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.