I wonder if you could query some of the ideas of Frege, Peano, Russell and see if it could through questioning get to some of the ideas of Goedel, Church and Turing - and get it to "vibe code" or more like "vibe math" some program in lambda calculus or something.

Playing with the science and technical ideas of the time would be amazing, like where you know some later physicist found some exception to a theory or something, and questioning the models assumptions - seeing how a model of that time may defend itself, etc.

There's an entire subreddit called LLMPhysics dedicated to "vibe physics". It's full of people thinking they are close to the next breakthrough encouraged by sycophantic LLMs while trying to prove various crackpot theories.

I'd be careful venturing out into unknown territory together with an LLM. You can easily lure yourself into convincing nonsense with no one to pull you out.

This is my curiosity too. Would be a great test of how intelligent LLM's actually are. Can they follow a completely logical train of thought inventing something totally outside their learned scope?