Das Kalenderblatt 090705

05/07/2009 - 00:23 von WM | Report spam
Modern mathematics as religion

[...] Most (but not all) of the difficulties of Set Theory arise from
the insistence that there exist `infinite sets', and that it is the
job of mathematics to study them and use them.
In perpetuating these notions, modern mathematics takes on many of the
aspects of a religion. It has its essential creednamely Set Theory,
and its unquestioned assumptions, namely that mathematics is based on
`Axioms', in particular the Zermelo-Fraenkel `Axioms of Set Theory'.
It has its anointed priesthood, the logicians, who specialize in
studying the foundations of mathematics, a supposedly deep and
difficult subject that requires years of devotion to master. Other
mathematicians learn to invoke the official mantras when questioned by
outsiders, but have only a hazy view about how the elementary aspects
of the subject hang together logically.
Training of the young is like that in secret societiesimmersion in
the cult involves intensive undergraduate memorization of the standard
thoughts before they are properly understood, so that comprehension
often follows belief instead of the other (more healthy) way around. A
long and often painful graduate school apprenticeship keeps the cadet
busy jumping through the many required hoops, discourages critical
thought about the foundations of the subject, but then gradually
yields to the gentle acceptance and support of the brotherhood. The
ever-present demons of inadequacy, failure and banishment are however
never far from view, ensuring that most stay on the well-trodden
The large international conferences let the fellowship gather together
and congratulate themselves on the uniformity and sanity of their
world view, though to the rare outsider that sneaks into such events
the proceedings no doubt seem characterized by jargon, mutual
incomprehensibility and irrelevance to the outside world. The official
doctrine is that all views and opinions are valued if they contain
truth, and that ultimately only elegance and utility decide what gets
studied. The reality is less ennoblingthe usual hierarchical
structures reward allegiance, conformity and technical mastery of the
doctrines, elevate the interests of the powerful, and discourage
There is no evil intent or ugly conspiracy herethe practice is held
in place by a mixture of well-meaning effort, inertia and self-
interest. We humans have a fondness for believing what those around us
do, and a willingness to mold our intellectual constructs to support
those hypotheses which justify our habits and make us feel good.

[Set Theory: Should You Believe?
N J Wildberger
School of Maths UNSW Sydney NSW 2052 Australia
webpages: http://web.maths.unsw.edu.au/~norman]


Gruß, WM

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#1 Herbert Newman
05/07/2009 - 00:40 | Warnen spam
Am Sat, 4 Jul 2009 15:23:21 -0700 (PDT) schrieb WM:

[N J Wildberger]

Mathematical crankhood as a religion

[...] Most (but not all) of the difficulties of "crank theories" arise from
the insistence that there doesn't (actually) exist 'infinite sets', and
that it _must not_ be the job of mathematics to study them and use them.
[Infinite sets are evil!] In perpetuating these notions, mathematical
[especially set-theoretic] crankhood takes on many of the aspects of a
religion; actually set-theoretic cranks very often act like religious
fanatics. [etc. etc.]


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