Re: A well kept secret?

[Ronnie Brown <ronnie.profbrown@btinternet.com>]

First a slight correction:  The paper referred to was I think

Wigner, E.P., The Unreasonable Effectiveness of Mathematics in the
Natural Sciences, Comm. in Pure Appl. Math. (1960), reprinted in
Symmetries and reflections: scientific essays of Eugene P. Wigner,
Bloomington Indiana University Press (1967). Here are some
quotations from this article:
-------------------------------------------------------------------------
... that the enormous usefulness of mathematics in the physical
sciences is something bordering on the mysterious, and that there is
no rational explanation for it.

Mathematics is the science of skilful operations with concepts and
rules invented just for this purpose. [this purpose being the
skilful operation ....]

The principal emphasis is on the invention of concepts. The depth of
thought which goes into the formation of mathematical concepts is
later justified by the skill with which these concepts are used.

The statement that the laws of nature are written in the language of
mathematics was properly made three hundred years ago; [it is
attributed to Gallileo] it is now more true than ever before.

The observation which comes closest to an explanation for the
mathematical concepts cropping up in physics which I know is
Einstein's statement that the only physical theories which we are
willing to accept are the beautiful ones. It stands to argue that
the concepts of mathematics, which invite the exercise of so much
wit, have the quality of  beauty.
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There is also a question of what is expected from a mathematical
area. At a conference in Baku in 1987 I was asked `what are the big
theorems in category theory? People sometimes want to know:`What are
the big problems in category theory?' That these `big' things may
not exist (comments?) does say something about the nature of
category theory, and also of mathematical progress, and what this is
conceived of by various groups of mathematicians.. Part of
Grothendieck's success was his aims for maximum generality and for
making things tautological. So some simple things (to category
theorists) like `left adjoints preserve colimits' are very useful in
a variety of fields, and make tautological some apparently difficult
procedures. And also allow analogies between different fields. Hence
my paper with Tim Porter: `Category theory: an abstract basis for
analogy and comparison'. (Just one aspect, of course.)

Ronnie Brown

Zinovy Diskin wrote:
 > 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.
 >
...

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