Carl Friedrich Gauss Quotes

His second motto: Thou, nature, art my goddess; to thy laws my services are bound. ~ Carl Friedrich Gauss

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. ~ Carl Friedrich Gauss

That this subject [of imaginary magnitudes] 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 example, +1, -1, and the square root of -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 the question. ~ Carl Friedrich Gauss

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

As is well known the principle of virtual velocities transforms all statics into a mathematical assignment, and by D'Alembert's principle for dynamics, the latter is again reduced to statics. Although it is is very much in order that in gradual training of science and in the instruction of the individual the easier precedes the more difficult, the simple precedes the more complicated, the special precedes the general, yet the min, once it has arrived at the higher standpoint, demands the reverse process whereby all statics appears only as a very special case of mechanics. ~ Carl Friedrich Gauss

Less depends upon the choice of words than upon this, that their introduction shall be justified by pregnant theorems. ~ Carl Friedrich Gauss

I have had my results for a long time: but I do not yet know how I am to arrive at them. ~ Carl Friedrich Gauss

You have no idea, how much poetry there is in the calculation of a table of logarithms! ~ Carl Friedrich Gauss

When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again. ~ Carl Friedrich Gauss

I am giving this winter two courses of lectures to three students, of which one is only moderately prepared, the other less than moderately, and the third lacks both preparation and ability. Such are the onera of a mathematical profession. ~ Carl Friedrich Gauss

It is not knowledge, but the act of learning, not the possession of but the act of getting there, which grants the greatest enjoyment. ~ Carl Friedrich Gauss

[On scientist Carl Friedrich Gauss]
[Carl Friedrich] Gauss told his friend Rudolf Wagner, a professor of biology at Gottingen University, that he did not believe in the Bible but that he had meditated a great deal on the future of the human soul and speculated on the possibility of the soul being reincarnated on another planet. Evidently, Gauss was a Deist with a good deal of skepticism concerning religion. ~ Gerhard Falk

I protest against the use of infinite magnitude ... , which is never permissible in mathematics. ~ Carl Friedrich Gauss

The mathematical giant [Gauss], who from his lofty heights embraces in one view the stars and the abysses ... ~ Farkas Bolyai

The importance of C.F. Gauss for the development of modern physical theory and especially for the mathematical fundament of the theory of relativity is overwhelming indeed; also his achievement of the system of absolute measurement in the field of electromagnetism. In my opinion it is impossible to achieve a coherent objective picture of the world on the basis of concepts which are taken more or less from inner psychological experience. ~ Albert Einstein

Mathematics is concerned only with the enumeration and comparison of relations. ~ Carl Friedrich Gauss

Arc, amplitude, and curvature sustain a similar relation to each other as time, motion, and velocity, or as volume, mass, and density. ~ Carl Friedrich Gauss

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. ~ Carl Friedrich Gauss

He is like the fox, who effaces his tracks in the sand with his tail.

{Describing the writing style of famous mathematician Carl Friedrich Gauss} ~ Niels Henrik Abel

With a thousand joys I would accept a nonacademic job for which industriousness, accuracy, loyalty, and such are sufficient without specialized knowledge, and which would give a comfortable living and sufficient leisure, in order to sacrifice to my gods [mathematical research]. For example, I hope to get the editting of the census, the birth and death lists in local districts, not as a job, but for my pleasure and satisfaction ... ~ Carl Friedrich Gauss

Theory attracts practice as the magnet attracts iron. ~ Carl Friedrich Gauss

[On Sophie Germain] When a person of the sex which, according to our customs and prejudices, must encounter infinitely more difficulties than men ... succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of [number theory], then without doubt she must have the noblest courage, quite extraordinary talents and superior genius. ~ Carl Friedrich Gauss

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. ~ Carl Friedrich Gauss

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

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. ~ Carl Friedrich Gauss

Mathematicians stand on each other's shoulders. ~ Carl Friedrich Gauss

In the last two months I have been very busy with my own mathematical speculations, which have cost me much time, without my having reached my original goal. Again and again I was enticed by the frequently interesting prospects from one direction to the other, sometimes even by will-o'-the-wisps, as is not rare in mathematic speculations. ~ Carl Friedrich Gauss

A reply to Olbers' attempt in 1816 to entice him to work on Fermat's Theorem. 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. [] ~ Carl Friedrich Gauss

