Navier–Stokes Controversy: You Don’t Know What You Don’t Know

The Problem of Awareness Paralysis

1. The Blind Spot

Something important is changing around us, but one of the hardest parts of technological change is that people often do not know what they should be noticing. We can continue using a new technology through the mental model of the old one. That creates a strange form of blindness: the technology changes faster than our understanding of what the technology has become.

That is what I mean by awareness paralysis. The problem is not simply that people underestimate AI. It is that they may not even have the conceptual framework required to recognize how much has changed.

2. We Are Measuring AI With the Wrong Ruler

For years, the natural question was whether a machine could beat a human at a particular task. Chess gave us a spectacular example. Stockfish and AlphaZero did not merely become better chess players; they changed the way we think about machine-generated analysis. The important question eventually became less about whether a machine could imitate a human player and more about what happens when a machine can search a space of possibilities at a scale an individual human cannot.

AI is now approaching a similar conceptual problem across cognitive work. How much of the cognitive work performed by humanity can increasingly be performed by machines? We do not need a machine to be universally superior to every human before the economic consequences become enormous. If it can outperform enough people on enough valuable cognitive tasks, the baseline changes.

3. The Problem of Awareness Paralysis

The capability frontier can move faster than public perception. A person may still think of an AI as a chatbot that writes emails, summarizes documents and occasionally gets things wrong, while somewhere else increasingly capable systems are being used for research, coding, mathematics, scientific exploration and large-scale problem solving.

This matters because you cannot protect what you do not recognize as valuable. You cannot protect a research direction if you do not realize that a direction itself has become valuable. You cannot protect commercially sensitive reasoning if you assume that the machine is merely a passive tool.

4. The Customer Who Is Also the Worker

There is another unusual feature of the AI economy. The user pays for the service, but the user may also contribute to improving the service. Questions, corrections, evaluations, examples, feedback and professional knowledge can all become useful signals. The exact treatment varies by product, account type, settings and policy, so this should not be reduced to the claim that every conversation directly trains a model.

But structurally, something new is happening: the roles can overlap. You may be paying to use the machine while also helping build the machine. The customer, user, evaluator and knowledge contributor can become the same person.

5. From Data Harvesting to Idea Harvesting

Data has always had value. But increasingly capable AI changes the question. What if the most valuable thing you give a system is not the answer you ask it to produce, but the direction you give it?

A promising research hypothesis, a new product idea, an unusual engineering approach or a commercial insight may be worth far more than the immediate response generated by an AI assistant. The critical resource can become direction: knowing where to look, which problem matters and which path may be worth pursuing.

Once a promising direction becomes visible to an organization with powerful models, enormous compute and teams capable of deploying those resources, the scale of the response can be radically different from anything an individual researcher can produce.

6. The Navier–Stokes Controversy

The recent Navier–Stokes controversy makes this problem tangible. OpenAI says it heard a rumor on September 1 that a Millennium Prize problem might have been resolved and then launched a large internal effort to investigate. According to OpenAI, the Navier–Stokes effort eventually involved roughly 10,000 concurrent AI agents, 2.7 million messages and about 130 billion output tokens, reaching its reported result after about 88 hours.

The human side of the controversy is equally important. NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge had been working on closely related problems with several AI systems, including OpenAI’s Codex and Astra. Buckmaster has questioned whether OpenAI’s effort benefited from knowledge of their unpublished work. OpenAI disputes that interpretation and says its researchers did not see their work before it was public. Sébastien Bubeck, who contacted the researchers, subsequently became part of the discussion about the relationship between the separate efforts and how the work should be handled.

Whatever the ultimate resolution, the episode exposes a new asymmetry: a human researcher can spend months or years developing a promising direction, while a company with enormous compute and powerful AI systems can hear about that direction and respond with a vastly larger machine. The scarce resource may no longer be the ability to solve a problem. It may be identifying the right problem, finding the right direction, and keeping it alive long enough to develop it.

That is particularly significant in light of Terence Tao’s discussion of how AI is changing mathematics. If AI can rapidly attack promising problems once they become known, the incentive to share promising research directions can weaken dramatically. The question becomes not merely who solves the problem, but who gets to decide when a promising direction becomes public.

Tao’s concern points to a deeper problem than credit. In mathematics, the value of solving a problem is often not merely the solution itself. Human attempts generate techniques, partial results, intuition and new questions that advance the field. If AI can suddenly produce solutions without making the underlying reasoning transparent or intellectually digestible, it may solve problems while weakening some of the developmental process that made those problems valuable in the first place. The paradox is striking: AI may make answers cheaper at precisely the moment when the human ability to identify valuable questions and understand why the answers matter becomes more important.

