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.

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

It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation.

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.

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.

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

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