The mathematicians know a great deal about very little and the physicists very little about a great deal. - William Rowan Hamilton

Euler calculated the force of the wheels necessary to raise the water in a reservoir … My mill was carried out geometrically and could not raise a drop of water fifty yards from the reservoir. Vanity of vanities! Vanity of geometry!

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience.

Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don't look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding.