Henri Poincare Quotes

Human intellect is incurably abstract.

I have an unusual type of thinking. I have no visual memory whatsoever. Everything is conceptual to me.

I am interested in ideas, not merely in visual products.

I am dominated by one thing, an irresistible, burning attraction towards the abstract.

The truth of a theory is in your mind, not in your eyes.

In mathematical analysis we call x the undetermined part of line a: the rest we don't call y, as we do in common life, but a-x. Hence mathematical language has great advantages over the common language.

The abstract kills, the concrete saves.

Through art we express our conception of what nature is not.

We think not in words but in shadows of words.

All representations of a thing are inherently abstract.

The intellectual life of man consists almost wholly in his substitution of conceptual order for the perceptual order in which his experience originally comes.

The question you raise, 'How can such a formulation lead to computations?' doesn't bother me in the least! Throughout my whole life as a mathematician, the possibility of making explicit, elegant computations has always come out by itself, as a byproduct of a thorough conceptual understanding of what was going on. Thus I never bothered about whether what would come out would be suitable for this or that, but just tried to understand - and it always turned out that understanding was all that mattered.

This is a gift that I have, simple, simple; a foolish extravagant spirit full of forms, figures, shapes, objects, ideas, apprehensions, motions, revolutions; these are begot in the ventricle of memory, nourished in the womb of pia mater, and delivered upon the mellowing of occasion.

All our thinking is of this nature, a free play with concepts.

Americans have no capacity for abstract thought, and make bad coffee.

The human mind has first to construct forms, independently, before we can find them in things.

No more fiction, for now we calculate; but that we may calculate, we had to make fiction first.

To arrive at abstraction, it is always necessary to begin with a concrete reality.

The mathematical life of a mathematician is short. Work rarely improves after the age of twenty-five or thirty. If little has been accomplished by then, little will ever be accomplished.

I don't think there is any scientific evidence about the question of whether we think only in language or not. But introspection indicates pretty clearly that we don't think in language necessarily. We also think in visual images, we think in terms of situations and events, and so on, and many times we can't even express in words what the content of our thinking is. And even if we are able to express it in words, it is a common experience to say something and then to recognize that it is not what we meant, that it is something else.

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.

I can imagine many things, but few clearly.

Imagination, not intelligence, made us human.

Imagination is the primary gift of human consciousness.

Mathematics as a science, commenced when first someone, probably a Greek, proved propositions about "any" things or about "some" things, without specifications of definite particular things.