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> Winning at Go is, theoretically, such an easy problem that I wouldn't extrapolate anything from it; the algorithm doesn't need to be really good at Go against

> Winning at Go is, theoretically, such an easy problem that I wouldn't extrapolate anything from it; the algorithm doesn't need to be really good at Go against arbitrary opponents; it just needs to beat other humans, which is a classical task for machine learning. Playing "against" math is not nearly so easy. I agree. Proving "arbitrary" mathematical conjectures is surely bound to fail but all I'm saying is it might be better than humans. This would free up a lot of mental resources for the humans to do more interesting things.

pron 10y ago
> all I'm saying is it might be better than humans. Well, there's certainly no theoretical limitation of doing it as well as humans (and maybe better, as a computer is better at remembering and recalling things), and there's a lot of interesting work on automated theorem proving. But the biggest breakthrough is still based on a SAT-solving algorithm from the '60s, and we still don't understand why it works well in practice. Like in "AI", there are algorithms that work surprisingly well for some tasks, but as we don't have a theory to understand them, we don't know how to make the next breakthrough (which is essential for getting significantly ahead), so it's very hard to put a time frame on these things. Much of the perceived progress in both automated proofs and "AI" is due to new hardware allowing us to run very old algorithms on usefully-sized data, so what we're really experiencing is just finally observing the utility of very old discoveries. It's a little like finally being able to build sensors that allow us to observe physical phenomena that were theoretically assumed for a long time. But unfortunately, significant conceptual progress has hardly been made in decades (in both fields), and progress of the kind I described does not predict an imminent next step.

pron 10y ago

> all I'm saying is it might be better than humans. Well, there's certainly no theoretical limitation of doing it as well as humans (and maybe better, as a computer is better at remembering and recalling things), and there's a lot of interesting work on automated theorem proving. But the biggest breakthrough is still based on a SAT-solving algorithm from the '60s, and we still don't understand why it works well in practice. Like in "AI", there are algorithms that work surprisingly well for some tasks, but as we don't have a theory to understand them, we don't know how to make the next breakthrough (which is essential for getting significantly ahead), so it's very hard to put a time frame on these things. Much of the perceived progress in both automated proofs and "AI" is due to new hardware allowing us to run very old algorithms on usefully-sized data, so what we're really experiencing is just finally observing the utility of very old discoveries. It's a little like finally being able to build sensors that allow us to observe physical phenomena that were theoretically assumed for a long time. But unfortunately, significant conceptual progress has hardly been made in decades (in both fields), and progress of the kind I described does not predict an imminent next step.