He was a school teacher in Frederikshald, from 1858 to 1898. He was a substitute lecturer at Christiania University in 1862, covering Galois theory; he posed then the question that was to lead to the Sylow subgroups and his theorems about them. He published the Sylow theorems in 1872.

Subsequently he was an editor of Abel’s papers, with Sophus Lie. He was appointed professor in 1898.