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.

A proof tells us where to concentrate our doubts.

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

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

On all levels primary, and secondary and undergraduate - mathematics is taught as an isolated subject with few, if any, ties to the real world. To students, mathematics appears to deal almost entirely with things whlch are of no concern at all to man.

There is no rigorous definition of rigor.

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.