Give it a verification loop and enough compute, and AI will soon cook algorithmic R&D like it cooked mathematics. There is just no question whatsoever of this happening, it is guaranteed.
Several of the items on that list are claimed to have been resolved by the recent OpenAI theorem-dump. Another is the Navier-Stokes question that's one of the Millennium Prize problems, also claimed to have been resolved by OpenAI's models.
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.
There is already a pre-print making the claim that the Navier-Stokes solution provided by OpenAI does not meet the criteria required by the prize (https://arxiv.org/html/2609.20803v1)
I'm not a mathematician, but looking at the Clay Institute's official problem statement [1] and that paper, I don't think it's claiming OpenAI's construction doesn't meet the Millennium Prize criteria.
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.
It is pretty straightforward for anyone who knows lean to verify that the OpenAI release satisfies the official criteria to the letter. You could reasonably argue that it shouldn't satisfy the official criteria because the official criteria are unreasonably generous in allowing any smooth external forcing function, but that would be a different claim.
Theoretical fields like mathematics inherently suffer from a form of Goodhart's Law. The progress in mathematics you hear of is almost never the kind of progress non-mathematicians would care about.
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.
Brute force would choke on a measly decillion of alternatives. It corresponds to an extremely short proof. A combinatorial explosion doesn't allow to use brute force for anything slightly longer than toy problems. Swarm of 10000 agents is a massive smart force.
Neither Euler, nor Gödel had proven the Navier-Stokes blowup, though. And it took generations of mathematicians to prove the Fermat's theorem (it's a kind of a very slow swarm, isn't it?)
Have you seen my drafts? For easy task I may write the straighforward solution, but for complicated stuff it's a mix of throwing stuff to the wall and see what sticks. It's informed search by experience, but AI also use weights to pick the attempts.
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. ;)
AI is not a calculator. OpenAI did not solve hundreds of open problems in math by "brute forcing the search space," there was a lot of intelligent and novel thought (gasp!) in the way AI chose the paths it did.
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.
