The embarrassing failures or misconceptions of math experts with regards to research level mathematics? Definitely a serious problem.

Though by your "Perelman and Wiles didn't need "AI" assistance" comment, you'd surely be there on the sidelines to ridicule them for each and every single one. I guess maybe that's where your concerns are coming from?

I can practically see how these concerns of yours would suddenly evaporate if they started using self-hosted models instead... ... yeah, right, who are we kidding?