After graduating from high school in 1859, Von der Mühll studied natural sciences and mathematics at the University of Basel, with amongst others, Gustav Heinrich Wiedemann, and from 1861 studied at the Georg-August University in Göttingen with Bernhard Riemann, Wilhelm Eduard Weber, Wilhelm Klinkerfues and Friedrich Wöhler.
From 1863, he continued his studies at the Albertus University in Königsberg, where he turned to mathematical physics under Franz Ernst Neumann and received his doctorate in 1866.
Shortly after, in 1868, he completed his studies in Leipzig in mathematical physics and in 1872 he became an associate professor at the university.
In 1887, he was elected a member of the German National Academy of Sciences Leopoldina.
[1][2] Having suffered from several bouts of depression throughout his life, Von der Mühll committed suicide in 1912 and is buried in the Wolfgottesacker cemetery in Basel.