A proof tells us where to concentrate our doubts.
Any civilization which is worth its name, tries to find the truth.
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.
God exists since mathematics is consistent, and the devil exists since we cannot prove the consistency.
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.
Logic is the art of going wrong with confidence.
Mathematicians create by acts of insight and intuition. Logic then sanctions the conquests of intuition.
Mathematics is a body of knowledge, but it contains no truths.
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.
Statistics: the mathematical theory of ignorance.
The most fertile source of insight is hindsight.
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.
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 sense tried by the present-day kaleidoscope of events.
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.
There is no rigorous definition of rigor.
Universities hire professors the way some men choose wives- they want the ones the others will admire.
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