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.

Is is by logic that we prove, but by intuition that we discover.

We invent by intuition, though we prove by logic.

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

It's through science that we prove, but through intuition that we discover.

C'est avec l'intuition qu'on trouve, c'est avec la logique qu'on prouve

C'est par la logique qu'on démontre, c'est par l'intuition qu'on invente.

Logic teaches us that on such and such a road we are sure of not meeting an obstacle; it does not tell us which is the road that leads to the desired end. For this, it is necessary to see the end from afar, and the faculty which teaches us to see is intuition. Without it, the geometrician would be like a writer well up in grammar but destitute of ideas.

Reason alone will not serve. Intuition alone can be improved by reason, but reason alone without intuition can easily lead the wrong way. They both are necessary. The way I like to put it is that when I have an intuition about something, I send it over to the reason department. Then after I've checked it out in the reason department, I send it back to the intuition department to make sure that it's still all right. That's how my mind works, and that's how I work. That's why I think that there is both an art and a science to what we do. The art of science is as important as so-called technical science. You need both. It's this combination that must be recognized and acknowledged and valued.

Some persons fancy that bias and counter-bias are favorable to the extraction of truth–that hot and partisan debate is the way to investigate. This is the theory of our atrocious legal procedure. But Logic puts its heel upon this suggestion. It irrefragably demonstrates that knowledge can only be furthered by the real desire for it, and that the methods of obstinacy, of authority and every mode of trying to reach a foregone conclusion, are absolutely of no value. These things are proved. The reader is at liberty to think so or not as long as the proof is not set forth, or as long as he refrains from examining it. Just so, he can preserve, if he likes, his freedom of opinion in regard to the propositions of geometry; only, in that case, if he takes a fancy to read Euclid, he will do well to skip whatever he finds with A, B, C, etc., for, if he reads attentively that disagreeable matter, the freedom of his opinion about geometry may unhappily be lost forever.

Just as feelings grow out of ignorance, intuition should grow out of knowledge.

Critique by creating.

The art of discovery is confused with the logic of proof and an artificial simplification of the deeper movements of thought results. We forget that we invent by intuition though we prove by logic.

It is not what we know, but what we can prove.