## How Math Can Defeat Bullies

I could mention my first introduction to Godel’s theorem about the essential incompleteness of mathematics; or my first encounter with the Banach-Tarski theorem in topology showing that a sphere the size of a pea can be decomposed into a finite number of pieces and put back together to get a sphere the size of a basketball; or Russell’s paradox about the set of all sets that do not belong to themselves; or any number of counterintuitive results in probability theory. All of these mathematical ideas excited me in high school and college, but I will concentrate instead on the thrill I felt in elementary school when I saw that the power of simple arithmetic was sufficient to vanquish a bully, my fifth grade teacher. It still evokes the same emotions in me that it did decades ago.

I was about ten years old and enthralled with baseball. I loved playing the game and aspired to be a major league shortstop. (My father played in college and professionally in the minor leagues.) I also became obsessed with baseball statistics and noted that a relief pitcher for the then Milwaukee Braves had an earned run average (ERA) of 135. (The arithmetic details are less important than the psychology of the story, but as I dimly recall, the pitcher had allowed the opposing team to score 5 runs and had got only one batter out. Getting one batter out is equivalent to pitching 1/3 of an inning, 1/27 of a complete 9-inning game––and allowing 5 runs in 1/27 of an inning translates into an ERA of 5/(1/27) or 135.)