On the Definition of Function


For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose. ... Formerly, when a new function was invented, it was in view of some practical end. Today they are invented on purpose to show that our ancestor’s reasoning was at fault, and we shall never get anything more than that out of them. If logic were the teacher’s only guide, he would have to begin with the most general, that is to say, the most weird functions.

— Poincaré, 1899



Russell O’Connor: contact me