Perhaps the greatest paradox of all is that there are paradoxes in mathematics... because mathematics builds on the old but does not discard it, because its theorems are deduced from postulates by the methods of logic, in spite of its having undergone revolutionary changes we do not suspect it of being a discipline capable of engendering paradoxes.

Mathematics and the Imagination, Paradox Lost and Paradox Regained (p. 193), Simon & Schuster. 1940