Permissions and Prohibitions: a mathematics q& a with teacher william walton
Dr. William Walton grew up the child of educators in Chattanooga, Tennessee; his father taught him AP Calculus BC at the McCallie School. His teaching career began at Carnegie Mellon University, where he was one of only five undergraduates selected to work alongside graduate students as teaching assistants in the Mathematical Sciences department. Since then in his career, Dr. Walton has taught every single mathematics course, from Sixth Grade math through AP Calculus BC and Multivariable Calculus. At San Domenico, he teaches Middle School math, and he is a devoted environmental protection advocate.
Q. Imagine yourself talking to a first-grade student and the child’s grandparents. How would you explain the importance of math in relation to computers? Nobel laureate Herb Simon once described mathematics as “a system of permissions and prohibitions.” Modern computers function very much in the same way: event trapping to manage graphical user interfaces built on functions in order to display and calculate
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what, precisely, a user needs. Thus, for our imagined first grade friends, I’d say something like, “Mathematics is a way of saying what you’re allowed to do and what you’re not allowed to do. Computers work in this way, too, in that they only do what they’re told to do when they’re told to do it. They actually just play one long game of Simon Says and, because mathematics is built on doing what you can do when you’re told to do it, it’s what we need in order to make computers work.”
Q. what is your favorite equation and why? For a mathematician, this is hard to answer because scientists are often more caught up with the fun of specific equations, which they like because they’re drawn to equations that model real-world phenomena. That said, the Pythagorean formula — x2+y2=z2, the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse — is certainly pretty famous and has drawn ingenious proofs over the years, including one by President James Garfield. Personally, I find Euler’s equation (a.k.a. Euler’s identity) eiπ+1=0 to be particularly beautiful, because it sums up three of
mathematics’ most famous constants: e, π, and i alongside trigonometric forms of complex numbers. Anecdotally, I once was pleasantly surprised to see this equation on display in the men’s section of Bloomingdale’s department store in the Century City Mall.
Q. why is math critical to our world in an unknown and quickly-changing future? Mathematics teaches us how to think, make claims, and argue those claims. Mathematicians are always asking, “What would happen if I changed this rule? What would result?” Or, “How can I say this more simply?” In fact, one of the most famous 20th-century mathematicians, G.H. Hardy, once opined, “Sometimes one has to say difficult things, but one ought to say them as simply as one knows how.” Mathematics has also been called both the queen and the servant of the sciences. It’s the servant because so many sciences turn to math in order to help
