The most beautiful thing we can experience is the mysterious. It is the source of all true art and science.
The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.
Well done is better than well said.
Life is good for only two things, discovering mathematics and teaching mathematics.
If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.
Education is what survives when what has been learned has been forgotten.
Mathematics is like draughts in being suitable for the young, not too difficult, amusing, and without peril to the state.
Just as houses are made of stones, so is science made of facts.
Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.
Mathematics are well and good but Nature keeps dragging us around by the nose.
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.
Beauty is the first test: there is no permanent place in the world for ugly mathematics.
Science without religion is lame, religion without science is blind.
Science is what we understand well enough to explain to a computer. Art is everything else we do.
When I am working on a problem, I never think about beauty but when I have finished, if the solution is not beautiful, I know it is wrong.
Young man, in mathematics you don't understand things. You just get used to them.
In mathematics alone each generations adds a new story to the old structure.
Standard mathematics has recently been rendered obsolete by the discovery that for years we have been writing the numeral five backward. This has led to reevaluation of counting as a method of getting from one to ten. Students are taught advanced concepts of Boolean algebra, and formerly unsolvable equations are dealt with by threats of reprisals.
Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.
The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.
The study of mathematics is apt to commence in disappointment.
I was x years old in the year x2.
A good mathematical joke is better, and better mathematics, than a dozen mediocre papers.
This therefore is Mathematics: She reminds you of the invisible forms of the soul; She gives life to her own discoveries; She awakens the mind and purifies the intellect; She brings light to our intrinsic ideas; She abolishes oblivion and ignorance which are ours by birth.
I'm sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that was all there was to it.
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