Carl Friedrich Gauss Quotes

Mathematics is the queen of the sciences.

Letter to Sophie Germain (30 April 1807) ([...]; les charmes enchanteurs de cette sublime science ne se décèlent dans toute leur beauté qu'à ceux qui ont le courage de l'approfondir. Mais lorsqu'une personne de ce sexe, qui, par nos meurs [sic] et par nos préjugés, doit rencontrer infiniment plus d'obstacles et de difficultés, que les hommes, à se familiariser avec ces recherches épineuses, sait néanmoins franchir ces entraves et pénétrer ce qu'elles ont de plus caché, il faut sans doute, qu'elle ait le plus noble courage, des talents tout à fait extraordinaires, le génie superieur.)

Pauca sed matura. (Few, but ripe.)

If the object of all human investigation were but to produce in cognition a reflection of the world as it exists, of what value would be all its labor and pains, which could result only in vain repetition, in an imitation within the soul of that which exists without it?

"It is beyond doubt that the happiness which love can bestow on its chosen souls is the highest that can fall to mortal's lot. But when I imagine myself in the place of the man who, after twenty happy years, now in one moment loses his all, I am moved almost to say that he is the wretchedest of mortals, and that it is better never to have known such happy days. So it is on this miserable earth: 'the purest joy finds its grave in the abyss of time'. What are we without the hope of a better future?

Even though much error and hypocrisy may often be mixed in such pietistic tendencies, nevertheless I recognize with all my heart the business of a missionary as a highly honorable one in so far as it leads to civilization the still semisavage part of earth s inhabitants. May my son try it for several years.

Bei Gegenstdnden mit denen ich mich noch nicht lange beschaftigt habe, bin ich gegen meine eigenen Ansichten, zumal wenn sie einem Laplace widersprechen, misstrauisch und nehme gern die von anderen entgegen. ["I am suspicious of my own views on subjects with which I have not long occupied myself, and gladly accept those of others, especially when my views contradict one of Laplace."]

The history of the apple is too absurd. Whether the apple fell or not, how can any one believe that such a discovery could in that way be accelerated or retarded? Undoubtedly, the occurrence was something of this sort. There comes to Newton a stupid, importunate man, who asks him how he hit upon his great discovery. When Newton had convinced himself what a noodle he had to do with, and wanted to get rid of the man, he told him that an apple fell on his nose; and this made the matter quite clear to the man, and he went away satisfied.

That this subject [of ] has hitherto been considered from the wrong point of view and surrounded by a mysterious obscurity, is to be attributed largely to an ill-adapted notation. If for instance, +1, -1, √-1 had been called direct, inverse, and lateral units, instead of positive, negative, and imaginary (or even impossible) such an obscurity would have been out of question.

The austere sides of life, at least of mine, which move through it like a red thread, and which one faces more and more defenselessly in old age, are not balanced to the hundredth part by the pleasurable. I will gladly admit that the same fates which have been so hard for me to bear, and still are, would have been much easier for many another person, but the mental constitution belongs to our ego, which the Creator of our existence has given us, and we can change little in it.

The function just found cannot, it is true, express rigorously the probabilities of the errors: for since the possible errors are in all cases confined within certain limits, the probability of errors exceeding those limits ought always to be zero, while our formula always gives some value. However, this defect, which every analytical function must, from its nature, labor under, is of no importance in practice, because the value of our function decreases so rapidly... that it can safely be considered as vanishing. Besides, the nature of the subject never admits of assigning with absolute rigor the limits of error.

But in our opinion truths of this kind should be drawn from notions rather than from notations.

Dark are the paths which a higher hand allows us to traverse here... let us hold fast to the faith that a finer, more sublime solution of the enigmas of earthly life will be present, will become part of us.

The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. … Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.

I protest against the use of infinite magnitude as something completed, which is never permissible in mathematics. Infinity is merely a way of speaking