1953) and at Princeton University, where he earned his Ph.D. in 1956 under Donald Spencer ("A Non-Self-Adjoint Boundary Value Problem on Pseudo-Kähler Manifolds").

He was a visiting professor at Harvard (1996–97), Prague, Florence, Mexico City (National Polytechnic Institute), Stanford, Berkeley, Scuola Normale Superiore (Pisa, Italy), and IHES (France).

Kohn's work focused, among other things, on the use of partial differential operators in the theory of functions of several complex variables and microlocal analysis.

In 1966, he was an invited speaker at the International Congress of Mathematicians in Moscow; he gave a speech on "Differential complexes".

[6] Kohn won the AMS' Steele Prize in 1979 for his paper "Harmonic integrals on strongly convex domains".