Maybe I'm unsure what we're arguing here. Did the guys kid drum that up himself or did he learn it from yt? Knowledge can be inferred or extracted. If it comes up with a correct answer and shows it's work, who cares how the knowledge was obtained?
Yeah, my son only knows about imaginary numbers as far as the veritasium "epic math dual" video.
As far as I can tell he inferred that |i+1| needs the Pythagorean theorem and that i and 1 are legs of the right triangle. I don't think anyone ever suggested that "absolute value" is "length". I asked him what |2i+2| would be an his answer of "square root of 8" suggests that he doesn't have it memorized as an answer because if it was he'd have said "2 square root two" or something similar.
I also asked if he'd seen a video about this and he said no. I think he just figured it out himself. Which is mildly spooky.
Ah, makes sense. I think that is indeed impressive to fill in the paths of reasoning between unknown to known based on even small nuggets of information combined possibly with "learned intuition" which your son seems to have obtained an ability for to understand how to use both. Very cool
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.
