Russell's appreciations of mathematics. It brings out that plato and russell used almost identical words in their recognition of the fact that mathematics, being a hypothetical and deductive science, is founded upon postulates which cannot be proved and therefore upon conventions; also that it provides a source of beauty and intellectual delight which reassuringly - though in apparent contrast to this view - conveys underlying truths. The article further displays russell's view of plato's love for mathematics and the progressive development, (...) perhaps formal rather than substantial, which russell's conception of that science has undergone. (shrink)