[Huxley] says ‘mathematical training is almost purely deductive. The mathematician starts with a few simple propositions, the proof of which is so obvious that they are called self-evident, and the rest of his work consists of subtle deductions from them’…we are told [by Huxley] that Mathematics is that study which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation.

I think no statement could have been made more opposite to the undoubted facts of the case, that mathematical analysis is continually invoking the aid of new principles, new ideas and new methods, not capable of being defined by any form of words, but springing directly from the inherent powers and activity of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world…that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords boundless scope for the exercise of the highest efforts of imagination and invention.