Morris Kline Quotes

The most fertile source of insight is hindsight.

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

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 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.

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.

predecessor of Isaac Newton at Cambridge University, maintained that irrational numbers have no meaning independent of geometric lengths.

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.

Universities hire professors the way some men choose wives - they want the ones the others will admire.

Perhaps the best reason for regarding mathematics as an art is not so much that it affords an outlet for creative activity as that it provides spiritual values. It puts man in touch with the highest aspirations and lofiest goals. It offers intellectual delight and the exultation of resolving the mysteries of the universe.

There is no rigorous definition of rigor.

All mathematical proofs must be deductive. Each proof is a chain of deductive arguments, each of which has its premises and conclusion.

The feeling that one must be an authority in a subject to say anything about it is unfounded. We are all laymen outside the field of our own specialty,