Mathematicians Are Trying to ‘Hear’ Shapes—And Reach Higher Dimensions
More than 50 years ago Polish-American mathematician Mark Kac popularized a zany but mathematically deep question in his 1966 paper “Can One Hear the Shape of a Drum?” In other words, if you hear someone beat a drum, and you know the frequencies of the sounds it makes, can you work backward to figure out the shape of the drum that created those sounds? Or can more than one drum shape create the exact same set of frequencies?
Kac wasn’t the first person to pose this or related questions, but he garnered considerable attention for the subject. In 1968 he won the Mathematical Association of America’s Chauvenet Prize, which is focused on mathematical exposition, for his 1966 paper. “It’s really well written and very widely accessible,” says Julie Rowlett, a mathematician at Chalmers University of Technology in Sweden.
Kac’s work pushed these problems, which fall into a mathematical field called isospectral geometry, further into the limelight, inspiring researchers to ask similar questions for different shapes and surfaces. Their work ignited an area of research that is still active and growing today.
