
By AnonymMorris 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.
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By AnonymMorris Kline
A elegantly executed proof is a poem in all but the form in which it is written.
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By AnonymMorris Kline
A proof tells us where to concentrate our doubts.
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By AnonymMorris 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.
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By AnonymMorris 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.
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By AnonymMorris Kline
Mathematicians create by acts of insights and intuition. Logic then sanctions the conquests of intuition.
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By AnonymMorris Kline
Mathematics is a body of knowledge, but it contains no truths.
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By AnonymMorris 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.
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By AnonymMorris 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.
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By AnonymMorris Kline
Psychologically, the teaching of abstractions first is wrong. Indeed, a thorough understanding of the concrete must precede the abstract.
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By AnonymMorris Kline
Statistics: the mathematical theory of ignorance.
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By AnonymMorris 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.
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By AnonymMorris Kline
The most fertile source of insight is hindsight.
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By AnonymMorris Kline
There is no rigorous definition of rigor.
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By AnonymMorris 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.
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By AnonymMorris 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.
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By AnonymMorris 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.
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By AnonymMorris 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.
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By AnonymMorris 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.
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