I must study politics and war that my sons may have liberty to study mathematics and philosophy.
Pure mathematics is, in its way, the poetry of logical ideas.
Mathematics is as much an aspect of culture as it is a collection of algorithms.
The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.
For the things of this world cannot be made known without a knowledge of mathematics.
Every moment dies a man, Every moment one is born.
The pursuit of mathematics is a divine madness of the human spirit.
The hardest arithmetic to master is that which enables us to count our blessings.
We could use up two Eternities in learning all that is to be learned about our own world and the thousands of nations that have arisen and flourished and vanished from it. Mathematics alone would occupy me eight million years.
A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
An unsophisticated forecaster uses statistics as a drunken man uses lamp-posts - for support rather than for illumination.
I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply the notes of our observations.
Mathematics is the science which draws necessary conclusions.
Mathematics is the only good metaphysics.
Angling may be said to be so like the mathematics that it can never be fully learned.
We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"
Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics.
Mathematics is a game played according to certain simple rules with meaningless marks on paper.
A mathematician is a blind man in a dark room looking for a black cat which isn't there.
We never know what we are talking about.
Beauty is the first test: there is no permanent place in the world for ugly mathematics.
Mathematics is not a deductive science - that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.
Mathematics consists in proving the most obvious thing in the least obvious way.
Many who have never had an opportunity of knowing any more about mathematics confound it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination.
The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience
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