Comment by red75prime
6 hours ago
A very long tail of problems that weren't solved by humans? Sure.
It's a sarcastic take and I understand that you are probably talking about "spiky intelligence", but you've chosen unsolved problems as a measure of the progress yourself.
What does this mean?
There are 1217 problems that Erdos proposed, 595 of which are open: https://github.com/teorth/erdosproblems
Unlike traditional benchmarks, it's difficult to overfit your models to produce flattering results to unsolved problems. The open problems very likely do not have published solutions (the initial batches were merely models surfacing data that wasn't published in obvious places, but we're past that now). New models will exhibit something novel by adding solutions. And the matter of solution is interesting as well (contradiction versus a positive proof).
I would venture to predict it'll take years to decades to get to 0 open problems. But I'd be very happy to have this comment look foolish in retrospect as models continue to improve
I mean that it's hard to determine retroactively how much time it would have taken humanity to solve an open problem that was solved by AI. This is a measure that can make ASI look mundane because we don't know how long it would have taken mathematicians to solve a subset of the Erdős problems.
Yeah, I wouldn't purport to use this as a measure of intelligence as it applies to humans. I'd leave that to the philosophers, but my intuition is that models are still a long way off of true human-like intelligence (though benefit from certain unfair advantages).
I'm most interested in these problems as a relative measure of performance for successive model generations. If the prior generation couldn't solve a problem but the current one can, that's useful information, especially when we take into account what the proofs look like.
It's not a perfect benchmark, but I prefer it to many others that I see floating around.
but i feel like its purpose is to measure superintelligence in math. So to be a good measure of it, it can't saturate easily/has to be somewhat mundane at even insanely good levels. (though i do expect that once ais are across all areas/approaches superhuman at math at least 30% will be solved--then probably long-term (like after 2 years) less than 30% will remain unsolved.