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.

There is no rigorous definition of rigor.

Statistics: the mathematical theory of ignorance.

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

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

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.

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

The tantalizing and compelling pursuit of mathematical problems offers mental absorption, peace of mind amid endless challenges, repose in activity, battle without conflict, refuge from the goading urgency of contingent happenings, and the sort of beauty changeless mountains present to senses tried by the present day kaleidoscope of events.

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

A proof tells us where to concentrate our doubts.

The writing in mathematics text is not only laconic to a fault it is cold, monotonous, dry, dull, and even ungrammatical... The books are not only printed by machines they are written by machines.