Pure mathematics is, in its way, the poetry of logical ideas.
As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.
The pursuit of mathematics is a divine madness of the human spirit.
Every moment dies a man, Every moment one is born.
Mathematics is as much an aspect of culture as it is a collection of algorithms.
We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"
Mathematics is the science which draws necessary conclusions.
Mathematics is the only good metaphysics.
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.
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.
The hardest arithmetic to master is that which enables us to count our blessings.
For the things of this world cannot be made known without a knowledge of mathematics.
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.
The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.
Angling may be said to be so like the mathematics that it can never be fully learned.
An unsophisticated forecaster uses statistics as a drunken man uses lamp-posts - for support rather than for illumination.
Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics.
We never know what we are talking about.
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.
A mathematician is a blind man in a dark room looking for a black cat which isn't there.
Beauty is the first test: there is no permanent place in the world for ugly mathematics.
Mathematics is a game played according to certain simple rules with meaningless marks on paper.
Mathematics consists in proving the most obvious thing in the least obvious way.
Mathematics - the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human affairs.
But mathematics is the sister, as well as the servant, of the arts and is touched with the same madness and genius.
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