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Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.

10 votes
4 answers
2k views

Why are operads so closely connected to mathematical physics?

Mark Sapir's question inspired me to ask the question in the title. A lot of mathematicians who have done work related to mathematical physics (e.g Kontsevich, Stasheff, Getzler, Manin, etc.) have don …
Jim Conant's user avatar
  • 4,898
39 votes

What makes four dimensions special?

It's the only dimension in which the smooth Poincare conjecture is still open. It's the only dimension in which $\mathbb R^n$ has a nonstandard smooth structure. (In fact uncountably many of them.) …