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I guess you can see this as an exploration problem, in pure maths, while the goal is to solve a conjecture, the limitation of humans on pure computational power led to the exploration of alternative paths. Sometimes, these paths weren't leading to solving the initial conjecture but opened new idea and new direction. Sometimes a less direct but more humanly natural path was taken to solve the conjecture which also led to new and humanly understandable questions. In some ways solving the question wasn't the most important part of the work, as this doesn't have direct impact on our life (as I saw people comparing this with drug discovery), but the path leading to the solution raised new conjectures and techniques that further developed the field.

I have a really hard time reading AI proof so this might be a biased statement, but most of them feels like having a superpowerfull machine, that would have bruteforce all the possible words of finite length in your logical syntax. You have the path to the solution, using tools that where already known and even direction that where abandoned because they seemed to fail for our human brain. But at the end, as a mathematician, you don't learn anything that is really new.

To me this is the main risk with AI and in general the one most mathematican try to explain but fail, we might miss a lot of alternative path that would have raised more interesting questions (I think this is already more or less what is happening). On top of that, we will run out of mathematicians as no one wants to pursue a career in the field anymore.

by XorNot12 hours ago|

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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.

by Tyyps12 hours ago|

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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.

by SiempreViernes14 hours ago|

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The most immediate answer is because the models are proprietary and only available to those who want to hype the big labs.

by QuadmasterXLII11 hours ago|

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We can speculate on whether it can’t, but its plain to see that so far it hasn’t.

by jfengel8 hours ago|

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Given how new it is, it seems premature to draw any conclusions from that.

If a human had solved these problems, we'd expect it to take years for people to digest them and formulate significant new advances.

by pfdietz8 hours ago|

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Given the demonstrated rate of improvement of AI in math this year, I don't understand the value of that latter observation.