A set of problems and and its concepts can be represented as a model. Mathematical modelling can help us better understand, reason and operate. The beauty of a mathematical model is that it can be adapted for a computer using well established techniques.
For example, if you have a model that has a lot of graph like data, use graph theory, If you have a lot of equations, use algebra.
A really good article on the matter is this one by Arnold Neumaier, it gives a great overview on the subject.