It's always easier to measure progress according to the internal metrics of the field than to evaluate the contributions to the wider understanding of the topic. In theoretical computer science (which I'm most familiar with), people have long complained about results focusing on shaving sublogarithmic factors from complexity bounds (while making the algorithm worse in practice) and about reviewers being impressed by the technical difficulty of proofs. But progress like that is easier to measure than new algorithmic ideas or conceptual understanding.
But it's not all bad. The researchers chasing the metrics are almost always genuinely interested in the topics they study. Their actual contributions mostly come from the ideas they explore while trying to achieve measurable progress. And because they are not expected to produce anything of direct value (Goodhart's Law for applied researchers), they can explore a wider range of ideas.
I personally noticed this when I moved from theoretical computer science to algorithmic bioinformatics. When I start a new project, the expectation is that researchers in genomics should be using sofware that uses the new algorithms five year from now. That expectation is useful, but it's also a strict constraint on what I can afford to try.
Weird, these are all still here? https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_m...
So: unless all those claims by OpenAI turn out to have been mistakes[1]: no, actually, those are not all still there.
[1] It's certainly possible that some will. They've already retracted a few things.
(and as noted on Wikipedia, the Clay institute still lists the problem as 'active' not solved https://www.claymath.org/millennium/navier-stokes-equation/)
The criteria for statement C (which OpenAI targeted) only require a C-infinity smooth force, whereas the paper considers constructions of the same kind as the OpenAI one but with a real analytic force. All real analytic functions are C-infinity smooth, but not vice versa [2]. Wikipedia says the Navier-Stokes problem for real analytic forces is still unsolved, so the question of whether a similar approach can be used there is presumably of some interest, but it doesn't appear to affect whether the Prize criteria have been satisfied and the paper doesn't explicitly make any claim that it does.
Re the problem still showing as "active": The Clay Institute don't consider problems solved until the solution has been fully digested by the mathematical community and is well established. In the case of the Poincare Conjecture that wasn't until 2010, 7 years after Perelman put his papers on the arXiv. Nobody is expecting them to mark Navier-Stokes solved any time soon.
Your comment was the first I've heard of that paper, BTW, so thanks for that. However, that's another indication that this probably doesn't bear on the Millennium Prize criteria. The lead author, Peter Constantin, is a leading expert on the problem and the Clay Institute's page on it has a video of a lecture by him. If he had come out and said OpenAI hadn't solved the problem as stated I'm sure there would have been a lot of noise about it. The paper is dated 17th of September so presumably there has been plenty of time.
[1] https://www.claymath.org/wp-content/uploads/2022/06/navierst...
[2] https://en.wikipedia.org/wiki/Non-analytic_smooth_function
Yes, AI can explore thousands of ideas at once, no, that's not "brute forcing the search space" because the search space is way larger than you think it is.
And there are so many indicators that it's not currently economically viable and will only be if retail price is massively increased and strong regulatory barriers to competitors are erected. ;)