If the knowledge was obtained by genuine reasoning, that implies that it could also derive/develop a novel solution to an unsolved problem that is not achieved

If the knowledge was obtained by genuine reasoning, that implies that it could also derive/develop a novel solution to an unsolved problem that is not achieved by random guesses. For example, the conception of a complex number in the first place, to solve a class of problems that, prior, weren't even thought to be problems. There's no evidence that any LLM can do that.