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In 1978, the editor Lynn Arthur Steen wrote in the preface of the volume Mathematics Today - Twelve
Informal Essays (New York: Springer, 1978):
It saddens me that educated people don't
even know that my subject exists.
- Paul R. Halmos
Mathematics does exist. It is inherent in the rational power of man, as much a part of his nature
and history as language, art, or religion. Today it is having an enormous (but often unnoticed) impact
on science and society. Abstract mathematical ideas, some more than a century old, helped make possible,
for instance, the revolution in electronics that transformed the way we communicate and the way we think.
Neither radio, television, telephone, satellites, calculators, nor computers would be possible were it not for
numerous results of pure mathematics. More recent advances in the mathematical sciences have helped improve our
ability to predict the weather, to measure the effect of environmental hazards, to study the origin of the universe,
and to project the outcomes of elections. Mathematical methods have become indispensible to the proper functioning
of our technical society.
As technology requires the techniques of applied mathematics, so applied mathematics requires the theories of the
core of pure mathematics. From mathematical logic to algebraic topology, from number theory to harmonic analysis,
abstract structures of pure mathematics are used extensively by the contemporary applied mathematician. Few specialties
of pure mathematics are immune to the demands of application. Problems and conjectures rooted in science and technology
create fast-growing thickets of theory that soon become nearly impenetrable. Across the landscape of contemporary
mathematics new species blend with old growth, creating a diverse and vigorous living resource for solving problems and
understanding structure.
Yet many educated people are oblivious to the existence or significance of this resource. What concerns they have
center on why Johnny can't add or on mathophobia , the modern jargon for the traditional feeling that
I never was any good at math . Visions of draconian teachers demanding insane memorization of meaningless
mumbo-jumbo prevent a large number of people from reacting normally to the opportunities offered by contemporary
mathematics.
A central task for history, philosophy, and didactics of mathematics is to clarify the picture of mathematics.
These sciences investigate the nature of mathematical knowledge and mathematical progress throughout
the incredibly
long and sophisticated history (Steen, ibid.) of mathematics.
During the past 20 years, history, philosophy, and didactics of mathematics gradually approached to
meet two great challenges concerning this task, both formulated in the above quote: To attach their research
closer to actual mathematical practice and
development, and to
communicate their results to a wider audience, involving the general public.
The history of the Novembertagung, as a platform for young researchers who
aim at an adequate understanding of the
nature of mathematics, also reflects this development.
Steen's observations are still pretty much up to date, as the impact of mathematics on our society and its
importance for
the understanding
of our environment has even increased.
Hence there is reason enough to keep the look off the stage of mathematics, and not to stop by just quoting:
A Mathematician is a machine for turning coffee into theorems (Paul Erdös) .
Eva Wilhelmus
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