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

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.

Statistics: the mathematical theory of ignorance.

Every paper published in a respectable journal should have a preface by the author stating why he is publishing the article, and what value he sees in it. I have no hope that this practice will ever be adopted.

There is no rigorous definition of rigor.

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

Psychologically, the teaching of abstractions first is wrong. Indeed, a thorough understanding of the concrete must precede the abstract.