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We often experience more regret over the part we have left, than pleasure over the part we have preferred.

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Henri Poincare

One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.

Desire, Development, Remember, Influence
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The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.

Dogmatists, Imagination, Science, Simplicity, Things

All that is not thought is pure nothingness; since we can think only thoughts, and all the words we use to speak of things can express only thoughts, to say there is something other than thought is therefore an affirmation which can have no meaning.

Affirmation, Express, Meaning, Thinking, Thought, Use

Mathematical discoveries, small or great are never born of spontaneous generation.

Discovery, Generation, Generations, Mathematical, Small, Spontaneity

So is not mathematical analysis then not just a vain game of the mind? To the physicist it can only give a convenient language; but isn't that a mediocre service, which after all we could have done without; and, it is not even to be feared that this artificial language be a veil, interposed between reality and the physicist's eye? Far from that, without this language most of the initimate analogies of things would forever have remained unknown to us; and we would never have had knowledge of the internal harmony of the world, which is, as we shall see, the only true objective reality.

Eye, Science, Reality, Unknown, True, Physicist

A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.

Independent, Science, Reality, World, External, Forever
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