In 1890, he earned his medical doctorate from the University of Bonn, and afterwards was an assistant to pathologist Eugen Bostroem (1850–1928) in Giessen and to internist Otto Michael Ludwig Leichtenstern (1845–1900) in Cologne.
In May 1918, while performing emergency surgery on a French POW who had a swollen larynx associated with diphtheria, Wilms became infected with the disease, and died within a few days at the age of 50.
Wilms is remembered for his work in the field of nephrology, and his pathological studies concerning the development of tumor cells.
Wilms made several contributions as a surgeon and is credited for introducing a partial rib resection used in the treatment for pulmonary tuberculosis.
[3] With surgeon Ludwig Wullstein (1864–1930), he co-authored and published Lehrbuch der Chirurgie, a surgical textbook that was translated into several languages.