[1] Davis is most known for his work in the fields of geometry and topology, with a focus on the methods for constructing aspherical manifolds and spaces.

He is the author of two books that include The Geometry and Topology of Coxeter Groups[2] and Multiaxial Actions on Manifolds.

He then completed a PhD in mathematics at the same institution under the supervision of Wu-Chung Hsiang in 1975[6] with a thesis titled "Smooth Actions of the Classical Groups".

Following his PhD, Davis held an appointment as a Moore Instructor of Mathematics at the Massachusetts Institute of Technology from 1974 to 1976.

[4] In collaborations with Tadeusz Januszkiewicz [pl][8] and Ruth Charney,[9] he established the "hyperbolization" method for using nonpositive curvature to construct aspherical manifolds.