Mathematics is an experimental science, and definitions do not come first, but later on.

Mathematics is an experimental science, and definitions do not come first, but later on.

It is shocking that young people should be addling their brains over mere logical subtleties in Euclid's Elements, trying to understand the proof of one obvious fact in terms of something equally .. obvious.

...there is no absolute scale of size in nature, and the small may be as important, or more so than the great.

Facts are of not much use, considered as facts. They bewilder by their number and their apparent incoherency. Let them be digested into theory, however, and brought into mutual harmony, and it is another matter.

Why should I refuse a good dinner simply because I don't understand the digestive processes involved?

Ohm (a distinguished mathematician, be it noted) brought into order a host of puzzling facts connecting electromotive force and electric current in conductors, which all previous electricians had only succeeded in loosely binding together qualitatively under some rather vague statements. Even as late as 20 years ago, "quantity" and "tension" were much used by men who did not fully appreciate Ohm's law.