alt Hacker News> But even if it had solved every problem in the Langlands program, to imagine that would have “solved number theory” would be as naive as saying that the construction of the periodic table solved chemistry.
Of course if you solve any existing problem, new ones appear. That's not the point. The point is that AI will be able to advance on any problem better than any human.
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Did any ai made any new interesting question or conjecture?
> The point is that AI will be able to advance on any problem better than any human.
Define "better".
I don’t think we know whether or not that’s true yet. Imagine a problem which requires a paradigm shift or new novel techniques to solve. There is no proof (yet) that an AI could create one.
ANY problem?
But the question is whether the AI will itself be able to decide on which problem to advance, and do it in an ethical and aligned way with humanity. And that if it does, its significance will be understood by humans.
Otherwise we're just creating a black box, easily manipulated by their owners, who would be ruling over human lives. That's not what people want
The thing about much human progress on various problems is that human mathematicians formulate a human comprehensible machinery for the purposes of solving a given problem and then that machinery naturally suggests (to humans) further questions which then give rise to more machinery - And, in a sense, the value is ultimately the machinery, which has tended in the past to be relevant to physics, computer science, logistics, sociology and philosophy.
When AI writes proof no human can understand, it doesn't advance mathematics this way. Maybe AIs can understand their own proofs - meaning not just verify them but extract a machinery/broader-perspective (but I wouldn't count on it). But even machinery an AI isn't necessarily useful for humanity/society.
But how do you know which problems are worth making progress on? Traditionally, you'd find those by working on solving previous problems.
> The point is that AI will be able to advance on any problem better than any human.
If that was true it would of course be significant.
If you had no morals, 2 trillion dollars to spend, ability to commit intellectual property theft without consequences, and most of the smartest people in the world actively working to advance your cause... ...you really think you couldn't compete with the clankers?
But in a human way? I don't think so. The 700+ solutions that were put out by openAI are in no way accepted as solved until humans say so. It's kind of like saying SC2 was solved when Alpha beat the best players. The professional community just went on playing much the same. Math should do the same. Just with better tools