This is *exactly* why I say we need *more* human mathematicians now than ever, not fewer! I watched the video, start to finish. I'm not a combinatorialist, but I understood every word, and could have understood every word as an undergrad. (The idea of counting things and showing that the count is positive, and therefore concluding that the things actually exist, is very familiar to number theorists!!..) I'm embarrassed I never even heard of this problem, despite my great Rutgers colleagues Szemeredi and Komlos and others (the Hungarian mafia) having worked on it. It's a beautiful problem, and beautiful solution. "From the BOOK", as a certain Hungarian might say :) If AI keeps coming up with amazing arguments like these, we, again, need many more mathematicians to go through them, make sense of them, incorporate the ideas in new research and textbooks, etc etc. So much work to be done; all hands on deck!