What you are seeing in math right now is a consequence of the jagged frontier, and a precursor of what is to come in other professions. Yes, mathematicians do math, but they also have other tasks they view as important (mentor students, maintain a scientific community, safeguard the future of a field, foster a love of math) that AI can't do.

At least one worry that mathematicians seem to have is that by focusing on the flashiest, most obvious element of what mathematicians do (make proofs), the AI companies are damaging the other tasks that AI can't do. AI can discover superhuman proofs, but that is not all that the math profession is about, and actually can undermine and reduce the attention to the other aspects of the job that are important to mathematicians. It becomes harder to defend the value of the many other tasks mathematicians do to the outside world if the most visible part is taken away.

I suspect we will see more of this across fields and professions that will increasingly be forced to help people understand that their jobs consist not only the most visible tasks that AI can do, but also tasks that the AI cannot do or does badly.