He specialized in internal medicine at Vienna General Hospital from 1993 to 2000. In 1995, Müller was a visiting researcher at the Laboratory for Diabetes Research in Gothenburg. From 2000 to 2001, he was guest professor at the University of Florida. In 2004, he was appointed full professor and head of the department of clinical pharmacology at the Medical University of Vienna.
Müller has published some 200 research papers, in outlets such as the New England Journal of Medicine.
In 2015 Müller was elected Rector of the Medical University of Vienna. Two years later, he was re-elected for another four-year term from October 2019 to September 2023.[1]
An historical review symposium was published by the Medical University of Vienna in 2017: "Medical Ethics in the 70 Years after the Nuremberg Code, 1947 to the Present". Müller wrote in his introduction that the Code constitutes one of the most important milestones in the history of medicine, providing for the first time a proper framework for research on human subjects. Sadly, this milestone was not a voluntary, precautionary measure resulting from enlightened humanity, it only came into existence in the aftermath of dreadful Nazi atrocities. Following its conception, the Nuremberg Code bore rich fruit in multiple legal regards, becoming a cornerstone of clinical research and bioethics. For Austrian science in particular, the discourse on Nazi crimes and, thus, the Nuremberg Code became a special warning from history due to the involvement of prominent Austrian physicians in Nazi experiments... For Austrian science in particular, the discourse on
Nazi crimes and, thus, the Nuremberg Code became a special warning from history due to the involvement of prominent Austrian physicians in Nazi experiments. In my inauguration speech as the newly elected rector, I drew attention to the fact that I consider the transfer of
attitudes to the next generation to be more important for a university than the transfer of mere technical skills."[2]