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This relies on the idea that AIs will only ever do the thing they just did, and nothing more.

It's the same argument which is invariably wrong yet comes up over and over again.

There's no real reason to think AIs solving lots of problems will stop further work on alternative paths - certainly a machine which never tires and can be trained on its own solutions is going to continue to improve.

There's precedent for this: just look at any overconfident post regarding what China will clearly never be able to do, despite decades of steady if frequently flawed progress.

There's no persuasive argument being presented as to why machine mathematical research should have a limit beyond hardware capabilities.

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I think you are missing the points of my argument, my argument don't stand on AI isn't capable of discovering new techniques, as I don't believe in new techniques from the sky. My argument is about any targeted goal based AI (which to the best of my knowledge is the case for LLMs as used now). My point is, if there exists a computationally bounded path from existing work that led to solving a conjecture and if the goal of the AI is to solve this conjecture, then alternative path that would have led to new discovery will be dismissed on the way (or lost in the computational trace if you prefer), leading to the conjecture being solved but maybe closing forever/for a long time new paths. I don't see how you could have as a goal to explore alternative path without a good metric of what is a good alternative path (like rating a chess position), which to me, seems unlikely to exist. If you don't have such metric then you would have a clear exponential blowup. More like a percolation problem if you prefer, a neglected approach might have introduced a concept that would make further discoveries accessible. Missing that concept could therefore leave a whole region unexplored, not just one branch of one proof.
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