Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.
Quoted in G Simmons Calculus Gems (New York 1992).
[upon losing the use of his right eye]
Now I will have less distraction.
Quoted in H Eves In Mathematical Circles (Boston 1969).
Madam, I have come from a country where people are hanged if they talk.
[In Berlin, excusing his taciturnity in conversation with the Queen Mother of Prussia, on his return from Russia]
Quoted in A Vucinich, Science in Russian Culture
Notable enough, however, are the controversies over the series 1 - 1 + 1 - 1 + 1 - ... whose sum was given by Leibniz as 1/2, although others disagree. ... Understanding of this question is to be sought in the word "sum"; this idea, if thus conceived -- namely, the sum of a series is said to be that quantity to which it is brought closer as more terms of the series are taken -- has relevance only for convergent series, and we should in general give up the idea of sum for divergent series.
Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena.
D'Alembert, that great genius, seems to be far too ready to pull down everything he has not himself built up. (letter to Lagrange).