Morris Kline Quotes & Sayings

The most fertile source of insight is hindsight. — Morris Kline

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. — Morris Kline

Just what did the Greeks seek in probing nature? They sought no material gain and no power over nature; they sought merely to satisfy their minds. Because they enjoyed reasoning and because nature presented the most imposing challenge to their understanding, the Greeks undertook the purely intellectual study of nature. Thus the Greeks are the founders of science in the true sense. — Morris Kline

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

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. — Morris Kline

A proof tells us where to concentrate our doubts. — Morris Kline

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. — Morris Kline

There is no rigorous definition of rigor. — Morris Kline

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 ... — Morris Kline

A good expository paper will benefit far more people than most research papers. A good text is worth a thousand of the usual trifles that appear in research journals. — Morris Kline

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. — Morris Kline

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

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

[The error in the teaching of mathematics is that] mathematics is expected either to be immediately attractive to students on its own merits or to be accepted by students solely on the basis of the teacher's assurance that it will be helpful in later life. [And yet,] mathematlcs is the key to understanding and mastering our physical, social and biological worlds. — Morris Kline

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. — Morris Kline

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. — Morris Kline

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

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

Statistics: the mathematical theory of ignorance. — Morris Kline

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

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, — Morris Kline

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. — Morris Kline

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

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. — Morris Kline