He attended several different universities in Germany studying the philosophical works of Heidegger and Husserl, but finally decided that mathematics was his real calling.

In early February 1933, a few days after Hitler became the Chancellor of Germany, Friedrichs met and immediately fell in love with a young Jewish student, Nellie Bruell.

He also did major research and wrote many books and papers on existence theory, numerical methods, differential operators in Hilbert space, non-linear buckling of plates, flows past wings, solitary waves, shock waves, combustion, magneto-fluid dynamical shock waves, relativistic flows, quantum field theory, perturbation of the continuous spectrum, scattering theory, and symmetric hyperbolic equations.

[2] With Cartan,[3][4] Friedrichs[5] gave a "geometrized" formulation of Newtonian gravitation theory—also known as “Newton–Cartan theory”— and later developed by Dautcourt, Dixon, Dombrowski and Horneffer, Ehlers, Havas, Künzle, Lottermoser, Trautman, and others.

[6][7] In November 1977, Friedrichs received the National Medal of Science from President Jimmy Carter "for bringing the powers of modern mathematics to bear on problems in physics, fluid dynamics, and elasticity."