When young, one is confident to be able to build palaces for mankind, but when the time comes one has one's hands full just to be able to remove their trash.

In art the best is good enough.

A noble person attracts noble people, and knows how to hold on to them.

A talent is formed in stillness, a character in the world's torrent.

Investigate what is, and not what pleases.

We can't form our children on our own concepts; we must take them and love them as God gives them to us.

The spirits that I summoned up, I now can't rid myself of.

One of the most striking signs of the decay of art is the intermixing of different genres.

The true, prescriptive artist strives after artistic truth; the lawless artist, following blind instinct, after an appearance of naturalness. The one leads to the highest peaks of art, the other to its lowest depths.

In limitations he first shows himself the master,And the law can only bring us freedom.

But among all the discoveries and corrections probably none has resulted in a deeper influence on the human spirit than the doctrine of Copernicus.... Possibly mankind has never been demanded to do more, for considering all that went up in smoke as a result of realizing this change: a second Paradise, a world of innocence, poetry and piety: the witness of the senses, the conviction of a poetical and religious faith. No wonder his contemporaries did not wish to let all this go and offered every possible resistance to a doctrine which in its converts authorized and demanded a freedom of view and greatness of thought so far unknown indeed not even dreamed of.

One never goes so far as when one doesn't know where one is going.

I have often felt a bitter sorrow at the thought of the German people, which is so estimable in the individual and so wretched in the generality. A comparison of the German people with other peoples arouses a painful feeling, which I try to overcome in every possible way.

Patriotism ruins history.

Should I not be proud, when for twenty years I have had to admit to myself that the great Newton and all the mathematicians and noble calculators along with him were involved in a decisive error with respect to the doctrine of color, and that I among millions was the only one who knew what was right in this great subject of nature?

All poetry is supposed to be instructive but in an unnoticeable manner; it is supposed to make us aware of what it would be valuable to instruct ourselves in; we must deduce the lesson on our own, just as with life.

I am more and more convinced that poetry is the universal possession of mankind, revealing itself everywhere and at all times in hundreds and hundreds of men. ... I therefore like to look about me in foreign nations, and advise everyone to do the same. National literature is now a rather unmeaning term; the epoch of world literature is at hand, and everyone must strive to hasten its approach.

One must be something in order to do something.

I have found a paper of mine among some others in which I call architecture 'petrified music.' Really there is something in this; the tone of mind produced by architecture approaches the effect of music.

If I work incessantly to the last, nature owes me another form of existence when the present one collapses.

The artist may be well advised to keep his work to himself till it is completed, because no one can readily help him or advise him with it...but the scientist is wiser not to withhold a single finding or a single conjecture from publicity.

America, you have it better than our continent, the old one.

Who is the happiest of men? He who values the merits of others, And in their pleasure takes joy, even as though 'twere his own. Not in the morning alone, not only at mid-day he charmeth; Even at setting, the sun is still the same glorious planet.

And now the sagacious reader, who is capable of reading into these lines what does not stand written in them, but is nevertheless implied, will be able to form some conception of the serious feelings with which I then set foot in Emmendingen.

Young Schopenhauer, a zealous and thorough-going Kantian, tried to explain that light would cease to exist along with the seeing eye. "What!" he said, according to Schopenhauer's own report, "looking at him with his Jove-like eyes,"-"You should rather say that you would not exist if the light could not see you?"

Nothing is great but truth, and the smallest truth is great. The other day I had a thought, which I put like this: Even a harmful truth is useful, for it can be harmful only for the moment and will lead to other truths, which must always become useful, very much so. Conversely, even a useful error is harmful, for it can be useful only for the moment, enticing us into other errors, which become more and more harmful.

The social contract between all people around the world only has one requirement: Don't kill. From there it's those who don't agree, those that agree but have some reactive justification, and those that agree and don't kill.

A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature. ...we work not only to obtain the positive results which, according to the profane, constitute our one and only affection, as to experience this esthetic emotion and to convey it to others who are capable of experiencing it.

It is the simple hypotheses of which one must be most wary; because these are the ones that have the most chances of passing unnoticed.

The task of the educator is to make the child's spirit pass again where its forefathers have gone, moving rapidly through certain stages but suppressing none of them. In this regard, the history of science must be our guide.

We do not have and cannot have any means of discovering whether or not we are carried along in a uniform motion of translation.

Everyone is sure of this [that errors are normally distributed], Mr. Lippman told me one day, since the experimentalists believe that it is a mathematical theorem, and the mathematicians that it is an experimentally determined fact.

Thought must never submit, neither to a dogma, nor to a party, nor to a passion, nor to an interest, nor to a preconceived idea, nor to whatever it may be, save to the facts themselves, because, for thought, submission would mean ceasing to be.

