Logic teaches us that on such and such a road we are sure of not meeting an obstacle; it does not tell us… — Henri Poincaré
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.
La logique nous apprend que sur tel ou tel chemin nous sommes sûrs de ne pas rencontrer d'obstacle ; elle ne nous dit pas quel est celui qui mène au but. Pour cela il faut voir le but de loin, et la faculté qui nous apprend à voir, c'est l'intuition. Sans elle, le géomètre serait comme un écrivain qui serait ferré sur la grammaire, mais qui n'aurait pas d'idées.
p. 130Source: Wikiquote · CC BY-SA 4.0
More from this book
It is because simplicity and vastness are both beautiful that we seek by preference simple facts and vast facts; that we take delight, now in following the giant courses of the stars, now in scrutinizing the microscope that prodigious smallness which is also a vastness, and now in seeking in geological ages the traces of a past that attracts us because of its remoteness.
p. 23
I think I have already said somewhere that mathematics is the art of giving the same name to different things.
p. 31
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.
p. 129
