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.

Theory attracts practice as the magnet attracts iron.

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.

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

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.

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

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

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

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

Mathematicians stand on each other's shoulders.

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

The Infinite is only a manner of speaking.

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.

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.

Mathematics is concerned only with the enumeration and comparison of relations.

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.

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.

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

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)

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.

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

I protest against the use of infinite magnitude ..., which is never permissible in mathematics.

The higher arithmetic presents us with an inexhaustible store of interesting truths - of truths, too, which are not isolated, but stand in a close internal connection, and between which, as our knowledge increases, we are continually discovering new and sometimes wholly unexpected ties.

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