https://x.com/MIRIBerkeley/status/2058034041203679712

https://x.com/YafahEdelman/status/2057223450205516179

Is there a question (like this market) where we have a $100k threshold for a millenium prize problem? None of the existing questions on manifold seem to be taking into account the cost for future hypothetic solutions to these problems. These AI solutions could potentially cost on the order of tens of millions of dollars or more right?

or maybe it's unlikely a frontier lab would be willing to spend that much

@0xseraphim Is there any reason to think this person has any idea what they're talking about? Tweets like this are a dime a dozen.

@pietrokc

https://epoch.ai/about/team/yafah-edelman

It's a fair question and I'm not one for credentialism so I won't argue the point about legitimacy. I shared it because I agree with her hot take on this topic.

@0xseraphim That's fine, everyone is entitled to their opinion. I'm just saying 99% of people with AI jobs don't know anything about mathematics.

I don't know Yafah and this could be wrong about her, but most people claiming millenium problems will be solved cannot even correctly state the problems. Thus, these people's opinions are presumably invariant with respect to the specific problems, ie if I changed the MPs to other problems, they would also claim the new hypothetical problems will be solved by 2032.

However, it is known that there are undecidable mathematical statements, as well as statements whose proofs require more steps than there are atoms in the universe. So there are some possible problems which AI is guaranteed not to solve by 2032.

@pietrokc then could you give a person whose opinion you would consider highly relevant?

(this discussion does illustrate what's nice about prediction markets: at the end of the day it doesn't matter what your credentials are / how much better you think your understanding is; your prediction is either right or wrong 😂)

@0xseraphim Well, each MP is from a different area of math so it's unlikely any one person will be able to comment relevantly on all of them. You want someone who is an expert in the area and also has used the latest models extensively. The latter can be hard to judge if they don't post online a lot. But the former is pretty easy: if someone doesn't have at least a PhD in math or has done equivalent work, you can probably dismiss their views as containing no information.

For Navier-Stokes (in the area of PDEs) and Riemann (analytic number theory) we are fortunate that Terence Tao satisfies both criteria and comments online often. There is a group at DeepMind actively trying to solve Navier-Stokes with AI in collaboration with experts so they would be worth listening to on that problem.

For Hodge (algebraic geometry) and Birch & Swinnerton-Dyer (algebraic number theory) the online person I know is Daniel Litt. I'm not familiar with these areas at all so I'm not a great source even for recommendations on who to listen to.

For Yang-Mills (mathematical physics) I don't have the first clue who to recommend. I don't know any experts OR online people who talk about it, because I'm very ignorant of this area.

For P vs NP I know a lot of experts but not many online people. Maybe Scott Aaronson?

Since there's lots of discussion here--I'm in no rush to resolve since I don't consider this to be a number theory paper (despite the use of some standard number-theoretic tools). That said if we see 2-3 similar papers in number theory (which I imagine will happen soonish) I'll resolve YES.

Think this resolves YES?

@0xseraphim I think not yet... But it is really really close

@Grothenfla ah, we're missing the repeat experiment?

@0xseraphim I think so, but I think this will be clear in the near future

legit amusing all the people who thought this wouldn't happen 😂

https://manifold.markets/TamayBesiroglu/will-ai-be-capable-of-producing-ann#79pqs0ao0xs

https://manifold.markets/TamayBesiroglu/will-ai-be-capable-of-producing-ann#blvkn42j6o

I have the feeling that many other related questions on manifold are going to follow this pattern over the next few years

https://openai.com/index/model-disproves-discrete-geometry-conjecture/

Tim Gowers:

There is no doubt that the solution to the unit-distance problem is a milestone in AI mathematics: if a human had written the paper and submitted it to the Annals of Mathematics and I had been asked for a quick opinion, I would have recommended acceptance without any hesitation. No previous AI-generated proof has come close to that.

@Bayesian "the construction and its analysis apply fairly sophisticated tools from algebraic number theory in an elegant and clever way." - Noga Alon. Not sure, but plausible that this result should resolve the bet altogether?

@AdamK i doubt it will count as repeatable, and also

The AI would receive no detailed guidance relevant to the mathematics research, and is required to accomplish this task autonomously.

maybe openai ppl picking the problem for the AI to focus on counts as detailed guidance? and the prompt is pretty detailed. not sure. but yeah this is gonna be very clear YES by eoy i think

@Bayesian Agreed on repeatability. But seems like even the prompt was AI-written? From the paper:

> This problem was solved in a completely automated fashion. Our internal model was given an AI-written statement of the problem, and its output was sent to an AI grading pipeline, which indicated high confidence that the solution was correct. It was only after this point that internal human researchers and mathematicians began to examine the solution carefully.

Bubeck seemed to say that the solution arose from a new sweep of the model over the Erdős problems, which implies they did not particularly suspect the model could solve this one.

@AdamK oh yeah true