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Notes -
I just want to add a little bit from Zvi's latest:
The abilities are impressive, and I actually wouldn't be surprised if it's able to perform admirably on Tier 4 "closed-answer" problems, especially as they get better and better at using rigorous back-end engines. But notice what they're expecting. They're expecting to have teams of top tier mathematicians spend a significant amount of time crafting "closed-answer problems". That really is probably where the bottleneck is, and Zvi's offhand comment is also in that vein. One possible end state is that these algorithms become an extremely useful 'calculator-on-steroids' that, like calculators, programming languages, and other automated theorem proving tools before, supercharges mathematical productivity under the guidance and direction of intuitive humans trying to push forward human understanding of human-relevant/human-interesting subject domains. Another possible end state is that the algorithms will get 'smart' enough to have all that human context, human intuition, and understanding of human-relevance/human-interestingness and be able to actually drop-and-replace human math folks. I suppose a third possible end state would be that a society of super advanced AIs go off and create their own math that humans can tell somehow is objectively good, but that they have to work and struggle to try to understand bits and pieces of (see also the computer chess championship). I really don't have any first principles to guide my reasoning of which of these end states we'll end up in. It really feels to me like a 'wait, watch, and see' situation.
I would put the last option as the most likely over a time frame greater than a decade or two, but the initial two options can be intermediate stages, albeit I don't expect any of them to last more than a few years. My reasoning is largely that much like chess, when the reward signal is highly legible, it becomes far easier to optimize for it, and diminishing returns!= nil returns, and probably PEV returns.
But you're right, only way to find out is to strap in for the ride. We live in interesting times.
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