Does compressed sensing count as math? If it does, here is a blog post from the horse's mouth.
Edit: For those who would like a popular article, here is a good one in Wired (by JSE if I'm not mistaken). Also, it is encouraged to read the highly upvoted comment by JSE below.
Because I don't think I can ever explain it better than Terence Tao's brilliant blog post or think I'm qualified either, I'll just refer to the blog, and here simply mention in which field I, as someone working on combinatorial design theory, personally stumbled on it as an interactions between fields (Please read the following only when you have nothing better to do.). I hope experts edit and improve this post.
I had heard good things about compressed sensing before, but the first paper I read was about its application to error correction by Candes, Rudelson, Tao, and Vershynin. I don't know if it's comparable to other recent truly remarkable progress in coding/information theory (e.g., polar coding, which could be a candidate for the answer to OP's question), but it was a refreshing read to me who dabble in coding theory. It's in one sense similar to normal linear codes in that the goal is to recover a vector $f \in R^n$ by knowing $y = Af +e$, where $A$ is an $m$ by $n$ matrix and $e \in R^m$ is the error vector. But the paper studies when $f$ is uniquely determined by $l_1$-minimization a la compressed sensing. Then I learned that some combinatorial design theorists I follow were applying design theory to compressed sensing, in a very rough sense, to give a nice deterministic method for explicitly providing ideal $A$. And when I checked what was up in quantum information these days (I also dabble in quantum information), I ran into this paper by Gross, Liu, Flammia, Becker, and Eisert, where compressed sensing is applied to quantum state tomography, a method for determining the quantum state of a system. And this is the one paragraph version of how I wound up with an endless to-read backlog of papers spanning multiple fields.