In 1978, he moved to Harvard University, where he served as the Dwight Parker Robinson Professor of Mathematics until his retirement in 2019.

[2] Schmid's early work concerns the construction of discrete series representations of semi-simple Lie groups.

Notable accomplishments here include a proof of the Langlands conjecture on the discrete series, along with a later proof (joint with Michael Atiyah) constructing all such discrete series representations on spaces of harmonic spinors.

In the 1970s, he described the singularities of the Griffith's period map by applying Lie-theoretic methods to problems in algebraic geometry.

[5] In 2012, he became a fellow of the American Mathematical Society[6] and in 2020 he was elected as a member of the U.S. National Academy of Sciences.