Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.

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

The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new, but to the continuous evolution of zoologic types which develop ceaselessly and end by becoming unrecognisable to the common sight, but where an expert eye finds always traces of the prior work of the centuries past. One must not think then that the old-fashioned theories have been sterile and vain.

One does not ask whether a scientific theory is true, but only whether it is 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.

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

Mathematical discoveries, small or great are never born of spontaneous generation They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.