Quotes by Henri Poincaré

“Thought is only a flash in the middle of a long night. But this flash means everything.””

“Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.””

“Consider now the Milky Way. Here also we see an innumerable dust, only the grains of this dust are no longer atoms but stars; these grains also move with great velocities, they act at a distance one upon another, but this action is so slight at great distances that their trajectories are rectilineal; nevertheless, from time to time, two of them may come near enough together to be deviated from their course, like a comet that passed too close to Jupiter. In a word, in the eyes of a giant, to whom our Suns were what our atoms are to us, the Milky Way would only look like a bubble of gas.””

“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.””

“How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.””

“Physicists believe that the Gaussian law has been proved in mathematics while mathematicians think that it was experimentally established in physics.””

“The philosophers make still another objection: "What you gain in rigour," they say, "you lose in objectivity. You can rise toward your logical ideal only by cutting the bonds which attach you to reality. Your science is infallible, but it can only remain so by imprisoning itself in an ivory tower and renouncing all relation with the external world. From this seclusion it must go out when it would attempt the slightest application.””

“It is through science that we prove, but through intuition that we discover.””

“Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue.””

“It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.””