There is no rigorous definition of rigor.

Actually, most mathematics courses do not teach reasoning of any kind. Students are so baffled by the material that they are obliged to memorize in order to pass examinations.

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.

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.

The stone that Dr. Johnson once kicked to demonstrate the reality of matter has become dissipated in a diffuse distribution of mathematical probabilities. The ladder that Descartes, Galileo, Newton, and Leibniz erected in order to scale the heavens rests upon a continually shifting, unstable foundation.

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.