A math professor noticed his kitchen sink at home was leaking. He called a plumber. The plumber came the next day, tightened a couple of nuts, and the sink worked perfectly again. The professor was delighted. But when, a minute later, the plumber handed him the bill, he was shocked. “This is a third of my monthly salary!” “Yeah, I get it…” said the plumber. “Why don’t you come work for our company as a plumber? You’ll make three times more than you do as a professor. Just remember: when you apply, say you only finished seventh grade. They don’t like hiring educated people.” So the professor got a job as a plumber, and his life really did improve. All he had to do was tighten a nut here and there every so often, and his salary was much higher. One day, the management of the plumbing company decided that every plumber had to attend evening classes to finish eighth grade. So our professor had to go too. By chance, the very first class was math. The evening school teacher, wanting to check what the students knew, asked for the formula for the area of a circle. They called the professor up to the board, and he suddenly realized he’d forgotten it. He started frantically reasoning it out, covering the board with integrals, differentials, and all sorts of fancy formulas to re-derive the result. In the end, he got: S = –π r² He didn’t like the minus sign, so he started again. Again he got a minus. No matter what he did, it kept coming out negative. He cast a panicked look at the class, and all the plumbers were whispering: “Swap the limits of integration!”