>where an AI system was trained as a 1870s mathematician and see if it can come up with set theory
a car or a future starship wouldn't climb a tree better than ancient human.
a car or a future starship wouldn't climb a tree better than ancient human.
and you don't see any issue here? When it takes people 2 years to understand a proof it means that the old ways are done, they hit cul-de-sac. Like in many situations, it is the highest point as well as it is a crisis at the same time.
>why shouldn't an AI system be able to replace a 1870s mathematician
my point isn't that whether it would be able to replace - i think it would. My point is that it doesn't matter. The tool is needed for the 2020s math with those proofs taking 2 years, not for the 1870s math with proofs fitting a several pages letter.
That is math of 1870s https://en.wikipedia.org/wiki/Cefn-coed-y-cymmer#/media/File... and that is what we need in 2020 https://en.wikipedia.org/wiki/Huajiang_Canyon_Bridge#/media/...
Edit in response to the comment below as i hit my post limit :
New mathematical fields require many years of work by many people. What seems to be coming is people would be able to explore various ideas in say days instead of those years. It means more fields will be discovered and built up. And by wider array of people, ie. by the less capable than the top dog people. Mathematics will be more like engineering. Including more practical applications - like exploring transformers trajectories mapped into manifolds in p-adic spaces and applying the dynamic systems chaos theory there - borderline gibberish that no human would spend meaningful time on, yet a one would be able to throw a couple bucks at Claude++ for it to play with it. That would mean more money into the math, not less.