Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what … - Henri Poincare

Same topic Authors

Quote of the day

. . . and then there was Johan Cruyff, who at 35 has added a whole new meaning to the word Anno Domini.

Henri Poincare

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the "logic piano" imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.

Demonstrate, Math, Mathematician, Mean, Piano, Transformed

Same Author Quotes

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