In 1895 he was awarded the doctorate under Carl Johannes Thomae with the subject Die einzweideutigen projektiven Punktverwandtschaften der Ebene and passed the Lehramtsprüfung in 1896.

In 1897 he was an assistant in Göttingen and in 1898 in Leipzig, where he was habilitated on the subject Über die Verbiegung der geschlossenen Flächen positiver Krümmung.

In 1920 he followed Paul Stäckel as professor at the Universität Heidelberg, where he became rector in 1926 and dean of the faculty of mathematics and natural science in 1923/1924 as well as in 1928/1929.

In 1935 he asked for retirement due to political pressure of the national socialists because of Liebmann's Jewish ancestry.

He discovered the construction of a triangle from its three angles by circle and ruler within hyperbolic geometry.