On 24 August 2002,[3] the International Society of Orthopaedic Surgery and Traumatology (SICOT) named him the "Orthopedic Surgeon of the Century" at a congress in San Diego.
This and another visit by a patient who had a hip implant made in Paris determined Müller to specialize in this area.
[3] After having worked in Jimma in Ethiopia, in Liestal, in Fribourg, and in Zürich, Müller habilitated in orthopedic surgery in 1957.
[6] Inspired by the work of Belgian surgeon Robert Danis, Müller developed within two years new tools and fixation implants for orthopedic surgery,[7] marketed by two Swiss companies and from the mid-1970 on also by Synthes USA.
[8] In 1967, Müller founded another company, Protek AG, to market his hip prostheses, which he had developed in the early 1960s, inspired by the work of John Charnley.