Re: Real world and mathematics

In article
<9036466.1216932569704.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
gandalf <gandalf1479@xxxxxxxxxxx> wrote:

John von Neumann:
"As a mathematical discipline travels far from its empirical source, or still
more, if it is a second and third generation only indirectly inspired by
ideas coming from "reality" it is beset with very grave dangers. It becomes
more and more purely aestheticizing, more and more purely I'art pour I'art.
This need not be bad, if the field is surrounded by correlated subjects,
which still have closer empirical connections, or if the discipline is under
the influence of men with an exceptionally well-developed taste. But there is
a grave danger that the subject will develop along the line of least
resistance, that the stream, so far from its source, will separate into a
multitude of insignificant branches, and that the discipline will become a
disorganized mass of details and complexities. In other words, at a great
distance from its empirical source, or after much "abstract" inbreeding, a
mathematical subject is in danger of degeneration."

V. I. Arnold also said pretty much the same things
(http://pauli.uni-muenster.de/~munsteg/arnold.html).

Of course no professional mathematician took either of them seriously,

Ridiculous, a complete nonstarter.

even
though both were/are highly accomplished mathematicians. How dare they break
ranks?

I totally understand and support what von Neumann and Arnold were saying.

Mathematics today has no resemblance to the real world, and never will have
again.

You are seriously out of touch with mathematics.

I sometimes feel there is almost a cartel at work, a massive clan of
academics, whose sole purpose is to justify their existence by developing
theory after more esoteric theory, none of which actually matters. They need
to do this because people need their PhDs, academics need to keep the
hundreds of millions of dollars of grants flowing, and they need to keep
publishing to go from being assistant processors to associate professors to
professors to emeritus.

Itâ??s their livelihood. Do we really expect them to rock the boat? What if the
grants stop, or if the public start questioning the value of keeping up these
behemoths that are pure maths departments?

Just like the credit crunch and the financial services industry today, the
higher mathematics community just another industry that is not interested in
governing itself. They couldn't care less.

Sometimes I think itâ??s even worse than that. I almost think mathematicians
actually enjoy living in their fairy-tale land, in their make-believe world
that they have created because they canâ??t handle the real world.

Here are some sample topics of recent papers taken from a randomly chosen
journal:
· "A Banach space without a basis which has the bounded approximation
property"
· "A characterization of all elliptic algebro-geometric solutions of the AKNS
hierarchy"
· "A class of idempotent measures on compact nilmanifolds"

If you think any of these have any resemblance with the world we live in (or
people writing these have the slightest interest about the real world), you
are living in the same cloud-cuckoo land.
.

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