Born in Munich, he originally studied mathematics, physics, and chemistry, graduating with a Ph.D. in 1886, before turning to philosophy. In 1894, he habilitated in philosophy and subsequently held a post in philosophy at the University of Munich (until 1903 as a Privatdozent). In 1910, Cornelius moved as a full professor to the Akademie für Sozialwissenschaften, which four years later would become a department of the newly founded University of Frankfurt. Among his students in Frankfurt were Max Horkheimer and Theodor Adorno.
