Mathematicians create by acts of insights and intuition. Logic then sanctions the conquests of intuition.

Statistics: the mathematical theory of ignorance.

In brief, the whole world is the totality of mathematically expressible motions of objects in space and time, and the entire universe is a great, harmonious, and mathematically designed machine.

A elegantly executed proof is a poem in all but the form in which it is written.

Mathematics is a body of knowledge, but it contains no truths.

There is no rigorous definition of rigor.

Though determinants and matrices received a great deal of attention in the nineteenth century and thousands of papers were written on these subjects, they do not constitute great innovations in mathematics.... Neither determinants nor matrices have influenced deeply the course of mathematics despite their utility as compact expressions and despite the suggestiveness of matrices as concrete groups for the discernment of general theorems of group theory.