Many academia mathematicians are happiest when they can find NO real world application to their research. They want to have nothing to do with reality and live in a world of math logic and symbols. They bemoan the fact that a significant portion of mathematics is currently applied to other problems. For example, Pierre-Simon Laplace created Laplace transforms to do research on Probability theory. Now we use Laplace transforms for many things, including hearing aids and speaker phones. But some mathematician professors work very hard to make their research applicable to something. They work to solve a specific problem. And sometimes they get very meaningful results. Helpful even!
Okay, but what happens next? How does the brilliant professor get his information to the hands of other who need it or could use it? Well, he usually starts by publishing a paper in order to get credit for his work. But the professor is not a publist. (In fact he might be quite socially awkward!) A speaker I heard this past week said something amazing about this process. He says we (academic professors) lob our papers over the Academic Great Wall and “hope to God someone is there to pick them up and use them!” I drew a sketch about it my feelings on the topic: