His thesis, titled The representation of projective spaces, was written under the direction of Oswald Veblen in 1930.

In 1934 he married the concert pianist Barbara Smyth, great-great-granddaughter of Elizabeth Fry and a cousin of Peter Pears; they had two sons.

Later, he joined the codebreakers at Bletchley Park, and by 1945 was one of some fifteen mathematicians working in the "Newmanry", a section headed by Max Newman and responsible for breaking a German teleprinter cipher using machine methods.

Whitehead's definition of CW complexes gave a setting for homotopy theory that became standard.

He introduced the idea of simple homotopy theory, which was later much developed in connection with algebraic K-theory.

The Whitehead problem on abelian groups was solved (as an independence proof) by Saharon Shelah.