[3][4] Rothe, whose father was a lawyer, attended Berlin's Königliches Wilhelms-Gymnasium and passed his Abitur in October 1913.
After completing two semesters at the University of Munich, he volunteered to join the German Army in a field artillery regiment.
There he studied mathematics, physics, and philosophy and in 1923 passed the Lehramtsexamen qualifying him to become a Gymnasium teacher.
His dissertation Über einige Analogien zwischen linearen partiellen und linearen gewöhnlichen Differentialgleichungen (About some analogies between linear partial and linear ordinary differential equations) was supervised by Erhard Schmidt and Richard von Mises.
[1] After being dismissed in 1935 from the German civil service because he was a Jew, Rothe with his wife and son escaped to Zurich and in emigrated in 1937 to the USA.
[11] In 1986 at the age of 91, Rothe published the 242-page book Introduction to Various Aspects of Degree Theory in Banach Spaces.
[1] His contributions to mathematical research reflect his great breadth: differential and integral equations, linear and nonlinear functional analysis, topology, calculus of variations.