It may be true that people who are merely mathematicians have certain specific shortcomings; however that is not the fault of mathematics, but is true of every exclusive occupation. Likewise a mere linguist, a mere jurist, a mere soldier, a mere merchant, and so forth. One could add such idle chatter that when a certain exclusive occupation is often connected with certain specific shortcomings, it is on the other hand always free of certain other shortcomings. ~ Carl Friedrich Gauss

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. ~ Carl Friedrich Gauss

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. ~ Carl Friedrich Gauss

Two centuries ago Carl Friedrich Gauss, one of the greatest mathematicians and a founder of number theory, described his brainchild as "the queen of mathematics." Queens are regal, but they are also largely decorative, and this nuance was not lost on Gauss. ~ Ian Stewart

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. ~ Carl Friedrich Gauss

Does the pursuit of truth give you as much pleasure as before? Surely it is not the knowing but the learning, not the possessing but the acquiring, not the being-there but the getting there that afford the greatest satisfaction. If I have exhausted something, I leave it in order to go again into the dark. Thus is that insatiable man so strange: when he has completed a structure it is not in order to dwell in it comfortably, but to start another. ~ Carl Friedrich Gauss

God does arithmetic. ~ Carl Friedrich Gauss

Ask her to wait a moment I am almost done. ~ Carl Friedrich Gauss

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. ~ Carl Friedrich Gauss

Mathematics is the queen of science, and arithmetic the queen of mathematics. ~ Carl Friedrich Gauss

In mathematics there are no true controversies. ~ Carl Friedrich Gauss

I believe you are more believing in the Bible than I. I am not, and, you are much happier than I. ~ Carl Friedrich Gauss

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

Life stands before me like an eternal spring with new and brilliant clothes. ~ Carl Friedrich Gauss

When a philosopher says something that is true then it is trivial. When he says something that is not trivial then it is false. ~ Carl Friedrich Gauss

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect. ~ Carl Friedrich Gauss

The higher arithmetic presents us with an inexhaustible store of interesting truths - of truths, too, which are not isolated, but stand in a close internal connection, and between which, as our knowledge increases, we are continually discovering new and sometimes wholly unexpected ties. ~ Carl Friedrich Gauss

The witch mania is shameful. How could we do it? How could we be so ignorant about ourselves and our weaknesses? How could it have happened in the most "advanced," the most "civilized" nations then on Earth? Why was it resolutely supported by conservatives, monarchists, and religious fundamentalists? Why opposed by liberals, Quakers and followers of the Enlightenment? If we're absolutely sure that our beliefs are right, and those of others wrong; that we are motivated by good, and others by evil; that the King of the Universe speaks to us, and not to adherents of very different faiths; that it is wicked to challenge conventional doctrines or to ask searching questions; that our main job is to believe and obey - then the witch mania will recur in its infinite variations down to the time of the last man. Note Friedrich von Spee's very first point, and the implication that improved public understanding of superstition and skepticism might have helped to short-circuit the whole train of causality. If we fail to understand how it worked in the last round, we will not recognize it as it emerges in the next. ~ Carl Sagan

Democracy means decision by those concerned. ~ Carl Friedrich Von Weizsacker

Unless you are as smart as Johann Karl Friedrich Gauss, savvy as a half-blind Calcutta bootblack, tough as General William Tecumseh Sherman, rich as the Queen of England, emotionally resilient as a Red Sox fan, and as generally able to take care of yourself as the average nuclear missile submarine commander, you should never have been allowed near this document. ~ Neal Stephenson

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. ~ Carl Friedrich Gauß

What was once thought can never be unthought. ~ Carl Joachim Friedrich

Nature is earlier than man, but man is earlier than natural science. ~ Carl Friedrich Von Weizsacker

The history of totalitarian regimes is reflected in the evolution and perfection of the instruments of terror and more especially the police. ~ Carl Joachim Friedrich

