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

TRANSFORMATION 171
And, now, rightly using the term " rhetoric" to
denote the art of expression by speech, my thesis is that
mathematicians are all of them devoted rhetoricians and
the best of them masters of the art. The thesis is not
difficult to maintain. For what does the art demand?
What are the first qualities of Style? Clarity? Energy?
Order? Unity? Convincingness? Restraint? Beauty?
In respect to these things no literature surpasses the
literature of mathematics. It may not indeed be easy
to understand, for the understanding of it requires a fair
measure of mind,-imagination, especially, and logical
sense,-but the difficulty inheres in the subject and not
in the manner of handling it, for the latter is clearclear in its definitions, clear in its enunciations, clear in
its demonstrations; its energy may not be easy to feel,
for the feeling of it requires a certain order of sensibility,
but energy is always present in a high degree-indeed
the whole vast symbolism of mathematics, invented with
a view to the effective use of intellectual energy, is charged
therewith beyond the measure of common words; its
order may not be easy to appreciate, for it is the order of
logic,, beginning with principles and pursuing their
destined consequences under the subtle rule of fate; its
unity may not be easy to grasp, for it is the unity of a
whole owing its integrity to the inner bond of implication;
its convincingness may not be easy to sense for it is disinterested, dispassionate, purely intellectual, ideal; its
restraint is the restraint of direct achievement by the
simplest means; and its-Beauty? Its beauty is twofold: the exquisite austere beauty of sheer form; and a
unique kind of dictional beauty, due to the union, in mathematical nomenclature, of two qualities not elsewhere
united. I mean a certain literary quality, not essential