Saturday, October 31, 2009

Mathematics and Physics

Let me have the luxury of day-dreaming a little about the connection between mathematics and physics. To me it seems that the separation took place only about a 100 years ago. Perhaps Poincare did not consider himself either a mathematician or a physicist, but both. But the reason for this post is a reaction to some thoughts that have been in my mind for some time. Today it was catalyzed by reading a news item about the Shaw prize which was awarded to Donaldson and Taubes. It seems to me that Taubes notable achievements are in the mathematics arising from gauge theories and quantum field theories. He is concerned with various monopole solutions in part of his work. So the connection is quite clear. The other reason is the claim of objectivity in these disciplines which is supposed to transcend subjectivity, unlike in other spheres of human endeavour. But is this really so? Atiyah has written that mathematics will get a big boost from string theory, while Langlands has said that it will get a boost from quantum field theory and statistical mechanics. While there is no dispute about these, it seems to me that these are really quite subjective views in which there is a human intervention. In other words, are these assessments really objective, or is it that mathematics and physics are also like any other enterprises, guided by taste and aesthetics. This is not to say that there are no rigorous standards. Let me welcome comments.

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