Without novel proofs. If AI can churn out proofs, then anybody's work can get "scooped." I've seen this happen to students in other fields, where it has reached the point that students refrain from giving conference talks in order to avoid revealing their research topic.

My thesis project, 30+ years ago, was protected by a unique assemblage of expensive equipment, some of it purpose-built. The people who wanted my result were perfectly happy to wait for me to finish it. I even shared my shop drawings, circuit diagrams, and source code with them as I progressed.

I think at the very least students need to know what to expect. Maybe it will settle down and we'll be OK.