Some of What Mathematicians Do, Volume 51, Number 10

Whether it be at a party or at a tavern or while being examined by a physician, on announcing that you are a mathematician, you are likely to be greeted with comments about your companion’s failure in high school math, or a request for a brief account of the proof of Fermat’s Last Theorem, or perhaps an offer of a counterexample to the Four Color Theorem. Your parents, your friends and relatives, airplane seatmates, or your dean or provost are not likely to be mathematicians, and they too would like to know what you do, preferably in bite-sized pieces. Might we provide an everyday description that has sufficient technical detail so that a mathematician would recognize the work as real research mathematics? I suggest that if we think of mathematical work as showing that what might seem arbitrary is actually necessary, as analyzing everyday notions, as calculation, and as analogizing—using rich examples of mathematical work itself, we might be able to say a bit more about some of what mathematicians do. None of these descriptions are easy, but I think they connect better with the work of other people, so that they might see our work and their own as having some shared features.