He was one of the founders of singularity theory, and did foundational work in manifolds, embeddings, immersions, characteristic classes and, geometric integration theory Hassler Whitney was born on March 23, 1907, in New York City, where his father, Edward Baldwin Whitney, was the First District New York Supreme Court judge.

He and Mary had two daughters, Sarah Newcomb (later a notable statistician, Sally Thurston), and Emily Baldwin.

Whitney and his first wife Margaret made an innovative decision in 1939 that influenced the history of modern architecture in New England, when they commissioned the architect Edwin B. Goodell, Jr. to design a new residence for their family in Weston, Massachusetts.

They purchased a rocky hillside site on a historic road, next door to another International Style house by Goodell from several years earlier, designed for Richard and Caroline Field.

As an undergraduate, with his cousin Bradley Gilman, Whitney made the first ascent of the Whitney–Gilman ridge on Cannon Mountain, New Hampshire in 1929.

[6] In accordance with his wish, Hassler Whitney's ashes rest atop mountain Dent Blanche in Switzerland where Oscar Burlet, another mathematician and member of the Swiss Alpine Club, placed them on August 20, 1989.

These theorems opened the way for much more refined studies of embedding, immersion and also of smoothing—that is, the possibility of having various smooth structures on a given topological manifold.

He was one of the major developers of cohomology theory, and characteristic classes, as these concepts emerged in the late 1930s, and his work on algebraic topology continued into the 40s.

An old idea, implicit even in the notion of a simplicial complex, was to study a singular space by decomposing it into smooth pieces (nowadays called "strata").

The work of René Thom and John Mather in the 1960s showed that these conditions give a very robust definition of stratified space.

The singularities in low dimension of smooth mappings, later to come to prominence in the work of René Thom, were also first studied by Whitney.

In his book Geometric Integration Theory he gives a theoretical basis for Stokes' theorem applied with singularities on the boundary:.

[19] These aspects of Whitney's work have looked more unified, in retrospect and with the general development of singularity theory.

Whitney's purely topological work (Stiefel–Whitney class, basic results on vector bundles) entered the mainstream more quickly.

[20] He spent four months teaching pre-algebra mathematics to a classroom of seventh graders and conducted summer courses for teachers.