Hassler Whitney

Hassler Whitney (23 March 1907 – 10 May 1989) was a US mathematician, who was one of the founders of singularity theory. He was born in New York City, and graduated from Yale University in 1928. He then did research work at Harvard University, under G.D. Birkhoff, writing a Ph.D in graph theory (1932). He then held positions at Harvard until 1952 (professor from 1946), moving to the Institute for Advanced Study at Princeton. He retired in 1977, and died in Switzerland.

He was awarded a Wolf Prize in mathematics in 1983, and a Steele Prize in 1985.

In 1935 Whitney proved that any differential manifold of dimension n may be embedded in R²ⁿ, and immersed in R^2n-1. This basic result shows that manifolds may be treated intrinsically or extrinsically, as we wish. It is often said that this paper contains the first accurate definition of 'manifold'; it certainly built on the work of Veblen and J.H.C. Whitehead published a few years earlier. It 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. The argument of Whitney is necessarily of general position type.

A few years later, Whitney wrote the foundational paper on matroids. This is apparently a chapter of combinatorics; it has in recent years been seen increasingly as related to the fine structure of Grassmannians. In fact the idea of stratification, used for that application and many others, was also introduced by Whitney, in a precise form (his conditions A and B).

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

His book Geometric Integration Theory gives a theoretical basis for Stokes' theorem applied with singularities on the boundary.

These aspects of Whitney’s work have looked more unified, in retrospect and with the general development of singularity theory in its aspect of the failure of smoothness. Whitney’s purely topological work (Stiefel-Whitney class, basic results on vector bundles) entered the mainstream more quickly.