Quotes of All Topics . Occasions . Authors
The present letter is a very long one, simply because I had no leisure to make it shorter.
It is not shameful for a man to succumb to pain and it is shameful to succumb to pleasure.
This paper gives wrong solutions to trivial problems. The basic error,however, is not new.
No one should ever be bored. … One can be horrified, or disgusted, but one can’t be bored.
A GREAT discovery solves a great problem but there is a grain of discovery in any problem.
I try to make puzzles range all the way from easy to hard, and to leave many open at once.
What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?
Heaven is angered by my arrogance; my proof [of the four-color theorem] is also defective.
Nations in their great ages have not been great in art or science, but in art and science.
The shortest path between two truths in the real domain passes through the complex domain.
I listen only to Bach, Beethoven or Mozart. Life is too short to waste on other composers.
With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.
The linear-programming was - and is - perhaps the single most important real-life problem.
Chess is a sport. The main object in the game of chess remains the achievement of victory.
The weight of evidence for an extraordinary claim must be proportioned to its strangeness.
If you have no authority to legislate my freedoms, then I'm truly free, at least from you.
The real satisfaction from mathematics is in learning from others and sharing with others.
From the very beginning of his education, the child should experience the joy of discovery.
Education which is not modern share the fate of all organic things which are kept too long.
A great society is a society in which its men of business think greatly of their functions.
I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof.
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.
If we examine our thoughts, we shall find them always occupied with the past or the future.
Few friendships would survive if each one knew what his friend says of him behind his back.
God has given us evidence sufficiently clear to convince those with an open heart and mind.
We must keep our thought secret, and judge everything by it, while talking like the people.
Thinking too little about things or thinking too much both make us obstinate and fanatical.
We must make good people wish that the Christian faith were true, and then show that it is.
Happiness is neither without us nor within us. It is in God, both without us and within us.
Between us and heaven or hell there is only life, which is the frailest thing in the world.
There have been only three epoch-making mathematicians, Archimedes, Newton, and Eisenstein.
Telegraphs are machines for conveying information over extensive lines with great rapidity.
It is success that colours all in life, Success makes fools admir'd, makes villains honest.
It is better to solve one problem five different ways, than to solve five problems one way.
In order to solve this differential equation you look at it until a solution occurs to you.
What is the difference between method and device? A method is a device which you use twice.
Music is a hidden arithmetic exercise of the soul, which does not know that it is counting.
The first test of potential in mathematics is whether you can get anything out of geometry.
Rationality of thought imposes a limit on a person's concept of his relation to the cosmos.
There probably is a God. Many things are easier to explain if there is than if there isn't.
A mathematician who is not also something of a poet will never be a complete mathematician.
There are two kind of mathematicians, smart ones, and dumb ones. I am one of the dumb ones.
The goal is to teach in such a way as to produce the most learning from the least teaching.
Unless in communicating with it one says exactly what one means, trouble is bound to result.
No science can be more secure than the unconscious metaphysics which tacitly it presupposes.
Apart from blunt truth, our lives sink decadently amid the perfume of hints and suggestions.
The least movement is of importance to all nature. The entire ocean is affected by a pebble.
Reason is the slow and torturous method by which those who do not know the truth discover it
Now, if the passions had no hold on us, a week and a hundred years would amount to the same.
The sweetness of glory is so great that, join it to what we will, even to death, we love it.