Carl Friedrich Gauss Quotes

All the measurements in the world do not balance one theorem by which the science of eternal truths is actually advanced.

Yes! The world would be nonsense, the whole creation an absurdity without immortality.

I scarcely believe that in psychology data are present which can be mathematically evaluated. But one cannot know this with certainty, without having made the experiment. God alone is in possession of the mathematical bases of psychic phenomena.

I believe you are more believing in the Bible than I. I am not, and, you are much happier than I. I must say that so often in earlier times when I saw people of the lower classes, simple manual laborers who could believe so rightly with their hearts, I always envied them, and now tell me how does one begin this?

Finally, a few days ago, it has been achieved - but not by my cumbersome search, rather through God’s good grace, I am tempted to say. As the lightning strikes the riddle was solved; I myself would be unable to point to a guiding thread between what I knew before, what I had used in my last attempts, and what made it work.

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 confess that Fermat's Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of.

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

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. So there are mere philologists, mere jurists, mere soldiers, mere merchants, etc. To such idle talk it might further be added: that whenever a certain exclusive occupation is coupled with specific shortcomings, it is likewise almost certainly divorced from certain other shortcomings.

The principle that the sum of the squares of the differences between the observed and computed quantities must be a minimum may, in the following manner, be considered independently of the calculus of probabilities. When the number of unknown quantities is equal to the number of the observed quantities depending on them, the former may be so determined as exactly to satisfy the latter. But when the number of the former is less than that of the latter, an absolutely exact agreement cannot be obtained, unless the observations possess absolute accuracy. In this case care must be taken to establish the best possible agreement, or to diminish as far as practicable the differences. This idea, however, from its nature, involves something vague. For, although a system of values for the unknown quantities which makes all the differences respectively less than another system, is without doubt to be preferred to the latter, still the choice between two systems, one of which presents a better agreement in some observations, the other in others, is left in a measure to our judgment, and innumerable different principles can be proposed by which the former condition is satisfied. Denoting the differences between observation and calculation by A, A’, A’’, etc., the first condition will be satisfied not only if AA + A’ A’ + A’’ A’’ + etc., is a minimum (which is our principle) but also if A⁴ + A’⁴ + A’’⁴ + etc., or A⁶ + A’⁶ + A’’⁶ + etc., or in general, if the sum of any of the powers with an even exponent becomes a minimum. But of all these principles ours is the most simple; by the others we should be led into the most complicated calculations.

The perturbations which the motions of planets suffer from the influence of other planets, are so small and so slow that they only become sensible after a long interval of time; within a shorter time, or even within one or several revolutions, according to circumstances, the motion would differ so little from motion exactly described, according to the laws of Kepler, in a perfect ellipse, that observations cannot show the difference. As long as this is true, it not be worth while to undertake prematurely the computation of the perturbations, but it will be sufficient to adapt to the observations what we may call an osculating conic section: but, afterwards, when the planet has been observed for a longer time, the effect of the perturbations will show itself in such a manner, that it will no longer be possible to satisfy exactly all the observations by a purely elliptic motion; then, accordingly, a complete and permanent agreement cannot be obtained, unless the perturbations are properly connected with the elliptic motion.

Believe me,... the bitterness of life, or at least of mine, which runs through it like a strand of red, and becomes less and less endurable as I grow older, is not compensated in the hundredth part by the joy of life. I will freely admit that these burdens, which to me have been so grievous, would have been lighter to many another; but our temperament is part of ourselves, given to us by the Creator with our very existence, and we have very little power to change it. I find, on the other hand, in this very consciousness of the vanity of life, which nearly all men must confess to as they draw near the end, my strongest assurance of the approach of a more beautiful metamorphosis. In this, my dear friend, let us find comfort, and endeavour to call up calmness to bear life out to the end.

May the dream which we call life be for you a happy dream, a foretaste of that true life which we shall inherit in our real home, when the awakened spirit shall labour no longer under the grievous bondage of the flesh, the fetters of space, the whips of earthly pain, and the sting of our paltry needs and desires. Let us carry our burdens to the end, stoutly and uncomplainingly, never losing sight of that higher goal. Glad then shall we be to lay down our weary lives, and to see the dropping of the curtain."

"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?

There is in this world a joy of the intellect, which finds satisfaction in science, and a joy of the heart, which manifests itself above all in the aid men give one another against the troubles and trials of life. But for the Supreme Being to have created existences, and stationed them in various spheres in order to taste these joys for some 80 or 90 years — that were surely a miserable plan.... Whether the soul were to live for 80 years or for 80 million years, if it were doomed in the end to perish, such an existence would only be a respite. In the end it would drop out of being. We are thus impelled to the conclusion to which so many things point, although they do not amount to a coercive scientific proof, that besides this material world there exists another purely spiritual order of things, with activities as various, as the present, and that this world of spirit we shall one day inherit.