Zehnder studied mathematics and physics at ETH Zurich from 1960 to 1965, where he also did his Ph.D. in theoretical physics, defending his thesis on the three-body problem in 1971 under the direction of Res Jost.

[1] He was a visiting professor at Courant Institute of Mathematical Sciences (invited by Jürgen Moser), visiting member of Institute for Advanced Study in Princeton from 1972 to 1974.

He was plenary speaker at the International Congress of Mathematicians (ICM) in 1986 at the University of California, Berkeley.

[3] Zehnder made fundamental contributions to the field of dynamical systems.

In particular, in one of his groundbreaking works with Charles C. Conley, he established the celebrated Arnold conjecture for fixed points of Hamiltonian diffeomorphisms, and paved the way for the development of the new field of symplectic topology.