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I must differ here as I do not see evidence (in domains I'm able to judge) of AI employing techniques and theory in its tasks. Ask it to mimic Stephen King and then compare the output to actual Stephen King. You'll understand what I mean.
I cannot speak to math here as I lack competency in that. But from what I hear from coders, its similar in that domain as well: AI can expurgate volumes of legible code, but it cannot utilize structure.
Humans have techniques and theories which inform their decisions high and low as they layer things together using judgement, intuition, etc., while AIs appear to generate text using probabilistic hacks. AI appears to be able to recreate low-complexity patterns from its dataset. I disagree that these processes are related except at a very basic level.
We have a good idea of how to train AI to solve mathematical problems, of virtually unbounded complexity. In the course of this, AI clearly learns "techniques" as shown here, if not "theories". I don't think King's prowess is theory-driven either, but in any case we don't have a good idea of how to train AI to be a good prose writer. We have some ideas, but are unlikely to act on them. There's not much money to be made in it, and plenty of highly motivated enmity – AI is already widely hated. and yes, autoregressive generation for the prompt "write like King" is not like King actually writing a novel. We have such tricks though.
My point is, it's not a general principle that AI will only rehash human techniques in some uninspired "probabilistic" way. If there is a hill to climb, such that "good" and "bad" outputs with regard to the problem statement can be distinguished, AI can bumble its way up the hill and also find new tricks. We've seen this before LLMs, with AlphaGo and move 37, we're starting to see it with LLMs.
Human mind runs entirely on probabilistic mush. Neural networks were invented as approximation of our own approximate learning. But probabilistic decision processes can have clear enough decision boundaries that they become able to operate with "abstractions", "symbols" or "theories". They also remain able to fail. For example, you are failing to update on evidence, because you haven't been trained to take input like "Terry Tao is surprised" seriously and think it's infinitely less interesting than your preconceived notions, basically some dweeb noise. Unlike an LLM, you can update at lifetime, so maybe you'll reread the above post and see how it contradicts your position.
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