Hacker News Reader

Comment by ChickeNES | Hacker News Reader

So what they are saying is that humans, in this case Charles Fefferman (a math prodigy, going by his history), failed to specify the problem correctly?

View on HN

No, that‘s not the issue. If you look at https://www.claymath.org/wp-content/uploads/2022/06/navierst..., second page, you will see an option C is one of the four that is asked to be solved. And that option is the one that allows for an external force, which is what OpenAI solved. There is no question that OpenAI solved what the Clay institute is looking for. But that specific option C isn’t what the larger math community cares about, it’s a pretty niche case

I think GP's point is that if the larger math community doesn't care about option C, Fefferman shouldn't have given that option in the first place.

Fefferman and the larger math community are not the same actor; a divergence between their concerns is not surprising.

I'm pretty sure Fefferman's formulation of the problem got a lot of vetting before the Clay Institute accepted it. As such, it probably does reflect the math community's understanding of the problem. The "problem" such as it is, is that it might be the least interesting case especially given the solution that was obtained.

But Clay chose Fefferman to represent "the larger math community"? I'm calling out Clay/Fefferman here, not the community. Though the community also had over 25 years to contest the problem statement, and had no problem with it until now.

> But Clay chose Fefferman to represent "the larger math community"?

Surprisingly enough, being chosen by another actor as proxy for some group doesn’t actually resolve the problem that an individual may not always be an accurate proxy for the concerns of the group (and especially for the same descriptive aggregate group a generation after the proxy acts on their behalf.)

A solution to any of the four options made by an LLM armed with a theorem solver and millions of dollars of compute would still not be that interesting to the math community since it is not likely that any new insights oe questions can be derived from the result

yes!

It is interesting that there's a gap between the "prove N–S existence" conditions, which assume no forcing term, and the "counterexample" conditions, which allow a nonzero forcing term. In theory both (A) and (C) could be true.

> There is no question that OpenAI solved what the Clay institute is looking for. But that specific option C isn’t what the larger math community cares about, it’s a pretty niche case

I think you are agreeing with me? My point is that "the larger math community" failed to set the bounds of the problem correctly.

Fefferman was right to include option C as someone could have come up with less contrived counterexample accompanied by some interesting theorems that actually shed light on the general case

Doesn't the way OAI's proof is formulated essentially rule that out, in that as long as an alternative solution concerns option C, it'd have to live in this same solution space they carved out?

Yes. And more humans—in this case OpenAI researchers—similarly failed in choosing how to direct the AI tools.

And yet another set of humans—Open AI marketers—made an error in how they sold the result of the preceding errors.

But its not news that computers are mere tools and that any error blamed on a computer involves at least two human errors, one of which is blaming the computer instead of the human(s) responsible.

Its perhaps a bit less obvious that every thing for which credit is given to a computer involves at least one human error—that of crediting the computer—and certainly can be more amusing when it involves a bunch of human errors.

Reply on news.ycombinator.com