Comment by ChickeNES
3 hours ago
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?
3 hours ago
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?
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.
2 replies →
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!
> 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.