Have any LLMs solved any of the big (or even lesser known) unanswered problems in math, physics, computer science?
It may appear that they are solving novel problems but given the size of their training set they have probably seen them. There are very few questions a person can come up with that haven't already been asked and answered somewhere.
Google's AlphaEvolve recently produced a novel matrix multiplication function slightly faster than the previous state of the art that couldn't have been in any training data. While not a hard unsolved problem, I think it's good evidence that an LLM is capable of synthesizing new solutions to problems.