It seems like an easy test: Train an LLM but restrict the data set to publications from <= year 1600, tell it that it's an expert geometrist, and ask for a formula yielding the area under a curve.

You could do the same for any number of more recent inventions, and see if the LLM is able to "innovate" the solution solely from what had been published prior to the actual human invention.

Has anyone done anything like this? It seems like an easy way to measure AI "innovative-ness". That or to dispel the idea that it exists, if it doesn't.