高斯说过哪些名言？

高斯说过不少话，我们也都熟悉。比如：

数学是科学的皇后，数论是数学的皇后 (Mathematics is the queen of sciences and arithmetic the queen of mathematics. )

下面的话出自高斯在1808年写给友人（发现非欧几何者之父，不过高斯说他其实早就发现了，回信说如果要赞扬他儿子，就是表扬自己）的一封信，很有意思：

It is not knowledge, but the act of learning, not possession but the act of getting there, not being but the act of becoming, which grants the greatest enjoyment.

给我最大的快乐，不是已懂得知识，而是不断的学习；不是已有的东西，而是不断的获取；不是已经达到的高度，而是不断的攀登。

我们将他的这两个名言印到了杯子上。

和艺术家一样，高斯希望他留下的都是十全十美的艺术珍品：“当一幢建筑物完成时，应该把脚手架拆除乾净。”

他还说过：

宁可少些，但要好些。

二分之一个证明等于0。

若无某种大胆放肆的猜测，一般是不可能有知识的进度的。

数学中的一些美丽定理具有这样的特性：它们极易从事实中归纳出来，但证明却隐藏的极深。

灵魂的满足是一种更高的境界，物质的满足是多餘的。至於我把数学应用到几块泥巴组成的星球，或应用到纯粹数学的问题上，这一点并不重要。但后者常常带给我更大的满足。

有些问题，如果能解答的话，我认為比解答数学问题更有超然的价值，比如有关人类和神的关系，我们的归宿，我们的将来等等。这些问题的解答，远超出我们能力之所及，也非科学的范围内能够做到。”

下面更多，就不一一翻译了：

...durch planmässiges Tattonieren.
(... through systematic, palpable experimentation.)
Response, when asked how he came upon his theorems.

— Carl Friedrich Gauss

Quoted in A.L. Mackay, Dictionary of Scientific Quotations (1994).

..und Juwele wägt man nicht mit der Krämerwaage
... and jewels are not weighed on a grocery scale.
Comment on Dirichlet's publication as being not prolific, but profound.

— Carl Friedrich Gauss

Letter to Alexander von Humbolt (9 Jul 1845). In Jagdish Mehra and Helmut Rechenberg, The Historical Development of Quantum Theory, 267. By

Pauca sed matura.
(Few, but ripe.)
His motto. He would limit his publications to work he regarded as complete and perfect.

— Carl Friedrich Gauss

Thou, nature, art my goddess; to thy laws my services are bound...
His second motto (from King Lear by Shakespeare).

— Carl Friedrich Gauss

A great part of its [higher arithmetic] 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

Quoted in H. Eves, Mathematical Circles (1977) .

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

Collected Works (1877), Vol. 5, 25-26. Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 412.

Ask her to wait a moment. I am almost done.
When told, while working, that his wife was dying.

— Carl Friedrich Gauss

Quoted in E.T. Bell, Men of Mathematics, (1937).

By explanation the scientist understands nothing except the reduction to the least and simplest basic laws possible, beyond which he cannot go, but must plainly demand them; from them however he deduces the phenomena absolutely completely as necessary.

— Carl Friedrich Gauss

From his memoir 'Erdmagnetismus und Magnetometer' in Collected Works (1877), Vol. 5, 315-316. Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 411.

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

Quoted in H. Eves, Mathematical Circles Squared, (1972).

For three days now this angel, almost too heavenly for earth has been my fiancée … Life stands before me like an eternal spring with new and brilliant colours. Upon his engagement to Johanne Osthof of Brunswick; they married 9 Oct 1805.

— Carl Friedrich Gauss

Letter to Farkas Wolfgang Bolyai (1804). Quoted in Stephen Hawking, God Created the Integers: The Mathematical Breakthroughs (2005), 567.

God does arithmetic.

— Carl Friedrich Gauss

Attributed. Quoted in A.L. Mackay, A Dictionary of Scientific Quotations (1991), 100.

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...geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.

— Carl Friedrich Gauss

Quoted in J Koenderink, Solid Shape (1990).

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

Letter to Friedrich Bessel (4 Dec 1808). In Gauss-Bessel Briefwechsel (1880), 107. In Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 158.

I confess that Fermat's Theorem as an isolated proposition has very little interest for me, for a multitude of such theorems can wasily be set up, which one could neither prove nor disprove. But I have been stimulated by it to bring our again several old ideas for a great extension of the theory of numbers. Of course, this theory belongs to the things where one cannot predict to what extent one will succeed in reaching obscurely hovering distant goals. A happy star must also rule, and my situation and so manifold distracting affairs of course do not permit me to pursue such meditations as in the happy years 1796-1798 when I created the pricipal topics of my Disquisitiones arithmeticae. But I am convinced that if good fortune should do more than I expect, and make me successful in some advances in that theory, even the Fermat theorem will appear in it only as one of the least interesting corollaries.
In reply to Olbers' attempt in 1816 to entice him to work on Fermat's Theorem. The hope Gauss expressed for his success was never realised.

