If you were to bet on solving problems like "P versus NP" using these technologies combined with human augmentation (or vice versa), what would be the provable time horizon for achieving such a solution? I think we should assume that the solution is also expressible in the current language of math/logic.
The hard part is in the creation of new math to solve these problems not in the use of existing mathematics. So new objects (groups rings fields) etc have to be theorized, their properties understood, and then that new machinery used to crack the existing problems. I think we will get to a place (around 5 years) where AI will be able to solve these problems and create these new objects. I don’t think it’s one of technology I think it’s more financial. Meaning, there isn’t much money to be made doing this (try and justify it for yourself) and so the lack of focus here. I think this is a red herring and there is a gold mine in there some where but it will likely take someone with a lot of cash to fund it out of passion (Vlad Tenev / Harmonic, or Zuck and Meta AI, or the Google / AlphaProof guys) but in the big tech world, they are just a minnow project in a sea of competing initiatives. And so that leaves us at the mercy of open research, which if it is a compute bound problem, is one that may take 10-20 years to crack. I hope I see a solution to RH in my lifetime (and in language that I can understand)
I understand that a group of motivated individuals, even without significant financial resources, could attempt to tackle these challenges, much like the way free and open-source software (FOSS) is developed. The key ingredients would be motivation and intelligence, as well as a shared passion for advancing mathematics and solving foundational problems.
Ok but how do you get around needing a 10k or 100k h100 cluster
It is well known that cloud services like Google Cloud subsidizes some projects and we don't even know if in a few years improvements will arise.