Mathematics are at the core of scientific economics.
Mathematics are at the core of technological progress, so implicitly at the core of economic progress.
However, mathematics are a rational approach while most decisions seem to be based on a bounded rationality approach or a political approach. This is true because there is never enough time and data available for a rational approach.
Mathematics come into place for programmed decisions, while they are of less use for non-programmed decisions.
Economic progress is driven by goals and resources allocation towards those goals. As goals are set by bounded rationality/political decisions, the allocation is where rationality plays a more important role. So i suspect mathematics can be used there, as while the goals are set, the allocation should be as rational as possible given the circumstances.