A mathematical proof can be the size of a novella. For example, Andrew Wiles’s published his famous proof of Fermat’s Last Theorem in two journal articles covering 129 pages. But proofs in introductory textbooks like Rosen often contain just a few sentences. It might seem obvious that these proofs are short because they’re easy. But that’s not exactly right. Last week, I wrote a moderately long post covering an “easy” proof about how the div operator behaves when the first argument is negative. Why was it so much longer than the version in the solution guide?