The mathematics of the everyday is often surprisingly deep and difficult. John Conway famously uses the departmental lounge of the Princeton mathematics department as his office. He claims to spend his days playing games and doing nothing with whomever happens to be in the lounge, but his conversations about seemingly mundane questions has led to no end of delightful and deep mathematics. Chatting with math folks about the everyday can quickly lead to undiscovered country.
A much loved tradition among any group of mathematicians is talking math in the department lounge at afternoon tea. Nearly every department has such a tea. Some are once a week, some every day. There may or may not be cookies. What is certain, though, is that everyone from the retired emeriti to undergraduate students are welcome to stop by for a revitalizing beverage and a chat. More often than not it leads to talk about interesting math. You can begin to imagine why John Conway hangs out in the Princeton math lounge and Alfréd Rényi joked "A mathematician is a device for turning coffee into theorems" .
You might think the conversation swirls around the work of the latest winners of the Abel prize or folks trying to impress by describing the deep results of their morning's efforts. There is some of that. But just as often the conversation turns into an energetic discussion about the mathematics of the everyday. Several years ago I was involved in a heated discussion about whether or not the election laws of the State of Georgia could allow for a certain local election to become caught in an endless loop of runoff votes. The local media's description of the electoral rules seemed to allow this absurdity. Of course the argument could easily be resolved with a quick Google search, but where's the fun in that? A search was done, but not until all possible scenarios were thoroughly thrashed out and a nickel wagered.
My colleagues, Kimball Martin and Ravi Shankar, asked themselves an innocuous tea-time question: "How often should you clean your room?" Easy to ask, the question is surprisingly difficult to solve. In math problems come in three flavors: so easy as to be not very interesting, so hard as to be unsolvable, and the sweet spot in the middle where the questions are both interesting and solvable. When to clean your room turns out to be a question of the third kind.