"Derrière la série de Fourier, d'autres séries analogues sont entrées dans la domaine de l'analyse; elles y sont entrees par la même porte; elles ont été imaginées en vue des applications.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."

"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."

"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."

"If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science."

"Mathematics is the art of giving the same name to different things."

"One geometry cannot be more true than another; it can only be more convenient."

"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."

"Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered."

"It is the simple hypotheses of which one must be most wary; because these are the ones that have the most chances of passing unnoticed."