4 GERO VON RANDOW

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.