In 1860, he started studying at University of Göttingen, where he acquired an interest in function theory under the tutelage of Bernhard Riemann.

Following the publication of an award winning article, he proceeded to study under Karl Weierstrass and Leopold Kronecker in Berlin.

Receiving his teaching qualifications a year after, he was promoted to an associate professor at Leipzig University in 1867.

His works on the theory of functions include 1870's Untersuchungen über die unendlich oft oscillirenden und unstetigen functionen and his 1871 article “Grenze” for the Ersch-Gruber Encyklopädie.

"[2] Furthermore, Hankel draws attention[3] to the linear algebra that Hermann Grassmann had developed in his Extension Theory in two publications.