Forty years ago, mathematician Mark Kac asked the theoretical question, "Can one hear the shape of a drum?" If drums of different shapes always produce their own unique sound spectrum, then it should be possible to identify the shape of a specific drum merely by studying its spectrum, thus "hearing" the drum's shape (a procedure analogous to spectroscopy, the way scientists detect the composition of a faraway star by studying its light spectrum). But what if two drums of different shapes could emit exactly the same sound? If so, it would be impossible to work backward from the spectrum and uniquely surmise the physical structure of the drum, because there would be more than one correct answer to the question. The drum research is important to the world of quantum mechanics.