ABSTRACT
Many students of Timothy Smiley have been interested in the philosophy of mathematics. We have seldom paused to ask what counts as mathematics. Certainly we have thought a good deal about the nature of mathematics-in my case, for example, about the logicist claim that mathematics is logic.1 But we took ‘mathematics’ for granted, and seldom refl ected on why we so readily recognize a conjecture, a fact, a proof idea, a piece of reasoning, or a subdiscipline, as mathematical. We asked sophisticated questions about which parts of mathematics are constructive, or about set theory. But we shied away from the naïve question of why so many diverse topics addressed by real-life mathematicians are immediately recognized as ‘mathematics’.
