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"Mathematicians stand on each other's shoulders."
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"The greatest problem for mathematicians now is probably the Riemann Hypothesis."
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"Mathematicians are born, not made."
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"Need we add that mathematicians themselves are not infallible?"
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"Mathematicians do not study objects, but relations between objects."
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"The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure."
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"Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians."
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"Mathematics is written for mathematicians."
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"Mathematicians stand on each other's shoulders."
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"Abel has left mathematicians enough to keep them busy for 500 years."
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"As I say, there was this movement to try to bring philosophers and mathematicians together into an organization where they would talk to each other. An organization wasn't effective unless you had a journal. That's about all I know."
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"I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect."
Conviction

"I have had my results for a long time: but I do not yet know how I am to arrive at them."
Result

"It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment."
Knowledge

"I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible."
Doubt

"God does arithmetic."
God

"Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated."
Science

"The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic."
Arithmetic

"When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again."
Darkness

"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."
Humility

"Mathematicians stand on each other's shoulders."
Mathematicians
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