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 In mathematics, homotopy theory is a systematic study of situations in which maps can come with homotopies between them. It originated as a topic in algebraic topology but nowadays is studied as an independent discipline. Besides algebraic topolog ...

. He was born in Chennai (then known as Madras), in India, and died in Princeton, New Jersey, in 1960.

Life

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 Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He is best known as the defining figure of the philosophical school known as process philosophy, which today has found applicat ...

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 space In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet ''at infinity''. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally ...

s'', 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.Paul Gannon, ''Colossus: Bletchley Park's Greatest Secret'', 2006, Atlantic Books; . p. 347 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 Magdalen College (, ) is a constituent college of the University of Oxford. It was founded in 1458 by William of Waynflete. Today, it is the fourth wealthiest college, with a financial endowment of £332.1 million as of 2019 and one of the s ...

. He became president of the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

(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 Whitehead Prize is awarded yearly by the London Mathematical Society to multiple mathematicians working in the United Kingdom who are at an early stage of their career. The prize is named in memory of homotopy theory pioneer J. H. C. Whitehea ...

; the second a biennially awarded Senior Whitehead Prize.

Joseph J. Rotman Joseph J. Rotman (May 26, 1934 – October 16, 2016) was a Professor of Mathematics at the University of Illinois at Urbana–Champaign and also a published author of 10 textbooks. Rotman was born in Chicago. He did his undergraduate and graduate ...

, 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. H. C. Whitehead." Whitehead died from an asymptomatic heart attack during a visit to Princeton University in May 1960. In the late 1950s, Whitehead had approached Robert Maxwell, then chairman of Pergamon Press, to start a new journal, ''Topology'', however Whitehead died before its first edition appeared in 1962.

Work

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

simple homotopy theory In mathematics, simple homotopy theory is a homotopy theory (a branch of algebraic topology) that concerns with the simple-homotopy type of a space. It was originated by Whitehead in his 1950 paper "Simple homotopy type". See also *Whitehead tor ...

, which was later much developed in connection with algebraic K-theory. The

Whitehead product In mathematics, the Whitehead product is a graded quasi-Lie algebra structure on the homotopy groups of a space. It was defined by J. H. C. Whitehead in . The relevant MSC code is: 55Q15, Whitehead products and generalizations. Definition ...

is an operation in homotopy theory. The Whitehead problem on abelian groups was solved (as an independence proof) by

Saharon Shelah Saharon Shelah ( he, שהרן שלח; born July 3, 1945) is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and Rutgers University in New Jersey. Biography Shelah was born in Jerusalem on July 3, ...

. His involvement with topology and the Poincaré conjecture led to the creation of the Whitehead manifold. The definition of crossed modules is due to him. He also made important contributions in

differential topology In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which ...

, particularly on triangulations and their associated smooth structures.

Selected publications

* * J. H. C. Whitehead, ''On incidence matrices, nuclei and homotopy types'', Ann. of Math. (2) 42 (1941), 1197–1239. * J. H. C. Whitehead, ''Combinatorial homotopy. I.'', Bull. Amer. Math. Soc. 55 (1949), 213–245 * J. H. C. Whitehead, ''Combinatorial homotopy. II.'', Bull. Amer. Math. Soc. 55 (1949), 453–496 * J. H. C. Whitehead, ''A certain exact sequence'', Ann. of Math. (2) 52 (1950), 51–110 * J. H. C. Whitehead, ''Simple homotopy types'', Amer. J. Math. 72 (1950), 1–57. *

Saunders MacLane Saunders Mac Lane (4 August 1909 – 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg. Early life and education Mac Lane was born in Norwich, Connecticut, near where his family lived in Taftville, ...

, J. H. C. Whitehead, ''On the 3-type of a complex'', Proc. Natl. Acad. Sci. USA 36 (1950), 41–48. * ( published posthumously)

References

External links

* * {{DEFAULTSORT:Whitehead, J. H. C 1904 births 1960 deaths 20th-century British mathematicians Topologists People educated at Eton College Alumni of Balliol College, Oxford Fellows of Magdalen College, Oxford Princeton University alumni Bletchley Park people Fellows of the Royal Society Fellows of Balliol College, Oxford Waynflete Professors of Pure Mathematics