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.

In my opinion instruction is very purposeless for such individuals who do no want merely to collect a mass of knowledge, but are mainly interested in exercising (training) their own powers. One doesn't need to grasp such a one by the hand and lead him to the goal, but only from time to time give him suggestions, in order that he may reach it himself in the shortest way.

Complete knowledge of the nature of an analytic function must also include insight into its behavior for imaginary values of the arguments. Often the latter is indispensable even for a proper appreciation of the behavior of the function for real arguments. It is therefore essential that the original determination of the function concept be broadened to a domain of magnitudes which includes both the real and the imaginary quantities, on an equal footing, under the single designation complex numbers.

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

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.

Sophie Germain proved to the world that even a woman can accomplish something in the most rigorous and abstract of sciences and for that reason would well have deserved an honorary degree.

...as our friend Zach has often noted, in our days those who do the best for astronomy are not the salaried university professors, but so-called dillettanti, physicians, jurists, and so forth.Lamenting the fragmentary time left to a professor has remaining after fulfilling his teaching duties.