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From: bhuber@sjuvax.UUCP
Newsgroups: net.philosophy,net.sci
Subject: Re: Completeness of Theories
Message-ID: <3008@sjuvax.UUCP>
Date: Wed, 2-Apr-86 08:47:50 EST
Article-I.D.: sjuvax.3008
Posted: Wed Apr  2 08:47:50 1986
Date-Received: Sat, 5-Apr-86 09:14:11 EST
References: <435@ccivax.UUCP> <13400007@uiucdcsp> <12239@ucbvax.BERKELEY.EDU> <695@hounx.UUCP> <721@hounx.UUCP> <12815@ucbvax.BERKEL
Reply-To: bhuber@sjuvax.UUCP (B. Huber)
Organization: St. Joseph's University, Phila. PA.
Lines: 45
Xref: linus net.philosophy:4541 net.sci:407
Summary: response to request for illustrations

In article <12815@ucbvax.BERKELEY.EDU> weemba@brahms.UUCP (Matthew P. Wiener) writes:
>In article <721@hounx.UUCP> kort@hounx.UUCP (B.KORT) writes:
>>It is interesting to note the see-saw leap frogging between the development
>>of new branches of mathematics, and their application to theoretical physics.
>>(Perhaps Matthew Wiener could help me illustrate this hand-in-hand evolution.
>>It is not an accident that Newton invented the Calculus.  It was a necessary
>>tool of thought for his elucidation of the laws of motion.)
>
>I don't plan to illustrate this hand-in-hand evolution.  I will point out
>that for about half a century, from 1915-1965, the two fields of study
>diverged quite strongly, with minimal interaction, at the expense of both
>fields.  But the last twenty years have seen a remarkable and rather
>surprising resurgence in fundamental ties and applications, both from
>mathematics to physics and vice versa.
>
>ucbvax!brahms!weemba   Matthew P Wiener/UCB Math Dept/Berkeley CA 94720

Gauss developed the intrinsic geometry of surfaces in order to survey a part
of what is now Germany, and made contributions to mechanics in his (successful)
attempts to predict motions of newly-discovered celestial objects (asteroids, I
believe).  Fourier's magnum opus La Theorie de la Chaleur indicates its
origin in physical theory.  Riemann in his habilitationschrift explicitly
speculates on the possible applications of his geometry to physics,
thereby anticipating Einstein's work forty years later.

Heisenberg et alii essentially redeveloped the theory of linear operators on
Hilbert spaces in order to suit their needs, which was a mathematical formal-
izations of the new quantum mechanics.  The theory of representations of
Lie groups was spurred on partly by the need for physicists to understand
representations of spin and orthogonal groups (1930's).

Departing a little from the pure realms of physics, it is worth remarking on
the strong and fruitful interplay between finite group/field theory and
developments in communication (e.g., Shannon's work) beginning in the middle
1940's and continuing until today.

I have not the historical knowledge or perspective to place these bits of
'mathematical culture' in any coherent framework, but they do suggest that
(in the last two centuries at least) there has never been an end to the
mutual influence of mathematical and physical inquiries.

                        bill huber ...allegra!sjuvax!bhuber
                        2 April