I sometimes have to defend math in the world. Normally, I follow Hardy and say that the reason to do math is not because it’s useful but because it’s beautiful. Every once in a while, though, it’s worth bringing up an application because it’s just so cool. Gunther Uhlmann in my department is on a team that’s closing in on making the cloak of invisibility a reality.
My understanding is that Gunther works on inverse problems, such as the one that oil companies are very interested in: if you have, say, sonar readings of an undersea or underground regions, can you figure out what’s down there? Gunther was working on general versions of the problem and noticed that under certain conditions the readings would totally miss pockets underground. And the same principle, perhaps, can be extended to light waves bouncing off objects. Pretty amazing stuff.