What type of mathematical problems interesting for TCS researchers?
Let us say I am able to give an algorithm which classifies all modules (algebraic structure) of some rank. Will that be interesting to TCS researchers?


Roughly speaking...


It will be interesting to applied mathematicians if they find that the algorithm is fast enough in practice in some sense. 
It will be interesting to pure mathematicians if the algorithm gives new insight into the structure of modules or lets them compute examples that can be used to test conjectures.
And will be interesting to TCS researchers if there are also lower bounds on how fast an algorithm for this problem can possibly be, or if this problem is related to algorithms for other problems such as classifying rings, module isomorphism etc.


An example that was interesting to all three to varying degrees is Tarski's theorem on the real field.