The next day, we booked travel on a steamer across the Analytic Ocean. All too soon, we found ourselves trudging through the desolate wasteland of Differential Topology following our newly hired guide, Hansel, a mathematician from Stockholm who spoke neither English nor Swedish. But he was quite good with hand signals.

Several weeks did it take us to cross the desert. Much did I learn on that journey. I learned that the tangent space at a point to an m-dimensional smooth manifold is a vector space. I learned that a nonsingular derivative at a point x of a smooth map f from Rⁿ to Rⁿ implies that f sends a neighborhood of x diffeomorphically onto a neighborhood of f(x). I learned not to share a pillow with Professor Lederhosen, as he drools in his sleep. Finally, after many tortuous days of slow progress, we found ourselves at the foot of Sard's Theorem.