Pasch was the son of a Jewish businessman from the Polish Rawitsch in Poznan. He studied from 1860 at the University of Breslau mathematics ( after initial study of chemistry ), where he became friends with Jakob Rosanes. His teachers were, inter alia, Rudolf Lipschitz, Paul Bachmann and Heinrich Schröter, where he received his doctorate in 1865 on a geometric theme. After that he studied in Berlin under Karl Weierstrass and Leopold Kronecker.
In 1870 he qualified as a professor in Giessen, where he fulltime care of his deceased father's business in 1866. In 1873 he became an associate professor at the University of Giessen in 1875 and full professor, after he had declined the offer to Wroclaw. 1885/86 he was Dean of the Faculty of Arts and 1893 quarters Rector of the University. In 1911 he retired, but published further into old age.
He was married in 1875 and had two daughters. He was honorary doctorates from the universities of Frankfurt and Freiburg im Breisgau.
He demanded, especially in his 1882 published book Lectures on newer geometry, a strictly logical approach in geometry, discovered some hitherto not perceived assumptions of Euclidean geometry, namely the axiom of Pasch, and was thus triggering to Hilbert's axiomatic development of the geometry and also to the simultaneous investigations of the school of Giuseppe Peano.
" What's axiomatics and how one has to formulate axioms that has been shown towards the end of the 19th century by Pasch; he learned it the Italian geometer and learned to Hilbert. "
- Lectures on newer geometry, Leipzig 1882
- Introduction to differential and integral calculus, Leipzig 1882
- Foundations of Analysis, Leipzig, 1908 Digitalisat