Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose.

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

Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.

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

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.

To invent is to discern, to choose.

This harmony that human intelligence believes it discovers in nature - does it exist apart from that intelligence? No, without doubt, a reality completely independent of the spirit which conceives it, sees it or feels it, is an impossibility. A world so exterior as that, even if it existed, would be forever inaccessible to us. But what we call objective reality is, in the last analysis, that which is common to several thinking beings, and could be common to all; this common part, we will see, can be nothing but the harmony expressed by mathematical laws.