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I'm not a mathematician but it seems to me that if all it took to solve the problem was an enthusiast level understanding of the domain and a few hundred dollar

by rurp 5d ago

I'm not a mathematician but it seems to me that if all it took to solve the problem was an enthusiast level understanding of the domain and a few hundred dollars of tokens then the result probably isn't that valuable. Even assuming you are the first person in the world to solve it, these kinds of LLM-friendly problems that are now easy to solve and easy to verify will almost certainly be picked off by one person or another in the near future. It's also possible that the result is already known and you just weren't aware of it. It's easy for someone outside of a field, or even one steeped in it, to not be aware of certain solutions.

pickleRick243 5d ago
sounds a bit like cope. Crouzeix's conjecture was solved exactly under these circumstances and I wouldn't describe it as "not that valuable". In any case, AI capabilities will increase dramatically over the next few years while human math capability will not. That means that there's a fixed target regarding whatever is currently considered a "serious math problem" and its difficulty level. Soon the average problem solved with a few hundred dollars of compute will be at that bar.
- smj-edison 5d ago
  > while human math capability will not. I actually partially disagree with this. What happened to all the excitement about Intelligence Augmentation (IA)? Now it's AI instead of IA. I think there's so much untapped potential for augmenting our intellect with the likes of https://dynamicland.org https://dynamicland.org and https://folk.computer https://folk.computer, as well as the work that's been going on in college math education, things like Lean, etc. I think the only reason human math capabilities haven't expanded that much is a failure of our imagination, not our potential.
  - omnicognate 5d ago
    I couldn't agree more. The way everyone thunders towards "replace" instead of "improve" is depressing.

by rurp 5d ago

pickleRick243 5d ago

sounds a bit like cope. Crouzeix's conjecture was solved exactly under these circumstances and I wouldn't describe it as "not that valuable". In any case, AI capabilities will increase dramatically over the next few years while human math capability will not. That means that there's a fixed target regarding whatever is currently considered a "serious math problem" and its difficulty level. Soon the average problem solved with a few hundred dollars of compute will be at that bar.

smj-edison 5d ago
> while human math capability will not. I actually partially disagree with this. What happened to all the excitement about Intelligence Augmentation (IA)? Now it's AI instead of IA. I think there's so much untapped potential for augmenting our intellect with the likes of https://dynamicland.org https://dynamicland.org and https://folk.computer https://folk.computer, as well as the work that's been going on in college math education, things like Lean, etc. I think the only reason human math capabilities haven't expanded that much is a failure of our imagination, not our potential.
- omnicognate 5d ago
  I couldn't agree more. The way everyone thunders towards "replace" instead of "improve" is depressing.