I can't argue for pure math. But atleast in applied areas such as pde a lot of the problems are motivated by real physical problems. To solve many of these would require theoretical breakthroughs I guess (cant be sure I dont have a phd). So perhaps funding pure math may not be such a bad idea.
I always find the example of PDEs interesting, depending on which mathematician you talk to PDEs could be anywhere from "as pure as it gets" to "extremely applied"
I believe this demonstrates the spectrum of pde research. You have people from both ends contributing. Since functional analysis gets used a lot in pdes especially when dealing with weak solutions it would make sense that it appeals to be pure math folks. But once you find ways to construct viable test functions it becomes the basis for writing numerical schemes. So that appeals to the applief guys and of course once you have the numerical solution this can be used for engineering. This demonstrates a good pipeline for "consuming" science (of course assuming this pipeline is indeed correct). However take any component out and the value creation wont be that high. Perhaps finding more such pipelines for pure math woulf help evaluate its valur.