In other words, our conscious representations are sometimes ordered (or arranged in a pattern) before they have become conscious to us. The 18th-century German mathematician Karl Friedrich Gauss gives an example of an experience of such an unconscious order of ideas: He says that he found a certain rule in the theory of numbers "not by painstaking research, but by the Grace of God, so to speak. The riddle solved itself as lightning strikes, and I myself could not tell or show the connection between what I knew before, what I last used to experiment with, and what produced the final success." The French scientist Henri Poincare is even more explicit about this phenomenon; he describes how during a sleepless night he actually watched his mathematical representations colliding in him until some of them "found a more stable connection. One feels as if one could watch one's own unconscious at work, the unconscious activity partially becoming manifest to consciousness without losing its own character. At such moments one has an intuition of the difference between the mechanisms of the two egos. ~ C.G. Jung

Classical physics has been superseded by quantum theory: quantum theory is verified by experiments. Experiments must be described in terms of classical physics. ~ Carl Friedrich Von Weizsacker

Counterfeit tolerance includes the opportunism of one who seeks, or accepts, tolerance for himself, as a minority, but who would deny it to others if ever he should be in a position to grant it. ~ Carl Joachim Friedrich

A book is proof that humans are capable of working magic. ~ Carl Sagan

Danger alone acquaints us with our own resources, our virtues, our armor and weapons, our spirit, and forces us to be strong. ~ Friedrich Nietzsche

Even top caliber hospitals cannot escape medical mistakes that sometimes result in irreparable damage to patients. ~ Carl Levin

Without analysis, no synthesis. ~ Friedrich Engels

Growing up in Europe, tight clothing is pretty standard. When I got to college, clothes were loose, so I was going toward more loose stuff. As soon as I got back to New York, I started wearing suits 25% of the year. Then, I realized how important it is for the suit to really fit you and be tight. ~ Carl Hagelin

He who has a why to live for can bear with almost any how. ~ Friedrich Nietzsche

Free from what? What does that matter to Zarathustra! Clearly, however, shall your eye show to me: free for what? ~ Friedrich Nietzsche

The greatest danger to liberty today comes from the men who are most needed and most powerful in modern government, namely, the efficient expert administrators exclusively concerned with what they regard as the public good. ~ Friedrich August Von Hayek

Out of damp and gloomy days, out of solitude, out of loveless words directed at us, conclusions grow up in us like fungus: one morning they are there, we know not how, and they gaze upon us, morose and gray. Woe to the thinker who is not the gardener but only the soil of the plants that grow in him. ~ Friedrich Nietzsche

Freedom granted only when it is known beforehand that its effects will be beneficial is not freedom. ~ Friedrich August Von Hayek

One loves ultimately one's desires, not the thing desired. ~ Friedrich Nietzsche

If our intelligence is either manipulated or if it's shaded or if in some way it is exaggerated, it is very, very dangerous for us, particularly as we go down the road and look at other threats,. ~ Carl Levin

I would be very ashamed of my civilization if we did not try to find out if there is life in outer space. ~ Carl Sagan

My soul is calm and clear, like the mountains in the morning. But they think I am cold, and a mocker with terrible jests. ~ Friedrich Nietzsche

The Moor has done his work, the Moor may go. ~ Friedrich Schiller

Invert. Always invert. ~ Carl Jacobi

Evangelical agencies with ready funding may have too little depth and vision to cope with the current conflict. God's kingdom is built not on perpetual motion, one-liners, and flashbulbs but on Christ. ~ Carl F. H. Henry

In the whole of the New Testament there is not one joke, that fact alone would invalidate any book. ~ Friedrich Nietzsche

It was clearly the Native American curse on the white man in action. After taking their land and converting everything that was holy and good into money, the white man became aged and foolish and then gambled all that money away at Native American casinos. The power of this magic was indisputable and in evidence all around me. Senior citizens chain smoked and dumped money into the machines, staring with eyes that only reacted to the prospect of making a buck from risk and self-destruction. Especially if this were enhanced by the notion of a fate that had their interests in mind in a way loosely connected to their Christian God who usually took their side in racial relations, if history were to be a judge. ~ Carl-John X. Veraja

French philosopher whom professional philosophers generally accord highest honors is Descartes. Montaigne and Pascal, Voltaire and Rousseau, Bergson and Sartre do not enjoy their greatest vogue among philosophers, and of these only Rousseau has had any considerable influence on the history of philosophy (through Kant and Hegel). ~ Friedrich Nietzsche

Once blasphemy again God was the greatest blasphemy; but God died, and thereupon those blasphemers died too. ~ Friedrich Nietzsche