John Milnor observed that a theorem due to Witt implied the existence of a pair of 16-dimensional tori that have the same spectrum but different shapes.

However, the problem in two dimensions remained open until 1992, when Gordon, with coauthors Webb and Wolpert, constructed a pair of regions in the Euclidean plane that have different shapes but identical eigenvalues (see figure on right).

In 1993 she found isospectral Riemannian manifolds which are not locally isometric and, since that time, has worked with coauthors to produce a number of other such examples.

[3][5] In 2001 Gordon and Webb were awarded the Mathematical Association of America Chauvenet Prize for their 1996 American Scientist paper, "You can't hear the shape of a drum".

In 1990 she was awarded an AMS Centennial Fellowship by the American Mathematical Society for outstanding early career research.