Examples of "Unrelated" Mathematics Playing a Fundamental Role in TCS? Please list examples where a theorem from mathematics which was not normally considered to apply in computer science was first used to prove a result in computer science.  The best examples are those where the connection was not obvious, but once it was discovered, it is clearly the "right way" to do it.

This is the opposite direction of the question Applications of TCS to classical mathematics?

For example, see "Green's Theorem and Isolation in Planar Graphs", where an isolation theorem (which was already known using a technical proof) is re-proven using Green's Theorem from multivariate calculus. 

What other examples are there?
Maurice Herlihy, Michael Saks, Nir Shavit and Fotios Zaharoglou got the Godel prize in 2004 for their use of algebraic topology in the study of some problems in distributed computing.