I am interested in mathematics only as a creative art.
I remember once going to see him [Ramanujan] when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways."
Yet what are all such gaieties to me whose thoughts are full of indices and surds?
Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? ... Where does the proof use the hypothesis?
In one word he told me the secret of success in mathematics: plagiarize; only be sure always to call it . . . research.
All these people that I used to know, they're an illusion to me now. Some are mathematicians, some are carpenters' wives.
Why waste words? Geometry existed before the Creation, is co-eternal with the mind of God, is God himself (what exists in God that is not God himself?): geometry provided God with a model for the Creation and was implanted into man, together with God's own likeness - and not merely conveyed to his mind through the eyes.
Thus God himself was too kind to remain idle and began to play the game of signatures signing his likeness unto the world: therefore I chance to think that all nature and the graceful sky are symbolized in the art of Geometria.
Now, as God the maker play'd he taught the game to Nature whom he created in his image; taught her the selfsame game which he played to her.
Premature optimization is the root of all evil.
Mathematical reasoning may be regarded.
I must study politics and war that my sons may have liberty to study mathematics and philosophy.
If I am given a formula, and I am ignorant of its meaning, it cannot teach me anything, but if I already know it what does the formula teach me?
I hope that posterity will judge me kindly, not only as to the things which I have explained, but also to those which I have intentionally omitted so as to leave to others the pleasure of discovery.
And believe me, if I were again beginning my studies, I should follow the advice of Plato and start with the mathematical sciences, which proceed very cautiously and admit nothing as established until it has been rigorously demonstrated.
We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.
It is now quite lawful for a Catholic woman to avoid pregnancy by a resort to mathematics, though she is still forbidden to resort to physics or chemistry.
Language is remarkable, except under the extreme constraints of mathematics and logic, it never can talk only about what it's supposed to talk about but is always spreading around.
If two wrongs don't make a right, try three.
If your experiment needs statistics, you ought to have done a better experiment.
My work always tried to unite the true with the beautiful; but when I had to choose one or the other, I usually chose the beautiful.
Everything of importance has been said before by somebody who did not discover it.
Our minds are finite, and yet even in these circumstances of finitude we are surrounded by possibilities that are infinite, and the purpose of life is to grasp as much as we can out of that infinitude.
How happy is the lot of the mathematician! He is judged solely by his peers, and the standard is so high that no colleague or rival can ever win a reputation he does not deserve. No cashier writes a letter to the press complaining about the incomprehensibility of Modern Mathematics and comparing it unfavorably with the good old days when mathematicians were content to paper irregularly shaped rooms and fill bathtubs without closing the waste pipe.
Fifty percent of all doctors graduate in the bottom half of their class - Hope your surgery went well!
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