Mathematics is more than establishing arbitrary facts (although some look like curiosities), it's also defining what interesting research directions are and establishing common language/notation. I think that will stay relevant?
Mathematics is more than establishing arbitrary facts (although some look like curiosities), it's also defining what interesting research directions are and establishing common language/notation. I think that will stay relevant?
In theory you can automate finding interesting research directions by identifying conjectures with many dependencies. And notation has never been mathematicians' forte, with them trying to cram the entirety of universe into single letters.
Why? How do you define interesting research directions? That used to be defined by testing the limits of human understanding i.e. some people can't figure something out. AI might have very different ideas about what is interesting and I am not sure what humans would get out of putting years into understanding AI proofs for what? What are we doing at that point? Like if you spend years understanding some AI proof of theorem 123456, why is that meaningful? I am actually asking why you think defining interesting research directions will stay relevant. In my opinion, people spend years acquiring knowledge so they can work on problems which is separate.
There's two points about this I am assuming 1) Mathematics actually has a significant subjectivity to it and is community oriented and not just climbing a never ending list of theorems that exists in the universe 2) A lot of mathematical research work is inside of a subfield and isn't directly motivated by applications. Sometimes it is but e.g. people don't work on obscure theorems about elliptic curves because of a dire need for that but more because the community found it interesting.
People become interested in things when they become invested in it personally, because they've contributed to it. So I don't think it will stay relevant...