Cipra, Barry, You can't hear the shape of a drum, Science 255 (27 March 1992) 1642-1643.
In 1966, Mark Kac asked "Can you hear the shape of a drum?" (American Mathematical Monthly 73 (4, Part II) 1-23). In one dimension, the answer is yes (the length of a violin string is determined by the lowest frequency produced by plucking it); in dimensions greater than two, the answer is no (there are "hyperdrums" of different shapes that make the same "hypersounds"). What about dimension 2? For a vibrating membrane, are the size and shape of the bounding curve uniquely determined by the eigenvalues of the wave motions of the membrane? Kac thought not, but "I may well be wrong and I am not prepared to bet large sums either way." Perhaps he should have trusted his intuition, because Carolyn Gordon and David Webb (Washington University) and Scott Wolpert (University of Maryland) have exhibited counterexamples at last.
This review was reprinted with permission from Mathematics Magazine, June 1992 issue.