"Philosophically, the reason research in math matters is that by pursuing math ideas that are deep and interesting for their own sake, you will get real-world applications in the future," Hofmann said.
"It is like making investments."
When I decide to indulge my students when they whine, "When are we ever gonna have to use this?", sometimes I point to my "When are we ever gonna have to use this" poster which lists dozens of jobs and the math knowledge necessary for those jobs. Other times I tell them about the laser--a device that had no practical application when it was invented in the 50s but now allows us to correct eyesight and listen to music.