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.

Mathematics is of two kinds, Rigorous and Physical. The former is Narrow: the latter Bold and Broad. To have to stop to formulate rigorous demonstrations would put a stop to most physico-mathematical inquiries. Am I to refuse to eat because I do not fully understand the mechanism of digestion?

Shall I refuse my dinner because I do not fully understand the process of digestion?

Euclid for children is barbarous.

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

The best result of mathematics is to be able to do without it.

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

Logic can be patient, for it is eternal.

If it is love that makes the world go round, it is self-induction that makes electromagnetic waves go round the world.

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

Theory is the essence of facts. Without theory scientific knowledge would be only worthy of the madhouse.

We do not dwell in the Palace of Truth. But, as was mentioned to me not long since, There is a time coming when all things shall be found out. I am not so sanguine myself, believing that the well in which Truth is said to reside is really a bottomless pit.

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.

However absurd it may seem, I do in all seriousness hereby declare that I am animated mainly by philanthropic motives. I desire to do good to my fellow creatures, even to the Cui bonos.