Before one can generalize, formalize, and axiomatize, there must be a mathematical substance.

The introduction of numbers as coordinates by reference to the particular division scheme of the open one-dimensional continuum is an act of violence whose only practical vindication is the special calculatory manageability of the ordinary number continuum with its four basic operations.

Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.

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

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.

A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details.

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