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.

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

Euclid for children is barbarous.

Electric and magnetic forces. May they live for ever, and never be forgot, if only to remind us that the science of electromagnetics, in spite of the abstract nature of its theory, involving quantities whose nature is entirely unknown at the present, is really and truly founded on the observations of real Newtonian forces, electric and magnetic respectively.

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?

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.

Criticized for using formal mathematical manipulations, without understanding how they worked: Should I refuse a good dinner simply because I do not understand the process of digestion?