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At some point we will lose track of all the ai discoveries that are worth remembering.

Academia with the publication system had a way of retrieving old discoveries and build upon them.

If my LLM session found something groundbreaking in between the billion tokens it produced, how would you ever know?

I think this is why Terence Tao created https://palomar-registry.org (I have no affiliation with them besides also having sent in a result there)

LLMs are excellent at doing searches of the math literature; presumably they'd also be good at doing searches of AI-generated results.