To be honest, mathematicians don’t do much. They drink coffee, frown at chalkboards. Drink tea, frown at students’ exams. Drink beer, frown at proofs they wrote last year and can’t for the life of them understand anymore.
It’s a life of drinking, frowning, and, most of all, thinking.
Rather, the verbs of the mathematician all boil down to actions of thought. When we calculate, we turn one abstraction into another. When we give proofs, we build logical bridges between related ideas. When we write algorithms or computer programs, we enlist an electronic brain to think the thoughts that our meat brains are too slow or too busy to think for themselves.
Every year that I spend in the company of mathematics, I learn new styles of thought, new ways to use that nifty all-purpose tool inside the skull: How to master a game by fussing with its rules. How to save thoughts for later, by recording them in loopy Greek symbols. How to learn from my errors as if they were trusted professors. And how to stay resilient when the dragon of confusion comes nibbling at my toes.
In all these ways, mathematics is an action of the mind.
