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?

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

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

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

Euclid for children is barbarous.

Waves from moving sources: Adagio. Andante. Allegro moderato.

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.