>Terence Tao is arguing that the human involvement in research is crucial, but doesn't convincingly justify why, in my opinion. He says that "human agency is a value of fundamental importance" and that we will need to build "thriving human communities that can understand [AI ideas] together" - not for the sake of correctness, which AI may surpass us on, but for, I guess, the possibility of reclaiming human meaning and purpose. I don't disagree with this at all, but it's not an argument, it's a statement of values. Unfortunately, the stark reality is that if AI does surpass humans, it will become the economically dominant strategy to not verify them and not double check them, but to just do whatever they say.

I think you have a fundamental misunderstanding here, and it's not really explained because I think it seems self-evident from within the field. In short: writing code is a means to an end; doing mathematics research is not, but is the end in itself.

The human involvement is crucial because the entire purpose of mathematics research is to increase human understanding of mathematics. It is pursued because it is interesting, not because it is economically useful. In this sense it's a lot closer to the humanities.

A black box oracle that just tells you whether statements are true or false is not the goal of mathematics and would not be particularly interesting to the field (except insofar as it could be harnessed to improve human understanding).

Coding is totally different from this, where it is essentially always done as a means to an end. Likewise with many other fields, like pharmaceutical research or materials science or what have you, that are oriented around solving problems for some practical purpose. Pure math isn't really like that for the most part.