One thing I've noticed is that some of the great problems, such as Fermat's Last Theorem, spawned entire fields of math, from which applications may have developed. It wouldn't shock me if some advances in cryptography were spinoffs of progress in pure math.

Then there's the prize for progress towards understanding the Navier-Stokes equation of fluid dynamics.

The answer to both is quite possibly, but we don't know. History has seen many mathematical curiosities gaining important practical applications, sometimes hundreds of years later. Indeed, much of computer science is based upon mathematics which was at one time impractical. A good example is strong encryption, the foundations for which were built long before we had machines that were able to implement it.