Einstein, then in a member of the Prussian Academy of Sciences in Berlin, was working on his general theory of relativity when he contacted Carathéodory asking for clarifications on the Hamilton-Jacobi equation and canonical transformations. He wanted to see a satisfactory derivation of the former and the origins of the latter. Einstein told Carathéodory his derivation was "beautiful" and recommended its publication in the "Annalen der Physik." Einstein employed the former in a 1917 paper titled "Zum Quantensatz von Sommerfeld und Epstein" (On the Quantum Theorem of Sommerfeld and Epstein). Carathéodory explained some fundamental details of the canonical transformations and referred Einstein to E.T. Whittaker's "Analytical Dynamics". Einstein was trying to solve the problem of "closed time-lines" or the geodesics corresponding to the closed trajectory of light and free particles in a static universe, which he introduced in 1917.