AI hasn't solved Navier-Stokes; the business is elsewhere

AI doesn't solve Navier-Stokes: confusing Fermat with brute force

The notion prevails that artificial intelligence has solved the equations describing how water flows. No one has proven anything, and much of what is presented as mathematical advancement is merely a search conducted via brute force given a new, marketable name.

Refuting is not proving: the asymmetry sold as a discovery

Finding a counterexample is easy; proving the general case is the work. Popper noted this asymmetry almost a century ago, and it continues to mark the boundary between two worlds. A computer has been running numbers in a loop since Turing, and that is not new mathematics: it is patience with electricity.

The underlying confusion is technical. The fact that a machine cannot decide if any given program halts does not imply it cannot verify a specific proof. The Halting Problem is undecidable in general; checking a written proof is mechanical. These are two distinct problems, and those who confuse them often announce a miracle.

Gödel, Penrose, and the jump nobody corrects

The second Incompleteness Theorem states something very specific: a consistent formal system, with sufficient arithmetic, cannot prove its own consistency. That's it. It doesn't speak of simulating, replicating, or modeling. Confusing 'you cannot prove your consistency from within' with 'you cannot simulate the system from within' is exactly the leap taken by Penrose, and it remains a leap.

Fermat dismantles that argument instead of sustaining it. Wiles' proof is standard mathematics — algebraic geometry, modular forms, Galois theory — and there is already a project underway using Lean to verify it line by line on a computer. If the machine verifies the entire proof, the proof did not use any inaccessible internal logic. It used the same as the machine possesses.

Those who master Navier-Stokes fit into a classroom

The thread holds that the number repeated—'thousands of mathematicians' working on the problem—is the same inflation seen in 'thousands of scientists' or 'thousands of parameters': those who truly master Navier-Stokes partial differential equations are a handful, and half of them are in industry or academia, not in the media circus. PDEs are not solved by popular vote.

There is also a recurring historical inaccuracy. Bell wrote in 1964 to ammunition Einstein against Bohr and ended up demonstrating the impossibility of local hidden variables; in 1966, he rescued Bohm's work, which orthodoxy had buried. That is what a mathematician does. Searching for needles in a haystack until one emerges is not the same thing.

The business isn't the theorem; it's the fine print

There is one part of this that does generate money: the ownership of what you deliver. The thread maintains that everything uploaded to Microsoft, Google, or the current Chinese provider ceases to be yours, and generative models are no different regarding fine print. Whoever enters their thesis into a chatbot to polish it is giving away the work. The precedent is not new; it is recalled in the debate: classic email accounts already included a waiver of intellectual property for what was sent.

And the bottleneck is not intelligence; it is fruta and energy. Hence the question running through the thread: if large companies possess similar capacities, where is the business? The advantage also lies in not making it public: if the differential becomes public, it dies before it can be monetized. The Grossman-Stiglitz paradox, reflexivity, and the microstructure of an auction explain why, and a full development of that reasoning takes an entire afternoon that doesn't fit here.

From the €30 Laptop to Hedonic Adjustment

The debt of states is in euros, dollars, and yuan, not 'units of technological pogre.' A model doing in a minute what once cost one hundred people does not reduce a cent of the debt, and it can worsen it if it destroys the fiscal basis supporting repayment.

This leads to the three usual outcomes: hyperinflation, restructuring, and financial repression. The latter degenerated into pure monetization, with the ECB buying its own debt. Yet, from 2008 to 2022, consumer CPI did not move, and when it did, it was due to energy and supply bottlenecks, not the printing press. The trick that fooled the printing press has a name: hedonic adjustment. Just as today's laptop is better than one from ten years ago, statistics say its price has fallen even if the ticket remains at 500 euros. The promise attributed to Bill Gates of a €30 laptop never reached the market.

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Fourteen years of a machine running at full estimulante ilegal, yet the bread remains unchanged. With that track record, anyone who promises that AI will dissolve public debt through productivity is selling something other than what they claim.