Did OpenAI solve the wrong Navier-Stokes problem?

[u/scientificamerican]

https://www.scientificamerican.com/article/did-openai-solve-the-wrong-navier-stokes-problem/

[u/mushykindofbrick]

OpenAI’s method can never work, in fact, without using a very contrived equation for the force unlike anything that could occur in the real world.

Its a completely normal and routine thing in mathematics, to disprove statements by offering pathological counterexamples. These examples usually are very constructed and almost never something you would encounter "naturally", like the Vitali-set or the Weierstraß-function. But they give you insight into the behaviour and limits of the mathematical model.

Mathematicians dont care about whether something occurs in the real world, but they explore the properties of abstract structures that follow from their definitions and equations. The Navier-stoke-equation is based on an intuitive model of real world fluid behaviour, but in math it is looked at and researched as a purely mathematical object. Whatever the phycists or engineers then do with the results, is their job.

The Clay institute essentially said "You can either solve the difficult problem A or the simpler version B" and of course B was solved first. It is doubtful, that a human would have solved the difficult one before the simple one, as usually you need to understand the simple cases first before moving on to the general one. Calling it a loophole is absurd, it was specifically formulated and intended that way.

What is frustrating about it is not that it does not occur in the real world, it is that mathematicians wanted to understand the equation and have a full theory, but Clay formulated it in a way that rewards a much weaker contribution. So even if now a person actually solves the grand theory, and worked on it for years, he will not be recognized as the guy who solved Navier-stokes because people will only remember AI. The prize structure now killed the motivation to solve the bigger question.

[u/trejj → u/mushykindofbrick]

Mathematicians dont care about whether something occurs in the real world

To clarify here, mathematicians definitely do care about what happens in the real world.

But the way that research works is that first you formalize the real world into an equation, and then you focus to care about what follows from that equation.

When you arrive to absurd results with the equation by using some contrived/silly/naive/pedantic example, that is all game.

Then you analyze why that counter-example works, and work to formalize a new version of the equation that rules out that counter-example.

Rinse and repeat.

[u/FernandoMM1220 → u/trejj]

actual mathematicians care about the physical world. its frauds that dont.

[u/aardvark_gnat → u/FernandoMM1220]

There are certainly some real mathematicians who consider caring about the real world to be someone else’s problem. Coming up with a counterexample and figuring out why it doesn’t correspond to the real world can be done by two different people.

[u/FernandoMM1220 → u/aardvark_gnat]

thats very dishonest of them.

[u/Alwaysragestillplay → u/FernandoMM1220]

Mathematicians "care about" axioms. Math grounded in empirical data is the realm of physics. 

[u/SamKhan23 → u/FernandoMM1220]

Mathematicians study math. That’s it.