I will not exaggerate. Theoretical abstraction and freedom of thought are
needed in every discipline, from theology to physics. Nor do mathematicians play
around arbitrarily with their axioms or ground rules. Not every freely chosen no-
tation, assumption, or transformation rule yields something meaningful, something
interesting, something practical, nor even a research contract for sure. Mathemat-
ical freedom is an idea that is never applied outside a framework. But it gives
strength to the discipline.
“The essence of mathematics lies in its freedom”, wrote Georg Cantor, the
great mathematician. This freedom should be made visible in elementary and high
school classes. This is not to be had without formal stringency, and not without
concentrated learning, I would say “cramming”.
Many beautiful rewards beckon to anyone who enrolls in mathematics, as a
pupil in an advanced course, as a student, or as a late entrant. These rewards
include the capacity to solve problems creatively—it is no accident that personnel
departments are so interested in mathematicians (and physicists)—and the abil-
ity to estimate the plausibility of claims and calculations. By the same token one
acquires the capacity to concentrate mentally. And one who knows the most im-
portant methods of mathematics can work himself quickly into a new area.
So in the meantime it has become cool to be a mathematician. I envy them
all, just for this reason.
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