Throughout history, mathematicians have expressed preference for solutions to problems that avoid introducing concepts that are in one sense or another “foreign” or “alien” to the problem under investigation. This preference for “purity” (which German writers commonly referred to as “methoden Reinheit”) has taken various forms. It has also been persistent. This notwithstanding, it has not been analyzed at even a basic philosophical level. In this paper we give a basic analysis of one conception of purity—what we call topical purity—and (...) discuss its epistemological significance. (shrink)

Many mathematicians have sought ‘pure’ proofs of theorems. There are different takes on what a ‘pure’ proof is, though, and it’s important to be clear on their differences, because they can easily be conflated. In this paper I want to distinguish between two of them.