Morris Kline
Morris Kline
Morris Klinewas a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects...
NationalityAmerican
ProfessionWriter
Date of Birth1 May 1908
CountryUnited States of America
real men ties
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.
math challenges mind
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.
knowledge math intuition
Mathematicians create by acts of insights and intuition. Logic then sanctions the conquests of intuition.
hindsight source insight
The most fertile source of insight is hindsight.
science definitions rigor
There is no rigorous definition of rigor.
science reality order
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.
should-have practice paper
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.
expression innovation groups
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....
teaching thorough-understanding firsts
Psychologically, the teaching of abstractions first is wrong. Indeed, a thorough understanding of the concrete must precede the abstract.
doubt proof mathematical-proof
A proof tells us where to concentrate our doubts.
knowledge math body
Mathematics is a body of knowledge, but it contains no truths.
space machines world
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.
spiritual art men
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.
men wife want
Universities hire professors the way some men choose wives - they want the ones the others will admire.