“The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were not beautiful it would not be worth knowing, and life would not be worth living. I am not speaking, of course, of the beauty which strikes the senses, of the beauty of qualities and appearances. I am far from despising this, but it has nothing to do with science. What I mean is that more intimate beauty which comes from the harmonious order of its parts, and which a pure intelligence can grasp.”
― Henri Poincaré (1854-1912)
The Scientist must set in order. Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.”
― Henri Poincaré (1854-1912)
Guessing before proving! Need I remind you that it is so that all important discoveries have been made?”
― Henri Poincaré (1854-1912)
“To doubt everything and to believe everything are two equally convenient solutions; each saves us from thinking.”
― Henri Poincaré (1854-1912)
“Is is by logic that we prove, but by intuition that we discover.”
― Henri Poincaré (1854-1912)
“Mathematics is the art of giving the same name to different things.”
― Henri Poincaré (1854-1912)
“Scientists do not study Nature because it is useful: they study it because it is beautiful. If Nature were not beautiful, it would not be worth knowing. And if Nature were not worth knowing, life would not be worth living.”
― Henri Poincaré (1854-1912)
“Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so lone as the relations remain unchanged. Content to them is irrelevant; they are interested in form only.”
― Henri Poincaré (1854-1912)
“Physicists believe that the Gaussian law has been proved in mathematics while mathematicians think that it was experimentally established in physics.”
― Henri Poincaré (1854-1912)
After the Fourier series, other series have entered the domain of analysis; they entered by the same door; they have been imagined in view of applications.”
― Henri Poincaré (1854-1912)
“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.”
― Henri Poincaré (1854-1912)
"Every good mathematician should also be a good chess player and vice versa."
― Henri Poincaré (1854-1912)
"One geometry cannot be more true than another; it can only be more convenient."
― Henri Poincaré (1854-1912)
"Mathematics is the art of giving the same name to different things.
[As opposed to the quotation: Poetry is the art of giving different names to the same thing]."
― Henri Poincaré (1854-1912)
"Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose."
― Henri Poincaré (1854-1912)
"Mathematicians are born, not made."
― Henri Poincaré (1854-1912)
"Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue."
― Henri Poincaré (1854-1912)