Vogt was born in
Tvedestrand, Norway. He was a son of physician Olaus Fredrik Sand Vogt and Mathilde Eliza Lie. He was the nephew of mathematician
Sophus Lie (1842–1899). Psychiatrist Ragnar Vogt (1870–1943) was a younger brother. Vogt studied at the Technical Institute in Dresden and in 1880 graduated from the
University of Christiania (now University of Oslo). Vogt was cand.min. from 1880. ==Career==