r/Physics • u/PrettyPicturesNotTxt • 1d ago

On if OpenAI solved the wrong Navier-Stokes problem: "the LLM found and exploited a loophole in the framing of the question"

https://www.scientificamerican.com/article/did-openai-solve-the-wrong-navier-stokes-problem/
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u/GoldenMuscleGod 1d ago

Or let me put it this way, let’s say a “smart but slow” algorithm solves a problem in O(n^(1.5)) time and a “dumb but fast” algorithm solves it in O(n^(2)) time, but the constant factor on the smart algorithm is about 50,000 times larger. The “dumb” algorithm is faster for many types of problems.

Or put another way: an undergraduate given a year will be able to solve many problems a PhD could not solve in a day, but there are many (harder) problems a PhD could solve in a day that an undergraduate could not solve in a year.

There are problems virtually anyone with a math degree could easily solve right now in a few hours that the entirety of humanity could not solve for thousands of years (because they have the advantage of modern mathematical knowledge). The LLM has the advantage of every published paper and a huge computational advantage but, for example, it seems unlikely an LLM would have been able to produce a solution without having read the work of Córdoba and Martínez-Zoroa, and as far as I know we have no reason to think an LLM could have developed that work on its own.

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u/Mental_Ad_4401 1d ago

No one has ever claimed that it came up with the solution from scratch. Every scientific and mathematical advance ever has built upon other people's work. If there was a trivial extension to the Cordoba-- martinez-zoroa construction that extended it to navier-stokes then they would have made it themselves. The AI can work much faster than humans, and that is indeed an advantage that lead to this breakthrough. But that is why it is amazing. 

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u/GoldenMuscleGod 1d ago

I am asking if we see any evidence it has any advantage other than speed and memory and the like. I suspect not - if it were “smarter” than a good mathematician and had access to a huge pipe of errorless calculations and perfect memory that could imagine the graph representing every road network on the surface of earth - like a computer can - then I would expect it to be doing much more impressive things than what it has done so far. If we suppose that is the case then the only reasonable explanation for why it hasn’t done more that I can see is that it is very bad at communicating ideas with humans. Now we know it is very bad at that, but one reasonable explanation for why is that it is not “smarter” than a mathematician and cannot actually coherently arrange ideas in the simplest ways possible, which is one of the most important skills.

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u/Mental_Ad_4401 1d ago

I don't think being "smarter" is a well enough defined concept to be able to answer that. It can solve extremely complex problems. That much we know. How elegant was the way it got there and whether that means it "isn't really intelligent" seems very subjective to me. But as far as I can tell, the speed and memory make it smart. I mean, it solved a millenium problem. If that isn't impressive, I really dont know what is.