weemba@brahms.BERKELEY.EDU (Matthew P. Wiener) (04/01/86)
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. "In the thirties, under the demoralizing influence of quantum-theoretic perturbation theory, the mathematics required of a theoretical physicist was reduced to a rudimentary knowledge of the Latin and Greek alphabets" -R Jost ucbvax!brahms!weemba Matthew P Wiener/UCB Math Dept/Berkeley CA 94720
bhuber@sjuvax.UUCP (04/02/86)
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
weemba@brahms.BERKELEY.EDU (Matthew P. Wiener) (04/05/86)
In article <3008@sjuvax.UUCP> bhuber@sjuvax.UUCP (B. Huber) writes: >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. True. But it was pretty poor in the half-century 1915-65 I listed. In particular, mutual inability to understand was extremely widespread, and unfortunately is still rather large. For example, physicists developed the notion of gauge field theories and mathematicians of principal fiber bundles, and the two fields had no idea that they were working with the same object for the longest time. The worst problem is that having gone their own ways, there is now an incredibly large language gap. ucbvax!brahms!weemba Matthew P Wiener/UCB Math Dept/Berkeley CA 94720