After leaving school, at the age of 16, he went to study at the universities of Breslau, Heidelberg - with Gustav Robert Kirchhoff - and Berlin - with Hermann Helmholtz.

In 1879, Felix Auerbach became an assistant to Oskar Emil Meyer at the physics department of the University of Wroclaw and in 1880 he became a lecturer there.

Besides Gropius, Max Bruch, Ida and Richard Dehmel, Edvard Munch, Henry van de Velde and Julius Meier-Graefe were among Auerbach's frequent guests and friends.

The rise of Adolf Hitler and the anti-Semitic climate in Germany made life unbearable for Felix and Anna Auerbach.

In his suicide note he stated that they "left the earthly life full of joy, after nearly 50 years of mutually blissful cohabitation".

Horst Bredekamp made mention in Die Zeit that the art historian Ulrich Müller had written that the Jena Professor of Physics, Felix Auerbach "was able to explain Einstein's Theory of Relativity in two papers, dated 1906 and 1921, and in particular impressed a number of artists because he had dealt with a physics of the arts for decades."

Together with physicist Wilhelm Hort (1878–1938), Auerbach began, as a septuagenarian, the publication of the Handbuch der physikalischen und technischen Mechanik ("Handbook of Physics and Engineering Mechanics", 1927–1931, 7 vols).

One of his classic works was Die Furcht vor der Mathematik und ihre Überwindung ("The Fear of Mathematics and Conquering It", 1925).