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

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

Carl Friedrich Gauss

mathematics infinite use

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

Carl Friedrich Gauss

exhausted darkness order

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

education winter science

I have a true aversion to teaching. The perennial business of a professor of mathematics is only to teach the ABC of his science; most of the few pupils who go a step further, and usually to keep the metaphor, remain in the process of gathering information, become only Halbwisser [one who has superficial knowledge of the subject], for the rarer talents do not want to have themselves educated by lecture courses, but train themselves. And with this thankless work the professor loses his precious time.

Carl Friedrich Gauss

teaching education science

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

corny philosopher truth

The Infinite is only a manner of speaking.

Carl Friedrich Gauss

infinite

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

determination real appreciation

[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

freedom men sex

To the distracting occupations belong especially my lecture courses which I am holding this winter for the first time, and which now cost much more of my time than I like. Meanwhile I hope that the second time this expenditure of time will be much less, otherwise I would never be able to reconcile myself to it, even practical (astronomical) work must give far more satisfaction than if one brings up to B a couple more mediocre heads which otherwise would have stopped at A.

Carl Friedrich Gauss

couple education winter

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

science hands people

Finally, two days ago, I succeeded - not on account of my hard efforts, but by the grace of the Lord. Like a sudden flash of lightning, the riddle was solved. I am unable to say what was the conducting thread that connected what I previously knew with what made my success possible.

Carl Friedrich Gauss

math success two

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

simple order science

Mathematics is the queen of the sciences.

Carl Friedrich Gauss

arithmetic queens math

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

Carl Friedrich Gauss

concerned relation math

Mathematical discoveries, like springtime violets in the woods, have their season which no human can hasten or retard.

Carl Friedrich Gauss

woods discovery science

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

occupation faults men

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

ties math interesting

A great part of its theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity on them, are often easily discovered by induction, and yet are of so profound a character that we cannot find the demonstrations till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simple methods may long remain concealed.

Carl Friedrich Gauss

simple success character

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

dignity idaho mean

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

sophie women degrees