I took Betty out to the backyard to chill and eat some breakfast. She was fine as long as the Pop-Tarts lasted, but she became very annoyed after we finished eating them because I then just sat in a chair and thought about calculus. Betty’s point is why think about calculus when a cool fall breeze is blowing, leaves are falling, and the now is calling? Really, says Betty, why are you wasting life on the abstract that definitely cannot be sniffed?
Betty might be right, but letting go of the abstract realm of mathematics is beyond my abilities. Calculus is so wonderfully addictive. I like to think about its history and how long it took to provide it with a rigorous foundation. Yes, calculus is the ultimate tool for understanding the physical universe, but I’ve always disliked including physical applications when I teach it. Leave the physical applications to the physicists and engineers who know more about them than I do. I want to teach calculus as a beautiful subject outside of the physical.
I don’t teach calculus much anymore—I teach cryptography instead. This pleases me. Cryptography is something all of us use many times each day, and yet it is pure mathematics. All modern cryptography can be understood in the mind—no apparatus is necessary. I can safely stay in the abstract when I teach cryptography without worrying that students won’t be able to use it.
