We think of the number "five" as applying to appropriate groups of any entities whatsoever - to five fishes, five children, five apples, five days... We are merely thinking of those relationships between those two groups which are entirely independent of the individual essences of any of the members of either group. This is a very remarkable feat of abstraction; and it must have taken ages for the human race to rise to it

Art flourishes where there is a sense of adventure, a sense of nothing having been done before, of complete freedom to experiment.

If you have had your attention directed to the novelties in thought in your own lifetime, you will have observed that almost all really new ideas have a certain aspect of foolishness when they are first produced, and almost any idea which jogs you out of your current abstractions may be better than nothing.

Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.

Intelligence is quickness to apprehend as distinct form ability, which is capacity to act wisely on the thing apprehended.

But you can catch yourself entertaining habitually certain ideas and setting others aside; and that, I think, is where our personal destinies are largely decided.

The consequences of a plethora of half-digested theoretical knowledge are deplorable.