Slaughtering Competition Problems with Quantifier Elimination

Chris Grossack just dropped a math mic: use Sage + QEPCAD (a tool that removes the tricky “for all/there exists” parts of a statement) to smash those contrived competition inequalities. The post shows how a computer can check hard-looking claims—like the MSE inequality—then instantly confirm the equality cases with a couple of lines. Cue chaos. The comment crowd split fast. Purists called it academic cheat codes, saying contests are about crafting clever proofs, not pressing a “nuke” button. Pragmatists fired back: computers are part of modern math—why gatekeep tools that teach and verify? One meme had Tarski (the theorems behind this trick) as a giant kaiju stomping Olympiad problems, with “sage -i qepcad” as the red launch switch. Others joked it’s “Math Olympiad speedrun%” and “press X to eliminate quantifiers.” There was even install drama: half the thread flexed their smooth setup; the other half claimed QEPCAD is an ancient beast that only installs if the planets align. Fans loved the clarity—quantifier elimination turns foggy algebra into simple checks. Critics warned it can kill intuition. Either way, the mood was loud, geeky, and hilarious, and the computer absolutely did the homework.