I think mathematics is (1) valuable as a way to develop human thinking; (2) useful for us to understand in (more or less practical) ways that will remain valid for the foreseeable feature; (3) enjoyable. This to me indicates we should find ways to keep funding mathematics for its own sake, i.e. just let mathematicians do whatever they think is best for their intellectual development, so that we keep enjoying those benefits. I think the question might then become: not how to keep people interested in becoming mathematicians as cited in this article, but how do we select good professionals to enact those benefits in the presence of very capable AI (e.g. just seeing how many theorems one has proven might be a pretty bad metric) -- I guess I'm referring to what we know as academic or research mathematics.

I think offline exams already work pretty well for this, although I think they do tend to favour a bit much a specific kind of student, so other types of exams could be mixed in, like the proposed digestions of Tao et al, maybe giving a lecture and have a student/professional panel give it a pass/fail, and so on (just throwing a few ideas!).

At least, as far as I can tell this is the urgent matter, along with convincing students that being a mathematician is still a valid choice, and funding agencies that mathematicians should still be funded. That last point is where I think the general public should speak in support of keeping funding, I am not sure at what level. I know there are many other issues in society, like people with food insecurity or just hunger in many parts of the world, preventable disease, etc., but I think it's worthwhile to keep professional mathematics (not sure at what level?) because of how much our complex society benefits if not relies on it still.