In 1891, Stäckel's habilitation thesis, Integration of Hamiltonian-Jacobian differential equations by means of separation of variables, was accepted by the University of Halle, near Leipzig, and he took up a lectureship there.
Sa 1891, Stäckel's habilitation sanaysay, Integration ng Hamiltonian-Jacobian kaugalian equation sa pamamagitan ng paghihiwalay ng variable, ay tinanggap ng University of Halle, malapit sa Leipzig, at siya ay kinuha ng isang paglelektyur doon.