Ha. I have a similar story with chemistry/spectroscopy and representation theory. I was taking a chemistry class where we were learning by rote how to apply th

Ha. I have a similar story with chemistry/spectroscopy and representation theory. I was taking a chemistry class where we were learning by rote how to apply the Grand Orthogonality Theorem. We were clearly computing inner products, but I couldn't suss out the big picture and the chem professor didn't know either, so I went to the math department and joined a seminar, which happened to be almost nextdoor to the chemistry class. The professor teaching it had never heard of the applications to chemistry/spectroscopy, though he was delighted to find out. Not 30 yards apart, two groups of people were approaching the same subject from opposite angles with zero awareness of each other. Silos are amazing.