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?

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?

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.

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.

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?