[2] After graduating from the Sophien-Gymnasium in Berlin, Rothe studied from 1892 under Hermann Amandus Schwarz, Johannes Knoblauch, Lazarus Immanuel Fuchs, and Ferdinand Georg Frobenius[3] at the Humboldt University of Berlin.
There in 1897 he received his Promotion (Ph.D.) with dissertation Untersuchungen über die Theorie der isothermal Flächen (Investigations on the theory of isothermal surfaces) supervised by Schwarz.
[4][5] In 1926 he was elected a member of the German National Academy of Sciences Leopoldina.
After the death of Johannes Knoblauch, Rothe completed the editing and publishing of the collected works of Karl Weierstrass.
Rothe was co-editor with Felix Auerbach of the Taschenbuch für Mathematiker und Physiker (Pocket-sized book for mathematicians and physicists), published by B. G. Teubner Verlag in 1911[7] and 1913[8][9] (and first published in 1909 by Auerbach alone).