The ones who are preoccupied by logic are above all; to read their works, one is tempted to believe they have advanced only step by step, after the manner of a Vauban who pushes on his trenches against the place besieged, leaving nothing to chance. The others are guided by intuition and, at the first stroke, make quick but sometimes precarious conquests, like bold cavalrymen of the advance guard.

Point set topology is a disease from which the human race will soon recover.

Thought is only a flash between two long nights, but this flash is everything.

To doubt everything or to believe everything are two equally convenient solutions; both dispense with the necessity of reflection.

There is no science apart from the general. It may even be said that the very object of the exact sciences is to spare us these direct verifications.

We can not... escape the conclusion that the rule of reasoning by recurrence is irreducible to the principle of contradiction. ...Neither can this rule come to us from experience... This rule, inaccessible to analytic demonstration and to experience, is the veritable type of the synthetic a priori judgment. On the other hand, we can not think of seeing in it a convention, as in some of the postulates of geometry. ...it is only the affirmation of the power of the mind which knows itself capable of conceiving the indefinite repetition of the same act when once this act is possible. The mind has a direct intuition of this power, and experience can only give occasion for using it and thereby becoming conscious of it.

But, one will say, if raw experience can not legitimatize reasoning by recurrence, is it so of experiment aided by induction? We see successively that a theorem is true of the number 1, of the number 2, of the number 3 and so on; the law is evident, we say, and it has the same warranty as every physical law based on observations, whose number is very great but limited. But there is an essential difference. Induction applied to the physical sciences is always uncertain, because it rests on the belief in a general order of the universe, an order outside of us. Mathematical induction, that is, demonstration by recurrence, on the contrary, imposes itself necessarily, because it is only the affirmation of a property of the mind itself.

Mathematicians do not study objects, but the relations between objects; to them it is a matter of indifference if these objects are replaced by others, provided that the relations do not change. Matter does not engage their attention, they are interested in form alone.

We see that experience plays an indispensable role in the genesis of geometry; but it would be an error thence to conclude that geometry is, even in part, an experimental science. If it were experimental it would be only approximative and provisional. And what rough approximation!...The object of geometry is the study of a particular 'group'; but the general group concept pre-exists... in our minds. It is imposed on us, not as form of our sense, but as form of our understanding. Only, from among all the possible groups, that must be chosen... will be... the standard to which we shall refer natural phenomena.Experience guides us in this choice without forcing it upon us; it tells us not which is the truest geometry, but which is the most convenient.Notice that I have been able to describe the fantastic worlds... imagined without ceasing to employ the language of ordinary geometry.

Is the position tenable, that certain phenomena, possible in Euclidean space, would be impossible in non-Euclidean space, so that experience, in establishing these phenomena, would directly contradict the non-Euclidean hypothesis? For my part I think no such question can be put. To my mind it is precisely equivalent to the following, whose absurdity is patent to all eyes: are there lengths expressible in meters and centimeters, but which can not be measured in fathoms, feet, and inches, so that experience, in ascertaining the existence of these lengths, would directly contradict the hypothesis that there are fathoms divided into six feet?

The Scientist must set in order. Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.

If we study the history of science we see happen two inverse phenomena... Sometimes simplicity hides under complex appearances; sometimes it is the simplicity which is apparent, and which disguises extremely complicated realities....No doubt, if our means of investigation should become more and more penetrating, we should discover the simple under the complex, then the complex under the simple, then again the simple under the complex, and so on, without our being able to foresee what will be the last term. We must stop somewhere, and that science may be possible, we must stop when we have found simplicity. This is the only ground on which we can rear the edifice of our generalizations.

It is often said that experiments should be made without preconceived ideas. That is impossible. Not only would it make every experiment fruitless, but even if we wished to do so, it could not be done. Every man has his own conception of the world, and this he cannot so easily lay aside. We must, for example, use language, and our language is necessarily steeped in preconceived ideas.

If, then, a phenomenon admits of a complete mechanical explanation, it will admit of an infinity of others, that will render an account equally well of all the particulars revealed by experiment.

Scientists believe there is a hierarchy of facts and that among them may be made a judicious choice. They are right, since otherwise there would be no science...

One need only open the eyes to see that the conquests of industry which have enriched so many practical men would never have seen the light, if these practical men alone had existed and if they had not been preceded by unselfish devotees who died poor, who never thought of utility, and yet had a guide far other than caprice.As Mach says, these devotees have spared their successors the trouble of thinking.

Time and Space ... It is not nature which imposes them upon us, it is we who impose them upon nature because we find them convenient.