I see the recent progress in mathematics and cybersecurity as signs that models are getting more capable more quickly than usual. The companies plans to develop them by recursive self improvement now seems like a real possibility and I don't think they should be allowed to attempt this.
Machines are already far beyond human capability in plenty of ways. Including cognitive tasks like chess. We've already created the technology we need to destroy ourselves (nuclear weapons), and yet so far (knock on wood), we're still around.
We've even already had programs that can prove (brute force) theorems. As far as I can tell this isn't much different, except the space of theorems that computers can solve has expanded. How far? We can't really say yet.
Does solving more theorems than before suddenly mean computers are capable of anything? No.
A "mathematician" is a human who decided to spend their lives studying mathematics. Mathematicians also tend to be smart, but intelligence is innate, not acquired, so studying mathematics doesn't make you smarter. This makes it obvious why they don't rule the world - if you want to rule the world you'd want to focus on that (for example, doing business or finance), and becoming a mathematician is just a waste of time.
LLMs don't work like that. Like in humans, all of their capabilities correlate, and unlike a human, their overall capabilities grow over time. Looking at LLM mathematical ability over time* therefore gives you info about the progress of their general capabilities, and ability to take over the world would be determined by the latter.
* In fact it'd be better to look at a mix of different capabilities, but that's growing too at about the same rate, see https://epoch.ai/eci
This is incorrect. Unless there is some new developments I'm unaware of (entirely possible) LLMs "learn" during the training phase, but after that they are static. They do not improve further or retain information when used for inference.
You might be confused because AI companies keep releasing new models and tinkering with the harnesses, sometimes under the same name such that "Zern 6" (or whatever) doesn't always mean the same thing.