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I think the blog says exactly the opposite, the AI is very bad at explaining its solution and core idea.
I think the interesting part is that explaining ideas is something that don't seem to have an obvious reward for RL to train on, unless mathematicians keeps handing them training data.
(OMG of course this guy is a rationalist ๐ซ
Both can be true at once - it is coming up with original ideas but explaining them poorly. I'm not a mathematician but I find that in my field (software development) the AI is much better at writing code than it is at writing documentation - it will write documentation if you ask it to, but the documentation will be unfocused and difficult to read, with explanations of things that don't matter and garden path sentences. I got this sentence from it recently:
That is actually not gibberish - it's technically correct, but it certainly isn't clear.
Maybe I miss understand what "extrapolate" means in your context. To me that means "extract the core idea and explain/apply them", as AI do not learn by producing output (unlike human), applying core idea requires it to be explained in clear language.
I was arguing that AI, at present, cannot effectively extract core idea which is what I would characterize as "extrapolate".
No, by "extrapolate" I mean to learn a pattern in the training data and then apply that pattern (in a useful way) to a problem outside the domain of the training data. An AI that cannot extrapolate would only be able to do the specific things that it had been taught to do, whereas an AI that can extrapolate is capable of solving new problems.
As for the language, I suspect that it is clear to the AI itself. During their training, programming AIs communicate with other programming AIs more than they do with humans, so they develop their own dialect of sorts which is good for exchanging information among themselves. This is just conjecture on my part, but my evidence is that if the AI really was internally confused about those math problems, it wouldn't have been able to solve them.
I think the ability to generalize is the very definition of "machine learning", without it, models would just be really slow databases. We observed these phenomena quite frequently, like the original Groking paper, where models remembers modular arithmetic and generalize it to produce an algroithm in its weight to solve all modular arithmetic.
It is kind of hard to say whether the model are "aware" of its weight and "understand" the algorithm it developed. We certainly don't have a good understanding of how our brain works.
"clearity" and "confusion" are really hard to assess for anything other than ourselves. It is certainly valid to say that if AI can solve math problem it must understand it. In other way, Dijkstra famously argued that the question of whether machine can "think" and "understand" is completely pointless.
But the end goal of code, math and many other subjects IMO is to "communicate", so that these knowledge can be maintained and transfered. Of course, unless we want to complete forefit our understanding to machine, which I feel can be a bit dangerous especially for foundational fields like mathematics, but we will see.