Henri Poincare Quotes

Mathematics deals exclusively with the relations of concepts to each other without consideration of their relation to experience.

Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only.

The essence of mathematics lies precisely in its freedom.

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.

Mathematics is the art of giving the same name to different things.

The mathematics is not there till we put it there.

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.

Modern mathematics, that most astounding of intellectual creations, has projected the mind's eye through infinite time and the mind's hand into boundless space.

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then suchand such another proposition is true of that thing.... Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

Algebra applies to the clouds.

Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.

A mathematician ... has no material to work with but ideas, and so his patterns are likely to last longer, since ideas wear less with time than words.

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

When a man knows that the abstraction ten exists - nothing on earth can stop him from looking for the fact of eleven.

Mathematics is the abstract key which turns the lock of the physical universe.

Nothing is more important for teaching us to understand the concepts we have than to construct fictitious ones.

Psychologically, the teaching of abstractions first is wrong. Indeed, a thorough understanding of the concrete must precede the abstract.

Strange! I don't understand how it is that we can write mathematical expressions and calculate what the thing is going to do without being able to picture it.

Imagination is cheap as long as you don't have to worry about the details.

Mental fire is what won't burn real sticks; mental water is what won't necessarily (though of course it may) put out even a mentalfire.

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

In the United States it's not important which religion you adhere to, as long as you have one.

The most important thing to the United States is not being able to attack our adversaries, the most important thing is to be able to defend ourselves. And we can't do that as long as we're subverting our own security standards for the sake of surveillance.

As long as we are enjoying ourselves, that's the most important thing

Life is like a snowball. The important thing is finding wet snow and a really long hill.