Bertrand Russell (1872–1970), logician, anti-war campaigner and the only mathematician so far to have been awarded the Nobel Prize for Literature, was rather fond of expressing himself paradoxically. Here’s one of his more famous statements.
Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.
(Mathematics and the Metaphysicians, in Mysticism and Logic, 1918).
As so often with Russell, the pithy phrase slightly obscures the point he’s making, which is to defend a logicist view of mathematics. In this view, the mathematician’s business is solely to consider logical inferences (if A then B) witħout being bothered about the “metaphysical” question of whether A or B is “true”. How satisfying Russell himself found this can probably be judged by the number of topics outside mathematics to which he turned his attention…