Re: A well kept secret?

[Zinovy Diskin <zdiskin@gmail.com>]

Dear Zoran,

You misunderstood my posting, or I phrased it badly, because

On Tue, Dec 22, 2009 at 11:59 AM, zoran skoda <zskoda@gmail.com> wrote:
>
> Dear Zinovy,
>
> I can say that I dislike your selling/marketing despair and do not share
> excitement in the existence of an easy niche market you propose.
>

in the list "despair-excitement-easy niche", only the second term is
true. Building mathematical models for engineering problems is a hard
business, and the suggestion to view it as a fruitful area for
categorical applications stems from optimism about the power of
category theory, rather than from despair.

I'm not going to defend the market metaphor -- it's doubtful anyway.
Still, I'd like to clarify a couple of points.

1) I think that both sources of mathematical development, the internal
one based on aesthetic criteria and consistency, and the external one
based on applications, are equally important and mutually beneficial.
Apart from posing interesting problems, applications provide novel
interpretations of formal constructs, which is always fruitful.  After
all, effectively applicable  mathematics turns out to be aesthetically
appealing as well (Eugene Vigner wrote a famous paper about this "On
inaccessible effectiveness of mathematics in natural sciences")

2) The problem of "category theory vs. mathematics" is beyond
mathematics as such. A lot of problems could be avoided if a taste for
categorical thinking were cultivated in high school, and the basics of
category theory were taught to mathematicians, scientists, engineers
at the undergrad level. But education is one of the most conservative
social institutes with a huge inertia. Turning mathematical education
towards category theory needs financial and administrative support,
and an external demand. Applications of category theory to engineering
problems would be beneficial in this respect too.

Z.


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