It's cool to look over Andrew Wiles' 100-page proof of Fermat's Last Theorem (i.e., prove that no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than two).
For mere mortals like myself, the Wikipedia article is cool as well. Obviously, the map between R and T is an isomorphism if and only if two abelian groups occurring in the theory are finite and have the same cardinality.
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