Mathematicians prove that you can deduce the shape of disk based on the frequencies it produces when you hit it with a stick.
> Is it possible to deduce the shape of a drum from the sounds it makes?
That's a known problem with a (very nice) negative answer https://www.ams.org/publicoutreach/feature-column/fcarc-1997...
IIUC this article is about the problem in the other direction, i.e. from the shape (a disk!) to the frecuencies of the sound (eigenvalues).It's not about an exact calculation, but about an aproximation of them.
> The conjecture bears on the estimation of the frequencies of a round drum or, in mathematical terms, the eigenvalues of a disk.
From the research paper:
> The celebrated Pólya’s conjecture (1954) in spectral geometry states that the eigenvalue counting functions of the Dirichlet and Neumann Laplacian on a bounded Euclidean domain can be estimated from above and below, respectively, by the leading term of Weyl’s asymptotics.
<guessing> The Weyl's asymtotics is probably a good estimation of the very high frecuencies/eigenvalues, and the conjeture is probabbly that you can use the estimation as upper or lower bounds instead of just an aproximation.<guessing> [Sorry, not my area and I have not enough time to read the paper.]