Hsiang served as chairman of the Department of Mathematics at Princeton University from 1982 to 1985 and was one of the most influential topologists of the second half of the 20th century.
Works by Hsiang, Julius Shaneson, C. T. C. Wall, Robion Kirby, Laurent Siebenmann and Andrew Casson led in the 1960s to the proof of the annulus theorem (previously known as the annulus conjecture).
For example, they gave a proof of the integral Novikov conjecture for compact Riemannian manifolds with non-positive sectional curvature.
He was an Invited Speaker at the International Congress of Mathematicians in 1970 in Nice, with a talk on Differentiable actions of compact connected Lie groups on
[9] and a Plenary Speaker in 1983 in Warsaw, with a talk on Geometric applications of algebraic K-theory.