  The present note is a feedback on the article by M.O. Katanaev in "Physica
Scripta" (2023, 98, 104001), where, in our opinion, a distorted view of the
classical theory of separation of variables in the Hamilton-Jacobi equation is
given. We show that the metrics given in this paper, addmiting separation of
variables, are special cases of V.N. Shapovalov metrics ("Siberian Mathematical
Journal", 1979, 20, 790), finally obtained in the 70s of the last century. The
results of the article in question, unlike the original ones, do not have
scientific novelty and contain omissions and incorrect statements.
