Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

404 MATHEMATICAL PHILOSOPHY
tice that what we are now to discuss is the psychology of
logic. For our present purpose it is better, however,
to say psychology of mathematics; the other title is too
unfamiliar.
It is my aim to signalize the importance of the subject, to suggest a few of its problems, and thus possibly
to incite some mathematician to acquire sufficient psychological competence, or some psychologist to acquire
sufficient mathematical competence, to deal with it effectively. The subject no doubt possesses great interest in
itself. "The genesis of mathematical discovery," says
Poincaré in Science and Method, "is a problem which
must inspire the psychologist with the keenest interest."
But that is not the main point. The main point is that
the general neglect of the subject by competent men
throughout the centuries has greatly retarded the progress of science; it has, in the first place, retarded the
progress of mathematics and it has thus retarded the
progress of all the sciences whose prosperity depends
upon that of mathematics. That such is the case, a few
considerations will make sufficiently evident.
Consider, for example, the birth and development of
the concept of hyperspaces, which, as we saw in a
previous lecture, is less than a hundred years old.
We have noted its great importance for mathematics,
for physical science and for philosophy. Why was
the advent of this great concept so long delayed? The
answer is: because the psychology of mathematics was
so little understood. For many centuries the concept in
question had been knocking at the door but it was not
admitted because psychologically ignorant mathematicians
and psychologically ignorant philosophers believed that
mathematical concepts, if they be not indeed concepts