This morning Ben Orlin gave the MAA Lecture for Students and Teachers, “Tic-Tac-Toe (or, What is Mathematics?)” as part of a day-long series of public lectures at the JMM. Orlin writes the blog Math With Bad Drawings, which was recently developed into a book of the same name. A charming high school math teacher with a knack for capturing poignant observations about math with google-eyed stick figures, his talk did not disappoint.
Orlin set the audience up to play two simple games. In the first, Quinceañera, two players took turns picking from the numbers 1 through 9 to see who could be the first to get a group of three summing to 15. In the second, Barn Rot, players take turns picking from the words “barn rot bit sob sir at no in as” with the goal of having a trio of words that share a letter in common. A few trials revealed that these games are both isomorphic to tic-tac-toe, which gave a great entry point for Orlin to talk about math as “the discovery and exploitation of isomorphism.”
Towards the end of the talk we were left with a few minutes to play a game of Ultimate Tic-Tac-Toe (also could be called Fractal Tic-Tac-Toe). This is a fun exercise largely because the rules were ambiguous. And at certain points in the game the pairs of players had to establish new rules once the preset rules became undoable.
Overall, the talk gave a great taste of what being a mathematician feels like, something between being a rule follower and a rule breaker/maker, and he defined it very succinctly: Mathematics is the logic game of inventing logic games.