Super Mario is mathier than you think

Here’s a problem you probably didn’t solve in school: You’re an ambitious young plumber from Brooklyn in a world inhabited by violent human-size mushrooms called Goombas. The love of your life has been kidnapped, so you embark on a quest to rescue her, venturing through stretches of pipe-filled and monster-­ridden terrain where your only means of protection are your powers of jumping and stomping. It’s a journey so arduous that no computer—real or hypothetical—is powerful enough to figure out if