... and it is probably that there is some secret here which remains to be discovered.

Mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics.

Mathematics is purely hypothetical: it produces nothing but conditional propositions.

...mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic, especially in its early stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be.

Generality is, indeed, an indispensable ingredient of reality; for mere individual existence or actuality without any regularity whatever is a nullity. Chaos is pure nothing.

This branch of mathematics [Probability] is the only one, I believe, in which good writers frequently get results which are entirely erroneous.

True science is distinctively the study of useless things. For the useful things will get studied without the aid of scientific men. To employ these rare minds on such work is like running a steam engine by burning diamonds.