He was the son of the theologianTheodosius Harnack and the twin brother of theologian Adolf von Harnack (who long outlived him) - all of them from Tartu, which in that time was known as Dorpat, in what is today Estonia. His father was a professor at the University of Tartu, and he studied also himself in the university. After his studies in Tartu, he moved to Erlangen to become a student of Felix Klein. He published his PhD thesis in 1875, and received the right to teach (venia legendi) at the university of Leibzig the same year. One year later he accepted a position at Technical University Darmstadt. In 1877 he married Elisabeth von Öttingen, and they moved to Dresden, where he acquired professorship in the Polytechnikum, which becomes a technical university in 1890. Harnack suffered from health problems from 1882 onwards, forcing him to spend long times in a sanatorium. He published 29 scientific articles and was a well-known mathematician at the time of his death.