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In 1872 Sturm was appointed assistant professor at the Technical College in Darmstadt. He became professor at Münster in 1878, then he returned to Breslau where he worked until his death.
Sturm worked on synthetic geometry and proved theorems stated, but not proved, by Steiner. He wrote extensively on geometry. He wrote a textbook Elemente der darstellenden Geometrie on descriptive geometry and graphical statics for his students in 1874.
Sturm studied third degree surfaces in their projective representations. In 1864 he shared with Cremona the Steiner prize of the Berlin Academy on investigations of surfaces.
He wrote a three volume work on line geometry and a four volume work on projective geometry, algebraic geometry and Schubert's enumerative geometry.
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