rationalskepticism.org

To be fair to pure mathematicians, their brief consists of examining the behaviour of the entities within their axiomatic systems, and pure mathematicians don't pretend (with the odd cranky exception) that the systems they work with are necessarily reflective of the real world. The job of deciding which of those sets of entities and interactions does model the real world is properly the purview of applied mathematicians. The pure mathematician's job is to make sure that the underlying mathematics chosen for a model is internally consistent and rigorous.