I have been wondering recently about a good test for checking whether LLMs can only parrot stochastically or do they manage to indeed learn some higher order co

I have been wondering recently about a good test for checking whether LLMs can only parrot stochastically or do they manage to indeed learn some higher order concepts inside their weights. What if we would take a bare LLM, train it only on the information (in Maths, physics, etc) that was available to, say, Newton and then try to prompt it to solve the problems that Newton solved? Will it be able to derive the calculus basics and stuff having never seen it before, maybe even with little bit of help from the prompts? Maybe it will be able to come up with something completely different, yet also useful? Or nothing at all...