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

LECTURE XIX
The Psychology of Mathematics
RETARDATION OF MATHEMATICS AND SCIENCE BY BACKWARD PSYCHOLOGY-PSYCHOLOGY OF MATHEMATICS
ESSENTIAL TO BEST MATHEMATICAL TEACHINGQUESTIONS FOR PSYCHOLOGISTS-SYMMETRY OF
THOUGHT AND ASYMMETRY OF IMAGINATION.
IN the preceding lecture we saw that a little study in
the "mathematics of psychology" led us quickly and
naturally into the "psychology of mathematics" and even
into that of science in general. Yet we are now going to
discuss the "psychology of mathematics" as if its field
were well defined and did not run into all other subjects,
which, in their turn, penetrate it. Nature does not greatly
respect our little academic custom of carving her up and
calling the pieces departments of study. Chemistry,
physics, mechanics, geometry, metaphysics, psychology,
logic, ethics, esthetics, and the rest all penetrate and
overflow the walls we surround them with, and mingle
their waters in one vast sea. In the great world of
Nature,-the subject of all thought,-there are emphases
indeed but no fixed divisions corresponding to our pretty
ologies, ographies, and ics, and even the emphases perpetually shift their incidence. And yet there is a sense
in which such divisions and walls are not artificial but are
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