If an entirely new problem, within a new field of mathematics were to appear tomorrow, I highly doubt a human mathematician would be useful at all on their own.

How have we got to the place we are today then? Someone must have made the first steps onto uncharted territory, otherwise we would be in a homogeneous state frozen in time.

I am not saying that LLM intelligence can not be the same, that they are uncapable of dicovering new fields/problems that they have no training on. I am just pointing out that historically it kind of "must" be true that humans are capalbe of this, but we have yet to see an LLM do something like this, something radically "new" in a sense. All of these breakthroughs appear to me (not a mathematician) to be more a case of "digging" through millions of existing attempts/work, patching it together into a result.

This would already make LLM's one of the greatest tool mankind has ever made, but it has yet to display what I would consider a necessity for human level intelligence, which is this ability to discover entirely "new" things.

Would an LLM, given enough time and only the currently available trainingdata with no further input from humans, be able to solve something that was discovered tomorrow?

For humans my answer would be: maybe, probably, because this has been done historically.

For LLM's I would not be comfortable in claiming that they could. I think they would not be any better at this than traditional computational bruteforce.