Nobody is in panic, but we are using these systems and seeing what are their capabilities and it's clear that their use has a big impact on the practice of mathematical research, probably far more impact than it has in other areas. Part of mathematics involves classifying structures - think of describing combinatorial objects - and this is a sort of game with which a well directed AI tool can be very effective. Part of mathematics involves being able to bring to bear on a problem a diversity of techniques, and AI is also very helpful in this regard.
The point is that people who spend their time classifying nilpotent Lie groups that admit structure X are out of work if they don't change their perspective. Maybe such problems were never really that interesting, although it was useful to have a group of people acting as human computers to work them out - but well used AI yields for such problems more complete and more reliable results - and so allows researchers to spend their time on other more interesting things. The problem for your run of the mill professional mathematician is that more interesting things are harder ...
The point is that people who spend their time classifying nilpotent Lie groups that admit structure X are out of work if they don't change their perspective. Maybe such problems were never really that interesting, although it was useful to have a group of people acting as human computers to work them out - but well used AI yields for such problems more complete and more reliable results - and so allows researchers to spend their time on other more interesting things. The problem for your run of the mill professional mathematician is that more interesting things are harder ...