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142 votes
17 answers
23k views

What makes four dimensions special?

Do you know properties which distinguish four-dimensional spaces among the others? What makes four-dimensional topological manifolds special? What makes four-dimensional differentiable manifolds ...
74 votes
16 answers
8k views

Geometric / physical / probabilistic interpretations of Riemann zeta($n>1$)?

What are some physical, geometric, or probabilistic interpretations of the values of the Riemann zeta function at the positive integers greater than one? I've found some examples: 1) In MO-Q111339 ...
67 votes
14 answers
23k views

A reading list for topological quantum field theory?

Can you suggest a reading list, or at least a few papers that you think would be useful, for a beginner in topological quantum field theory? I know what the curvature of a connection is, know basic ...
97 votes
9 answers
7k views

Examples where physical heuristics led to incorrect answers?

I have always been impressed by the number of results conjectured by physicist, based on mathematically non-rigorous reasoning, then (much) later proved correct by mathematicians. A recent example is ...
147 votes
43 answers
61k views

Where does a math person go to learn quantum mechanics?

My undergraduate advisor said something very interesting to me the other day; it was something like "not knowing quantum mechanics is like never having heard a symphony." I've been meaning to learn ...