They aren't, but the problem is that open problems tend to emerge when people are working on other problems. If fewer people are spending time deeply thinking about current problems since a handful of labs are solving them with AI without an eye towards understanding and only on verification, the pool of open problems won't be continuously growing. There is a fear that there will be a chilling effect on the community if people are disincentivized from trying to solve deep problems or study them for understanding as opposed to simply focusing on verification. It's more of a social and community problem than a fundamental problem with mathematics itself becoming "completed".

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hkalbasi an hour ago | parent | next [-]

So we can let the ai generate some math problems based on the solutions found? Other fields (computer science, physics, ...) can generate math problems too.

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mlyle an hour ago | parent [-]

There's an infinite number of possible math problems, but the things that make these open problems worthwhile is they're interesting to people who have worked in related areas.

They're good to give to new mathematicians, and they're good to help humans understand the shape of the problem space and relative difficulty with the tools we have.

Cheesing these problems with LLMs gets rid of both the training benefit and our ability to create good related problems. There's an aesthetic part of this, too, that LLMs do not capture.

	▲	jordanb 40 minutes ago \| parent \| next [-]
		This kinda reminds me of the guys who decided to industrialize digging up dinosaur fossils, in order to feed the dinosaur fossil collector market. They were amazed that paleontologists were so "inefficient" at finding and digging up dinosaur fossils. But from paleontologists' perspective, they go out looking for dinosaur fossils when they have questions that digging up a fossil may answer. The metric they're focusing on isn't tons of fossil mined out of the ground, it's a developing understanding of extinct life.
	▲	chorizo 29 minutes ago \| parent \| prev [-]
		These open problem solutions often reveal tighter bounds on prior conjectures. Even if the solutions produced are far from elegant and only machine verifiable, we do learn new information. But I agree that just like writing prose and code, brainstorming frontier math proofs is a perishable skill

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ryoshu 41 minutes ago | parent | prev [-]

tl;dr - it's content creation rather than process and understanding

	▲	porcoda 25 minutes ago \| parent [-]
		My more cynical take is that it’s press release generation intended solely to message “behold, we have built the most capable machine humans have ever known: please line the dump trucks full of money up for us now.” Bulldozing an intellectual forest into oblivion is an acceptable cost for them if their only goal is huge piles of cash.