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Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.
Both Herman Weyl and john von Neumann opined that mathematics can get too ornate and Gothic if it gets too far from physical sciences (The World of Mathematics). But the same Weyl said that Galois Theory is one the greatest achievements of the humand mind (some thing to that effect quoted in Jacobson's Basic Algebra) and I do not see any connection with Physics in the theory or its origins. I think that Arnold has strong opinions and there is some truth in such statements.
Hi SwarupI thought I would post the comment because it is so far from the mainstream. I think it is too limted a view, but then Arnold is a far greater mathematician than I will ever be.. And I think his point is perfectly valid in matters of teaching. Cheers!
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