i just want to clarify that this isn't reflective of advanced intelligence, it's a reflection of extreme computational ability. the ai didn't find an ingenious trick to get an elegant solution, it ran zillions (a zillion is defined as a big number) of mundane, simple computations and came up with the answer via brute force by just doing the calculation over and over. this is how humans have been dealing with solving differential equations (which is what this is) for a long time. the tactic is called numerical methods. again, if you had a million calculus doing monkeys on a million typewriters, you could solve navier-stokes, but you'd have to enslave millions of humans for millions of years to get an outcome. this is a valid use of super computers, and it's a great result, but it's a function of the power of the machine to do rote math and not of any deep intelligence.

and i want to propose some caution. in fact, computers are very bad at rote math and need to do tremendous amounts of error correction. the results need to be double checked by humans. people that work with this kind of thing will tell you that normal logic gate binary computers - not quantum computers - make an uncomfortable number of mistakes that are essentially reduced to round off errors arising from the need to convert from binary to base 10 and the fact that the computers do all of their math in base 2, which is necessary but crazy.

in fact, there's some circular logic here that i might be cautious about. i haven't looked at this and i'm not going to look at it but computers use euler's method to do almost everything because they need to constantly approximate solutions and are constantly cutting off rounding errors. this is called floating point error.

i would strenuously recommend that the math be doublechecked by hand for errors in arithmetic resulting from floating point errors. if it holds up, i might even suggest it's dumb luck. if it doesn't, it demonstrates the limitations of computers in solving math problems.

https://www.newscientist.com/article/2588063-openai-has-solved-the-navier-stokes-millennium-problem-using-15m-of-ai-effort/