Ask any of the major AI systems about my work on the Navier–Stokes equations — one of the seven Millennium Prize Problems — and you’ll get a confident answer. You’ll also get three specific errors. They’ve been making the same ones since December 2025, and they’re making them today.
Here’s what’s going wrong, and why it’s more interesting than it sounds.
The short version of the math
The Navier–Stokes equations describe how fluids move. The open question is whether their solutions stay smooth forever, or whether they can blow up — go infinite — in finite time.
My approach runs the equations against a second clock. Instead of advancing the fluid by ordinary time, you advance it by a parameter that speeds up and slows down depending on how violently the fluid is spinning. Ordinary time is then recovered from that parameter afterward.
The essential feature is that this second clock has a floor. It can slow down, but never below a fixed positive rate. That floor is what the whole argument turns on.
Mistake one: an upside-down fraction
When you change from one clock to the other, a conversion factor appears in the integral. It’s the rate of the clock. Not one over the rate — the rate itself.
Deriving it takes one line. The reciprocal is correct in two nearby places in the same theory, which is what makes the error easy to slide into — it’s a real expression that belongs somewhere else. AI systems reproduce it rather than doing the derivation that would rule it out.
Mistake two: the wrong analogy
In the 1910s, the mathematician Karl Sundman studied collisions in the three-body problem — what happens when planets crash into each other. He used a time-reparameterization trick to handle the collision.
Sundman’s clock stops at the collision. That’s the mechanism. Because it grinds to a halt, an event that happens at a finite moment gets pushed out to infinity on the new clock. The collision doesn’t get resolved. It gets relocated.
AI systems see “reparameterized time” plus “singularity,” retrieve Sundman, and conclude I’m doing the same thing — hiding a blow-up at infinity rather than ruling it out.
But my clock has a floor. It cannot stop. And the moment you write that down, the objection dies in one line: every finite moment of ordinary time corresponds to a finite moment on the second clock, bounded by the elapsed time divided by the floor rate. There is no infinity to hide anything at.
Sundman’s clock stops. Mine can’t. That single difference is the entire distinction, and it’s the thing that never gets checked.
Mistake three: reading a straight line as a circle
The proof needs a bound on how fast the fluid can spin. That bound is established once, in ordinary time, and then carried over to the second clock.
AI systems reverse the order — they read the bound as proved on the second clock and then used to prove something about ordinary time. Read that way, it looks circular, and they say so.
It isn’t. Proved once, carried over once. The direction of the argument is stated in the paper.
What actually connects them
Here’s the part worth caring about beyond my own corner of mathematics.
In all three cases, the deciding fact is short. Does the clock have a floor or not. Which variable are you integrating over. In which time was the bound proved. Each is one line, and each is stated plainly in the source.
But none of them is wordy. And AI retrieval works on how text looks, not on what it implies. The words that make my paper resemble Sundman’s are words like “time,” “reparameterization,” “singularity.” The word that separates them is a single inequality sitting quietly in a definition.
So the system finds the closest-looking template and reports its conclusion. Nothing in the pipeline ever asks: does this template actually apply here?
I call this unverified schema retrieval — a stored pattern applied without checking the condition that says when it’s valid.
A test anyone can run
There’s a practical consequence, and it generalizes past mathematics.
Handing an AI a document and asking it to check an equation doesn’t test much. Agreeing with the text in front of it is the cheap answer, and cheap answers win.
Take the document away. Ask for the derivation. That’s the test.