Talk with M. Hermite. He never evokes a concrete image, yet you soon perceive that the more abstract entities are to him like living creatures. - Henri Poincaré

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

... les traités de mécanique ne distinguent pas bien nettement ce qui est expérience, ce qui est raisonnement mathématique, ce qui est convention, ce qui est hypothèse.

Logic sometimes breeds monsters. For half a century there has been springing up a host of weird functions, which seem to strive to have as little resemblance as possible to honest functions that are of some use. No more continuity, or else continuity but no derivatives, etc. More than this, from the point of view of logic, it is these strange functions that are the most general; those that are met without being looked for no longer appear as more than a particular case, and they have only quite a little corner left them. Formerly, when a new function was invented, it was in view of some practical end. Today they are invented on purpose to show our ancestors' reasoning at fault, and we shall never get anything more than that out of them.