I think there are three main issues (though I might be overlooking something):

1. AI taking over peoples work is as much an issue for mathematicians here, as it is for programers, artists, writers, etc. elsewhere.
2. We still need to check if these 700 papers are correct (AI makes mistakes at least as often as humans, usually more often). This involves a huge amount of effort. And if it turns out that they contain a bunch of mistakes, OpenAI is unlikely to care. To them, these papers have already served their purpose (generating headlines).
3. Solving a problem in mathematics means being able to (formally) convince other people that your opinion is correct (massively simplified, but imo that is what mathematics boils down to), by getting them to understand why your opinion is correct. Having a pile of linear algebra spit out 700 texts about certain math problems removes the whole “human understanding” part of that.

However, it’s not entirely unprecedented for a computer to provide a proof that we don’t completely understand. I forgot the details (and I’ll edit them in if I can find it), but there was at least one problem that was solved using a computer and brute force trying millions of cases. That produces a proof much longer than any human could read in a lifetime, and iirc there where quite a few mathematicians unhappy about it at the time too.

Running Docker inside a VM is the recommended way to run Docker on Proxmox.

Personally, I just run Docker inside LXC containers. Aparently, this is supposed to be not entirely stable, but its never given me any problems. (I commit an entirely different sin against efficiency, by keeping each service in its own LXC container, each with its own Docker host.)

I also run Immich (in Docker inside a container), and haven’t noticed any performance issues. But I’m the only user, and I don’t use it heavily, so ymmv.