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.

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

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

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

Euclid for children is barbarous.

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

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?