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Mathematics is often called the language of science, yet mathematics --
like a natural language -- is constantly evolving. (Note that Newton
had to found an entirely new branch of mathematics in order to describe
the physics of motion.) Most of the mathematics which is part of the
standard physics curriculum today is from the 19th century or earlier.
Is 19th century mathematics adequate for 21st century physics? I
believe that it is not, and will give examples drawn from condensed
matter as well as high energy theory.
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