[1] Family records indicate that he had siblings and cousins, but their names have yet to be confirmed except for an older brother, Julius, with whom he developed an arithmetical theory for complex continued fractions circa 1890.

Following two years at the University of Göttingen, in 1884 he was invited to become an Extraordinary Professor at the Albertus Universität in Königsberg; there he encountered the young David Hilbert and Hermann Minkowski, on whom he had a major influence.

Throughout his time in Zürich, Hurwitz was in continual ill health, which had been originally caused when he contracted typhoid whilst a student in Munich.

He was one of the early students of the Riemann surface theory, and used it to prove many of the foundational results on algebraic curves; for instance Hurwitz's automorphisms theorem.

[5] In 1884, whilst at Königsberg, Hurwitz met and married Ida Samuel, the daughter of a professor in the faculty of medicine.