Heinrich Jung was born as the son of a Bergrat (a mining officer of high rank) in Essen and studied from 1895 to 1899 mathematics, physics, and chemistry in Marburg/Lahn and Berlin under outstanding professors including Friedrich Schottky, Kurt Hensel, Lazarus Immanuel Fuchs, Hermann Amandus Schwarz, Ferdinand Georg Frobenius, and Max Planck.
In his 1899 doctoral dissertation Über die kleinste Kugel, die eine räumliche Figur einschließt (About the smallest sphere enclosing a spatial figure) under Schottky he proved the eponymous Jung's Theorem.
Afterwards he was a Studienrat (teacher at a secondary school, i.e., Gymnasium) in Hamburg, before he became in 1913 a professor ordinarius in Kiel.
Jung's fame derives mainly from his arithmetic theory of algebraic functions in two variables.
During the Weimar Republic, Jung was a member of the anti-republican Alldeutschen Verband and also Der Stahlhelm.