  Democritus is also said to have contributed to mathematics, and to have posed a problem about the nature of the cone.  He argues that if a cone is sliced anywhere parallel to its base, the two faces thus produced must either be the same in size or different.  If they are the same, however, the cone would seem to be a cylinder; but if they are different, the cone would turn out to have step-like rather than continuous sides.  Although it is not clear from Plutarch's report how (or if) Democritus solved the problem, it does seem that he was conscious of questions about the relationship between atomism as a physical theory and the nature of mathematical objects.