— Carl Friedrich Gauss

Letter to Heinrich Olbers (21 Mar 1816). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 413.

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 onlyHalbwisser [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

Letter to Heinrich Olbers (26 Oct 1802). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 414.

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

Quoted in A. Arber, The Mind and the Eye (1954).

I have the vagary of taking a lively interest in mathematical subjects only where I may anticipate ingenious association of ideas and results recommending themselves by elegance or generality.

— Carl Friedrich Gauss

Letter to Heinrich Schumacher (17 Sep 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.

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

Quoted in G. Simmons, Calculus Gems (1992).

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

— Carl Friedrich Gauss

Quoted in J. R. Newman (ed.), The World of Mathematics (1956).

In general I would be cautious against … plays of fancy and would not make way for their reception into scientific astronomy, which must have quite a different character. Laplace's cosmogenic hypotheses belong in that class. Indeed, I do not deny that I sometimes amuse myself in a similar manner, only I would never publish the stuff. My thoughts about the inhabitants of celestial bodies, for example, belong in that category. For my part, I am (contrary to the usual opinion) convinced ... that the larger the cosmic body, the smaller are the inhabitants and other products. For example, on the sun trees, which in the same ratio would be larger than ours, as the sun exceeds the earth in magnitude, would not be able to exist, for on account of the much greater weight on the surface of the sun, all branches would break themselves off, in so far as the materials are not of a sort entirely heterogeneous with those on earth.

— Carl Friedrich Gauss

Letter to Heinrich Schumacher (7 Nov 1847). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 411.

In mathematics there are no true controversies. (1811)

— Carl Friedrich Gauss

This quote is usually seen without any specific source citation. The sense of it is given, not in quotation marks, as “In 1811 Gauss stated that there are no true controversies in mathematics,” in G. Waldo Dunnington, Jeremy Gray and Fritz-Egbert Dohse, Carl Friedrich Gauss: Titan of Science (2003), 418. If you know the primary source, please contact Webmaster.

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

Letter to Heinrich Schumacher (2 Oct 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.

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

Letter to Ernst Weber (21 May 1843). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.

It is always noteworthy that all those who seriously study this science [the theory of numbers] conceive a sort of passion for it.

— Carl Friedrich Gauss

Letter to Jonos Boyai (2 Sep 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 413.

It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again; the never-satisfied man is so strange if he has completed a structure, then it is not in order to dwell in it peacefully,but in order to begin another. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others.

— Carl Friedrich Gauss

Letter to Farkas Wolfgang Bolyai (2 Sep 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.

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

Letter to Heinrich Schumacher (1-5 Jan 1845). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 414.

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

— Carl Friedrich Gauss

Quoted in E.T. Bell, The Development of Mathematics (1945).

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

— Carl Friedrich Gauss

Quoted in E. T. Bell, The Development of Mathematics (1945).

Mathematics is the queen of the sciences and arithmetic [number theory] is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations, she is entitled to first rank.

— Carl Friedrich Gauss

I>Sartorius von Waltershausen: Gauss zum Gedächtniss (1856), 79. Quoted in Robert Edouard Moritz, Memorabilia Mathematica (1914), 271.

My young friend, I wish that science would intoxicate you as much as our good Göttingen beer! Upon seeing a student staggering down a street.

— Carl Friedrich Gauss

Attributed. Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.

Referring to the decimal system of numeration or its equivalent (with some base other than 10): To what heights would science now be raised if Archimedes had made that discovery!
Gauss regarded this oversight as the greatest calamity in the history of science.

— Carl Friedrich Gauss

Quoted in James Roy Newman, The World of Mathematics, 328.

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

Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 68.

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

Theoria Residiorum Biquadraticorum, Commentario secunda', Werke (1863), Vol. 2. Quoted in Robert Edouard Moritz, Memorabilia Mathematica (1914), 282.

The enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it. But when a woman, who because of her sex and our prejudices encounters infinitely more obstacles that an man in familiarizing herself with complicated problems, succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of them, without doubt she must have the noblest courage, quite extraordinary talents and superior genius.

— Carl Friedrich Gauss

in a letter to Sophie Germain (c.April 1807)

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.

— Carl Friedrich Gauss

Disquisitiones Arithmeticae (1801), Article 329

Theory attracts practice as the magnet attracts iron.

— Carl Friedrich Gauss

Attributed. Quoted in Speaking of Science: Notable Quotes on Science, Engineering, and the Environment (2000), 53.

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

Quoted in J.R. Newman, The World of Mathematics (1956), 314.

There have been only three epoch-making mathematicians, Archimedes, Newton, and Eisenstein.

— Carl Friedrich Gauss

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

Letter to Friedrich Bessel (4 Dec 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 415.

We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.

— Carl Friedrich Gauss

Letter to Friedrich Bessel (1830).

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

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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

Letter to Heinrich Olbers (26 Oct 1802). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 415.

You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length.

— Carl Friedrich Gauss

Quoted in G. Simmons, Calculus Gems (1992).

…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

Letter to Heinrich Olbers (26 Oct 1802). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 415.