Quotes of All Topics . Occasions . Authors
Euclid for children is barbarous.
Logic can be patient, for it is eternal.
Waves from moving sources: Adagio. Andante. Allegro moderato.
The best result of mathematics is to be able to do without it.
Shall I refuse my dinner because I do not fully understand the process of digestion?
Mathematics is an experimental science, and definitions do not come first, but later on.
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.
...there is no absolute scale of size in nature, and the small may be as important, or more so than the great.
If it is love that makes the world go round, it is self-induction that makes electromagnetic waves go round the world.
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.
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?
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.
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.
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.
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?
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.
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.
Now, in the development of our knowledge of the workings of Nature out of the tremendously complex assemblage of phenomena presented to the scientific inquirer, mathematics plays in some respects a very limited, in others a very important part. As regards the limitations, it is merely necessary to refer to the sciences connected with living matter, and to the ologies generally, to see that the facts and their connections are too indistinctly known to render mathematical analysis practicable, to say nothing of the complexity.