Henri Poincare Quotes

Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.

Through the very culture of representation through form, we have come to see that the abstract - like the mathematical - is actually expressed in and through all things, although not determinately.

Now the word-symbols of conceptual ideas have passed so long from hand to hand in the service of the understanding, that they have gradually lost all such fanciful reference.

I used to think that the great thing about sculpture was that, like Stonehenge, it was something that stood against time in an adamantine way, and was an absolute mass in space. Now I try to use the language of architecture to redescribe the body as a place.

Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express.

Mathematics is a game played according to certain simple rules with meaningless marks on paper.

That sometimes clear ... and sometimes vague stuff ... which is ... mathematics.

Everybody who reasons carefully about anything is making a contribution ... and if you abstract it away and send it to the Department of Mathematics they put it in books.

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

The whole of mathematics consists in the organization of a series of aids to the imagination in the process of reasoning.

But think of Adam and Eve like an imaginary number, like the square root of minus one: you can never see any concrete proof that it exists, but if you include it in your equations, you can calculate all manner of things that couldn't be imagined without it.

Mathematics is pure language - the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms.

... numbers have neither substance, nor meaning, nor qualities. They are nothing but marks, and all that is in them we have put into them by the simple rule of straight succession.

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience

Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.

For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.

Do mathematics have a relation to reality or are they only a mathematical symbol?

Nothing is so convenient as a decisive argument ... which must at least silence the most arrogant bigotry and superstition, and free us from their impertinent solicitations. I flatter myself, that I have discovered an argument ... which, if just, will, with the wise and learned, be an everlasting check to all kinds of superstitious delusion, and consequently, will be useful as long as the world endures. For so long, I presume, will the accounts of miracles and prodigies be found in all history, sacred and profane.

Some persons have contended that mathematics ought to be taught by making the illustrations obvious to the senses. Nothing can be more absurd or injurious: it ought to be our never-ceasing effort to make people think, not feel.

Form displays the relation [to beings] itself as the state of original comportment toward beings, the festive state in which the being itself in its essence is celebrated and thus for the first time placed in the open.

Much scientific truth proved to be as hypothetical as poetic allegory. The relationshiip of those rod-connected blue and red balls to an actual atomic structure was about the same as the relationship of Christianity to the fish or the Lamb.

The concept of number is the obvious distinction between the beast and man. Thanks to number, the cry becomes a song, noise acquires rhythm, the spring is transformed into a dance, force becomes dynamic, and outlines figures.

No form of love is wrong, so long as it is love, and you yourself honour what you are doing. Love has an extraordinary variety of forms! And that is all that there is in life, it seems to me.

The ifs and buts of history...form an insubstantial if intoxicating diet.

In the contexts of religion and politics, words are not regarded as standing, rather inadequately, for things and events; on the contrary things and events are regarded as particular illustrations of words.