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

Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.

You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length.

Theory attracts practice as the magnet attracts iron.

It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again; the never-satisfied man is so strange if he has completed a structure, then it is not in order to dwell in it peacefully,but in order to begin another. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others.

You have no idea, how much poetry there is in the calculation of a table of logarithms!

Life stands before me like an eternal spring with new and brilliant clothes.

There have been only three epoch-making mathematicians, Archimedes, Newton, and Eisenstein.

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

If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries.

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.

The Infinite is only a manner of speaking.

Mathematicians stand on each other's shoulders.

Does the pursuit of truth give you as much pleasure as before? Surely it is not the knowing but the learning, not the possessing but the acquiring, not the being-there but the getting there that afford the greatest satisfaction. If I have exhausted something, I leave it in order to go again into the dark. Thus is that insatiable man so strange: when he has completed a structure it is not in order to dwell in it comfortably, but to start another.

The enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it.

Mathematics is the queen of science, and arithmetic the queen of mathematics.

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.

There are problems to whose solution I would attach an infinitely greater importance than to those of mathematics, for example touching ethics, or our relation to God, or concerning our destiny and our future; but their solution lies wholly beyond us and completely outside the province of science.

Sin^{2} φ is odious to me, even though Laplace made use of it; should it be feared that sin^{2} φ might become ambiguous, which would perhaps never occur, or at most very rarely when speaking of sin(φ^{2}), well then, let us write (sin φ)^{2}, but not sin^{2} φ, which by analogy should signify sin (sin φ)

Ask her to wait a moment - I am almost done.

I have a true aversion to teaching. The perennial business of a professor of mathematics is only to teach the ABC of his science; most of the few pupils who go a step further, and usually to keep the metaphor, remain in the process of gathering information, become only Halbwisser [one who has superficial knowledge of the subject], for the rarer talents do not want to have themselves educated by lecture courses, but train themselves. And with this thankless work the professor loses his precious time.

Finally, two days ago, I succeeded - not on account of my hard efforts, but by the grace of the Lord. Like a sudden flash of lightning, the riddle was solved. I am unable to say what was the conducting thread that connected what I previously knew with what made my success possible.

When a philosopher says something that is true then it is trivial. When he says something that is not trivial then it is false.

I believe you are more believing in the Bible than I. I am not, and, you are much happier than I.

The total number of Dirichlet's publications is not large: jewels are not weighed on a grocery scale.

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