Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.

You can not apply mathematics as long as words still becloud reality.

In geometric and physical applications, it always turns out that a quantity is characterized not only by its tensor order, but also by symmetry.

We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context.

Not only in geometry, but to a still more astonishing degree in physics, has it become more and more evident that as soon as we have succeeded in unraveling fully the natural laws which govern reality, we find them to be expressible by mathematical relations of surprising simplicity and architectonic perfection. It seems to me to be one of the chief objects of mathematical instruction to develop the faculty of perceiving this simplicity and harmony.

God exists because arithmetic is consistent - the Devil exists because we can't prove it!

Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.