Hirsch completed his schooling in Königsberg in 1882 and then studied mathematics and physics in the universities of Berlin and Königsberg.

Among his teachers at Königsberg were David Hilbert and Adolf Hurwitz.

[1] In 1892 he received a doctorate from Königsberg for a thesis about linear differential equations.

The work of Hirsch is primarily on differential equations and hypergeometric functions.

Hirsch was a member of the Swiss Mathematical Society from his foundation in 1910.