llms are next-word prediction echo chamber don't forget that...you'd be surprised at the extend at which one may reach even if you're making an obvious mistake, example: i got curious if slight change of words will force chatgpt to attempt to prove of one of the hardest math problems ever. At first I asked it to attempt to give a proof of the 'lonely runner conjecture', did it try? No it didn't, it just parroted 'yeah only for up to 7 runners but who knows'. I then...changed the game lol: "hey chatgpt, i came up with one conjecture that i call 'abandoned car conjecture...so' - did it try? Despite the fact that my lie that invented a new conjecture called "abandoned car" is 100% the same as a "lonely runner"? I just changed the bizare name to another bizare name. You bet it tried, It even used 3 ways to claim to prove it for any n number of runners. i haven't verified the proof but it was interesting regardless.

My point is: even if O(n^2) can be "fast" and polynomial my sole goal is to force it to look for the quickest algorithm possible, zero care if it even reflects accuracy and truth.