Supported by Abbe, he presented his habilitation Rechnungsmethoden, die sich auf eine Erweitung des Grössenbegriffes gründen, essentially a work on abelian groups and invariant theory, to the University of Jena in 1874 and was appointed as a Privatdozent in mathematics in Jena in May of that year.
Suportado ng Abbe, ipinapahayag niya ang kanyang habilitation Rechnungsmethoden, die sich auf eine Erweitung des Grössenbegriffes gründen, isang mahalagang trabaho sa abelian grupo at invariant teorya, sa Unibersidad ng Jena sa 1874 at ay hinirang bilang isang Privatdozent sa matematika sa Jena sa Mayo ng na taon.