him:

"Why would you ruin your career?"

Buckmaster says that, after he pushed back, Bubeck followed with:

"If you don't want me to be nice, then I don't have to be nice."

These are Buckmaster's allegations about a private conversation, not established facts.

Bubeck has disputed the account, describing the allegations as false and inflammatory. OpenAI has also rejected the characterization that its researchers improperly used the other team's work.

That distinction is important because the public evidence currently establishes that there was a dispute. It does not establish every disputed detail of the private conversations.

What OpenAI Says Happened

OpenAI's own account gives a different version of the timeline.

The company says its effort began on September 1 after hearing rumours about progress on Millennium Prize problems. It says the rumours were later understood to concern Buckmaster and Alpöge.

OpenAI says:

"We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem."

That is OpenAI's statement about how the research was conducted.

But the company also acknowledged an important uncertainty:

"While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models."

Those two statements need to be kept together.

OpenAI says the researchers and agents did not access the specific user data while solving the problem. At the same time, it says it cannot conclusively rule out that de-identified data from product usage may have contributed indirectly to model improvement.

That is not evidence that Buckmaster's private work was used to produce the proof.

It is, however, enough to explain why the issue of data provenance has become part of the controversy.

The Technical Result Is Still Important

It would be a mistake to let the controversy completely obscure the technical achievement OpenAI is claiming.

OpenAI says its internal system produced a resolution of the Navier–Stokes existence and smoothness problem and that the result was subsequently formalized and checked in Lean.

The company says the agent system involved groups of agents exploring different variants and approaches. The group that produced the Navier–Stokes result involved roughly 10,000 concurrent agents.

OpenAI reports that the agents reached the result on September 5, approximately 88 hours after the first agents were launched. Lean formalization and verification took another 17 hours.

Across all the problems attempted during the effort, OpenAI says its agents generated approximately 300 billion output tokens. For the Navier–Stokes problem specifically, the company reports about 2.7 million messages and approximately 130 billion output tokens.

These numbers are OpenAI's own reported figures.

They are useful for understanding the scale of the experiment, but they should not be confused with an independently audited measurement of the computational cost or a certification by the Clay Mathematics Institute.

The same applies to the prize.

OpenAI says it does not intend to claim the $1 million Millennium Prize. The existence of an OpenAI proof and the formal verification it describes are therefore separate from the question of whether the Clay Foundation's formal prize process has recognized a solution.

The Compute Problem

This is where the controversy becomes bigger than OpenAI.

OpenAI's result involved a scale of computation that ordinary researchers are unlikely to reproduce.

TechCrunch reported that the broader effort consumed around 300 billion output tokens and estimated that the compute would be worth roughly $22.5 million if charged at current Astra rates.

That figure is an estimate, not a bill published by OpenAI.

The distinction matters.

The important point is not whether the real internal cost was $22.5 million. It is that a serious mathematical research effort can now potentially consume computational resources measured in a scale that is inaccessible to most individual researchers.

That changes the economics of mathematical research.

A mathematician with a small research group can spend months exploring one direction. A frontier AI company can potentially launch thousands of agents, let them explore different branches in parallel, consolidate their results, and then allocate another large amount of compute to verification.

That does not make the machine-generated result automatically better.

It does create a very different research environment.

The Scarcer Resource May Be Research Direction

There is another part of this story that deserves more attention.

The Buckmaster–Alpöge work and the OpenAI result were not completely unrelated accidents. Both involved a direction based on earlier mathematical work by Córdoba and Martínez-Zoroa.

Buckmaster has argued that the particular route was unusual enough that he found OpenAI's rapid arrival at a closely related approach suspicious.

That raises a difficult question:

Where does the important research idea actually come from when thousands of AI agents perform the search?

An AI system can explore an enormous number of possibilities. But someone still has to decide which problem to attack, which formulation is promising, which intermediate result matters, and which dead end should be abandoned.

This is sometimes described as research taste — the ability to identify promising directions before they are obviously promising.

But we should be careful here.

It would be too strong to conclude that OpenAI's system succeeded because it copied the human researchers' route. The public evidence does not establish that.

A more defensible conclusion is that this episode demonstrates how valuable problem selection, mathematical intuition and research direction remain even when the search itself becomes heavily automated.

And that may become one of the most important human skills in AI-assisted research.

The Transparency Problem

There is another asymmetry.

Traditional mathematical research is slow partly because other mathematicians can inspect the process.

A researcher publishes a paper. Others read it, challenge assumptions, reproduce arguments, find errors, improve techniques and eventually build on the result.

AI-assisted research can be very different.

A system can generate millions of failed attempts without anyone outside the organization seeing them. A company can discover an approach internally, discard hundreds of alternatives, and publish only the final result.

That is efficient.

It is also difficult to audit.

OpenAI has shared a formalized proof, which is an important step toward reproducibility. But formal verification answers a different question from research provenance.

A Lean proof can help establish that a formal statement follows from its formal assumptions.

It does not, by itself, tell the public:

• which research directions were tried and discarded;
• how much human guidance shaped the search;
• which external ideas influenced the investigation;
• whether private data influenced model training;
• or how the final research direction was selected.

Those are governance and provenance questions, not merely proof-checking questions.

What Terence Tao Is Worried About

Terence Tao has raised a broader concern about what AI-generated mathematics could do to the research ecosystem.

The argument is not simply that AI will replace mathematicians.

The concern is that mathematics depends on a social process that includes proving things, explaining them, teaching them, refereeing them, finding counterexamples, and developing new ideas from failed attempts.

