Re: Real world and mathematics

On Jul 25, 4:20 am, "porky_pig...@xxxxxxxxxxx" <porky_pig...@my-
deja.com> wrote:
On Jul 24, 4:48 pm, gandalf <gandalf1...@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, even though both were/are highly accomplished mathematicians. How dare they break ranks?

**********************************************************

J. von Neumann was giving his personal opinion when he wrote the
above. he wasn't doing any maths and, of course, there is no proof of
his words. Plainly an opinion.

Arnold, from the very start, throws himself into a well of nonsense:
he begins stating that mathematics is a part of physics: complete
rubbish. After that little is worth reading.

Nevertheless, I must agree with some of the words of Neumann. We have,
for example, that piece of huge nonsense called "category theory"
which, under the disguise of dealing with mathematical structures, in
particular algebraic ones, builds up a huge, smoking pile of BS.
Of course, there are PARTS in categories that can be handy in several
instances: some functorial properties (e.g., in algebraic topology),
some universal ones, etc., but to call this a "theory" and make it a
part of mathematics worth studying by itself seems to me a big
nonsense. Of course, this is only my opinion.

Regards
Tonio
.

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