Hey, I'm a mathematician, not a physicist. We tend only to get as far as "oh yeah, here's all this pretty math we care about. I hear it has some applications to physics..."
Sure. Moonshine I know a lot about, relative to physics at least. Given that I now work somewhere that specializes in term embeddings, it kind of feels like I've spent half my life injecting stuff into vector spaces...
I originally wrote the puzzle without reference to string theory, then added the "extra credit" part mainly as a hint.