Connections of theory of computability and Turing machines to other areas of mathematics The question is quite straightforward:
Could you point out some reference papers that highlight (in a way that is fairly accessible) the connections between (1) theory of computability, algorithms, and Turing machines and (2) other areas of mathematics.

Linear and Integer Programming utilize these a lot. I read a paper for my IP class showing that there is no algorithm to solve IPs with quadratic constraints. It was proven by a reduction to Hilbert's Tenth Problem, which is unsolvable. The reduction had a standard computability feel to it. Hilbert's Tenth Problem deals with satisfying arbitrary Diophantine equations.
Graph theory and combinatorics are the obvious places where algorithms come into play. 
Game theory is really starting to benefit from computer science and algorithms. Algorithmic game theory is a very hot topic with applications to economics and AI. Computability comes up some too: 
http://arxiv.org/abs/1204.0198 
http://link.springer.com/article/10.1007%2FBF01212014 
http://econpapers.repec.org/paper/fthcambri/153.htm
