Domestication of Mathematical Pathologies

Abstract

Abstract Certain mathematical objects bear the name “pathological” (or “paradoxical”). They either occur as unexpected and (temporarily) unwilling in mathematical research practice, or are constructed deliberately, for instance in order to delimit the scope of application of a theorem. I discuss examples of mathematical pathologies and the circumstances of their emergence. I focus my attention on the creative role of pathologies in the development of mathematics. Finally, I propose a few reflections concerning the degree of cognitive accessibility of mathematical objects. I believe that the problems discussed in the paper may attract the attention of philosophers interested in concept formation and the development of mathematical ideas.