Further reading: OpenAI’s account · Financial Times · Nature · WIRED · Terence Tao

7. The Hidden AI Problem

The public interface may not represent the full frontier of the technology. A consumer sees a product. Behind that product may be larger models, internal evaluations, specialized systems, agentic infrastructure and computing resources that are not available to ordinary users.

This creates a fundamental information asymmetry. You may be interacting with one layer of an AI ecosystem without knowing what the organization behind it can do with the information you provide. That does not mean a company is secretly doing something improper. It means the user should not assume that the visible interface defines the entire capability landscape.

8. We May Be Training Our Own Replacement

The larger loop is uncomfortable. Human intelligence produces questions, examples, corrections, judgments and ideas. AI systems process those interactions. Under the relevant product policies and settings, some of that information can contribute to system improvement. Better systems then perform more cognitive work, which creates more opportunities to transfer work from humans to machines.

This is not necessarily malicious, and it is not necessarily illegal. It is a structural possibility. We are training our own replacement for free is deliberately provocative language, but it captures the underlying asymmetry: humans can supply enormous amounts of cognitive material while ownership of the resulting models and infrastructure remains concentrated.

9. Legal Does Not Automatically Mean Ethical

Terms of service and copyright law matter, but they do not answer every ethical question. A user may have technically agreed to a policy without having a meaningful understanding of all the consequences of secondary data use. Contracts can define permissions, but permission is not identical to informed consent in the broader ethical sense.

The same distinction matters when people invoke fair use. Copyright law generally does not protect ideas as such, and fair use is a fact-specific legal doctrine rather than a universal permission slip for every form of AI training. More importantly for this discussion, training on copyrighted expression, learning from user interactions, extracting a novel idea, recognizing its commercial value, and acting on that idea are not necessarily the same activity.

A legal system may eventually draw lines around these activities. Ethics asks a broader question: even when an action is permitted, is it fair to the person who trusted the system with the information?

10. The Psychotherapist Analogy

Consider the intuition behind a private conversation with a psychotherapist. The professional relationship creates an expectation that intimate information is being shared for a particular purpose, not simply harvested as raw material for unrelated commercial exploitation. AI assistants are not legally or professionally equivalent to psychotherapists, so the analogy should not be pushed that far.

The useful point is about trust. People often reveal information because they believe they are interacting with a tool for a specific purpose. Legal permission can be narrower or broader than the user’s intuitive understanding of that relationship. The ethical question begins where formal permission stops being a sufficient explanation.

11. The Rich Get the Intelligence

There is an economic consequence to all of this. The organizations that own frontier models, compute, data pipelines, research teams and distribution channels can potentially capture a disproportionate share of the value created by increasingly capable machine intelligence.

The issue is not simply that wealthy companies become more profitable. It is that intelligence itself may become concentrated as an economic asset. Millions of people can contribute fragments of knowledge and cognition, while a relatively small number of organizations control the systems that turn those fragments into scalable capability. This connects directly with the idea explored in Raw Intelligence: what happens when human intelligence itself becomes scalable?

12. The Great Blindness

This brings us back to awareness. The most dangerous part of the transition may not be a dramatic moment when AI suddenly takes over a profession. It may be the quieter process in which people continue using AI according to yesterday’s assumptions while the underlying technology moves somewhere else.

Awareness is becoming a strategic resource. The person who understands what information has become valuable, what a system can actually do, and what kinds of human contributions can scale through AI has an advantage over someone who sees only a convenient chatbot.

13. From Awareness Paralysis to Information Seclusion

There is a paradox here. AI systems encourage people to share more. The more people share, the more useful the systems can become. But if users begin to understand that promising ideas, research directions and commercially sensitive reasoning may have value beyond the immediate conversation, the incentive can reverse.

That leads to Information Seclusion: people deliberately withholding their most valuable information from systems they do not fully control. Researchers may stop describing their most promising directions. Entrepreneurs may stop discussing their next product. Professionals may keep their best heuristics offline. The very success of AI could therefore make some of the most valuable human information harder to access.

14. The Counter-View

There is, however, a legitimate counter-view. The Navier–Stokes episode does not by itself prove that OpenAI copied unpublished mathematics or improperly used the researchers’ work. OpenAI says its team did not see Buckmaster and Alpöge’s work before it became public. A rumor about a problem being solved is not the same thing as possessing another researcher’s proof.

There is a real difference between copying someone’s work and independently pursuing a problem after learning that it may be solvable. The available evidence does not allow us to collapse those two things into one. Nor should an accusation of an intellectual heist be treated as established fact simply because the timing is uncomfortable.

We do not need to assume that AI companies are secretly harvesting every idea, or that every interaction is being converted directly into a superior model, to recognize the structural issue. The important thing is that the capability gap, the ownership gap and the user’s awareness of both can move at different speeds.

And that may be the defining problem of this phase of AI: we don’t know what we don’t know.

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