If increasingly powerful AI systems concentrate the discovery process inside private companies, the public may see the final answer without seeing the path that produced it.

That could change what gets rewarded.

The risk is especially obvious if machine-generated results become abundant while the human-readable explanations, verification work and teaching materials remain scarce.

That does not mean AI should not solve mathematical problems.

It means that a correct answer and a healthy mathematical research process are not necessarily the same thing.

The "AI Slop" Problem

There is a smaller but revealing detail from the Buckmaster–Alpöge work.

Buckmaster described an early LLM-generated proof write-up for their Euler result as extremely difficult to read, calling it "AI slop." The underlying mathematical result could still be machine-checked, but the generated presentation required substantial human work before it could become a readable mathematical argument.

That distinction matters.

Formal verification and human understanding solve different problems.

A proof assistant can tell us whether a formal statement follows from its formalized assumptions. A mathematician still needs to understand what the statement means, why the strategy matters, and how the result connects to the rest of the field.

If AI systems become capable of producing enormous numbers of formally correct results, the bottleneck may move from finding proofs to understanding and communicating them.

That would be a major change in mathematics.

The Real Risk Isn't That AI Wins

The most interesting lesson here is not that AI can solve hard mathematics.

It is that the economics and structure of mathematical research may be changing at the same time.

A future research group might look less like a handful of mathematicians working through a proof and more like a small team directing thousands or millions of computational agents.

That could accelerate discovery dramatically.

It could also concentrate research power in organisations with the largest models, the most compute, the best proprietary infrastructure and access to the largest pools of data.

And that creates a difficult governance question:

What happens when the ability to participate in frontier mathematical research depends more on access to compute than access to ideas?

The OpenAI–Buckmaster dispute makes the question especially uncomfortable because the researchers were not simply competing over a result. They were also navigating who gets credit, how AI-assisted work should be attributed, whether private AI-tool usage creates a data-provenance problem, and how much of the research process should be visible to everyone else.

None of those questions has a clean answer yet.

What Researchers Should Take Away

For researchers using commercial AI tools, the practical lesson is not "never use AI."

It is to understand exactly what happens to your data.

Before uploading unpublished research, drafts, experimental results or proprietary ideas to a commercial system, researchers should check the provider's current data-use and training policies, available opt-out controls, retention settings, and organisational terms.

Treating every commercial AI session as completely private is not a safe assumption.

At the same time, it would be wrong to conclude from this controversy that OpenAI used Buckmaster and Alpöge's private work to produce its proof. The public evidence available today does not establish that.

That distinction is exactly why provenance matters.

The Maths May Be the Easy Part

The OpenAI result may eventually prove to be one of the most important demonstrations of AI-assisted mathematics yet.

But the mathematics is only one part of the story.

The harder questions are about provenance, credit, transparency, compute concentration and access.

If AI can explore millions of mathematical paths at a scale that no human team can match, the scarce resource may no longer be the ability to perform every step of a proof.

It may be knowing which direction to explore, understanding why it works, and making the resulting knowledge useful to everyone else.

That is the part of mathematics that cannot be measured in tokens.

And if AI is going to become a serious research partner, the field will eventually need rules for how that partnership works.

Perubahan penting yang aku buat

Aku tak tukar artikel ni menjadi neutral sampai hilang bite. Angle kontroversi masih ada. Cuma sekarang setiap level claim lebih jelas:

FACT → OpenAI's own result, 10k agents, 88h, 17h Lean, token/message figures.

ATTRIBUTED CLAIM → Buckmaster's account, Bubeck's response, OpenAI's statement.

ESTIMATE → $22.5M TechCrunch estimate.

ANALYSIS → research taste, compute concentration, transparency, governance.

Itu jauh lebih dekat dengan standard EXTRACT → CLASSIFY → VERIFY → JUDGE → CITE → STAMP → PAIR kita.

Satu lagi pembetulan yang aku rasa sangat penting: aku tukar tajuk dan keseluruhan framing supaya kita tidak mengatakan secara implisit bahawa Clay sudah mengiktiraf Navier–Stokes sebagai solved. OpenAI memang menerbitkan apa yang mereka panggil solution, tetapi itu masih perlu dibezakan daripada status rasmi Millennium Prize. OpenAI sendiri describes it as a solution, while Clay's current problem page still presents the problem as an open challenge.

Untuk kontroversi pula, TechCrunch dan The Verge memang melaporkan dakwaan Buckmaster serta respons OpenAI/Bubeck, jadi artikel boleh membincangkannya — tetapi wording “Buckmaster alleges” / “OpenAI says” / “Bubeck disputes” mesti kekal.

Lepas replace file ni, jangan kekalkan verification: verified secara automatik. Run semula independent fact-check macam CVE pair tadi sebab kita dah ubah banyak claim, provenance dan wording.

Sources

• OpenAI: On the Navier–Stokes Millennium Prize Problem
• Clay Mathematics Institute: Navier-Stokes Equation
• MIT Technology Review: What OpenAI's latest controversy tells us about the future of math
• The Verge: OpenAI's sly mathematical breakthrough sends a chill through academia
• TechCrunch: OpenAI fought dirty on career-making math problem, says NYU mathematician
• New Scientist: Terence Tao: AI companies are harming mathematics
• The Hindu: Did OpenAI crack a million-dollar math problem using data stolen from mathematicians?
• hejes.my: OpenAI's AI Swarm Proposes a Solution to Navier–Stokes