"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."

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

"Geometry is the art of correct reasoning from incorrectly drawn figures."

"The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful."

"[T]he different branches of Arithmetic - Ambition [G]eometry is not true, it is advantageous."