John Henry Constantine Whitehead FRS (11 November 1904 – 8 May 1960), known as Henry, was a British mathematician and was one of the founders of homotopy theory. He was born in Chennai (then known as Madras), in India, and died in Princeton, New Jersey, in 1960.
J. H. C. (Henry) Whitehead was the son of the Right Rev. Henry Whitehead, Bishop of Madras, who had studied mathematics at Oxford, and was the nephew of Alfred North Whitehead and Isobel Duncan. He was brought up in Oxford, went to Eton and read mathematics at Balliol College, Oxford. After a year working as a stockbroker, at Buckmaster & Moore, he started a PhD in 1929 at Princeton University. His thesis, titled The representation of projective spaces, was written under the direction of Oswald Veblen in 1930. While in Princeton, he also worked with Solomon Lefschetz.
He became a fellow of Balliol in 1933. 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. In 1936, he co-founded The Invariant Society, the student mathematics society at Oxford.
During the Second World War he worked on operations research for submarine warfare. 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. Those methods included the Colossus machines, early digital electronic computers.
From 1947 to 1960 he was the Waynflete Professor of Pure Mathematics at Magdalen College, Oxford.
He became president of the London Mathematical Society (LMS) in 1953, a post he held until 1955. The LMS established two prizes in memory of Whitehead. The first is the annually awarded, to multiple recipients, Whitehead Prize; the second a biennially awarded Senior Whitehead Prize.
Joseph J. Rotman, in his book on algebraic topology, as a tribute to Whitehead's intellect, says, "There is a canard that every textbook of algebraic topology either ends with the definition of the Klein bottle or is a personal communication to J.