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 Chennai (, ), formerly known as Madras ( the official name until 1996), is the capital city of Tamil Nadu, the southernmost Indian state. The largest city of the state in area and population, Chennai is located on the Coromandel Coast of th ...

(then known as Madras), in

India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...

, and died in

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...

, 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 Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the ...

, 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

, went to

Eton Eton most commonly refers to Eton College, a public school in Eton, Berkshire, England. Eton may also refer to: Places *Eton, Berkshire, a town in Berkshire, England * Eton, Georgia, a town in the United States * Éton, a commune in the Meuse dep ...

and read mathematics at

Balliol College Balliol College () is one of the constituent colleges of the University of Oxford in England. One of Oxford's oldest colleges, it was founded around 1263 by John I de Balliol, a landowner from Barnard Castle in County Durham, who provided the f ...

. After a year working as a stockbroker, at Buckmaster & Moore, he started a PhD in 1929 at

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

. 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 Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905; while this was lon ...

in 1930. While in

Princeton Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ni ...

, he also worked with

Solomon Lefschetz Solomon Lefschetz (russian: Соломо́н Ле́фшец; 3 September 1884 – 5 October 1972) was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear o ...

. He became a fellow of Balliol in 1933. In 1934 he married the concert pianist Barbara Smyth, great-great-granddaughter of

Elizabeth Fry Elizabeth Fry (née Gurney; 21 May 1780 – 12 October 1845), sometimes referred to as Betsy Fry, was an English prison reformer, social reformer, philanthropist and Quaker. Fry was a major driving force behind new legislation to improve the tr ...

and a cousin of

Peter Pears Sir Peter Neville Luard Pears ( ; 22 June 19103 April 1986) was an English tenor. His career was closely associated with the composer Benjamin Britten, his personal and professional partner for nearly forty years. Pears' musical career started ...

; 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 Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve deci ...

for submarine warfare. Later, he joined the codebreakers at

Bletchley Park Bletchley Park is an English country house and estate in Bletchley, Milton Keynes ( Buckinghamshire) that became the principal centre of Allied code-breaking during the Second World War. The mansion was constructed during the years following ...

, and by 1945 was one of some fifteen mathematicians working in the "

Newmanry The Newmanry was a section at Bletchley Park, the British codebreaking station during World War II. Its job was to develop and employ statistical and machine methods in cryptanalysis of the Lorenz cipher. It worked very closely with the Testery wh ...

", a section headed by

Max Newman Maxwell Herman Alexander Newman, FRS, (7 February 1897 – 22 February 1984), generally known as Max Newman, was a British mathematician and codebreaker. His work in World War II led to the construction of Colossus, the world's first operatio ...

and responsible for breaking a German

teleprinter A teleprinter (teletypewriter, teletype or TTY) is an electromechanical device that can be used to send and receive typed messages through various communications channels, in both point-to-point and point-to-multipoint configurations. Initia ...

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 Waynflete could refer to: *William Waynflete (1395–1486), English Lord Chancellor and bishop of Winchester *Waynflete Professorships at Magdalen College, Oxford, named after William Waynflete *Waynflete School, a private day school in Portland, M ...

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. Whiteh ...

; the second a biennially awarded

Senior Whitehead Prize The Senior Whitehead Prize of the London Mathematical Society (LMS) is now awarded in odd numbered years in memory of John Henry Constantine Whitehead, president of the LMS between 1953 and 1955. The Prize is awarded to mathematicians normally ...

. 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. 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 Ian Robert Maxwell (born Ján Ludvík Hyman Binyamin Hoch; 10 June 1923 – 5 November 1991) was a Czechoslovak-born British media proprietor, member of parliament (MP), suspected spy, and fraudster. Early in his life, Maxwell escaped from N ...

, then chairman of

Pergamon Press Pergamon Press was an Oxford-based publishing house, founded by Paul Rosbaud and Robert Maxwell, that published scientific and medical books and journals. Originally called Butterworth-Springer, it is now an imprint of Elsevier. History The cor ...

, to start a new journal, ''Topology'', however Whitehead died before its first edition appeared in 1962.

Work

Whitehead's definition of

CW complex A CW complex (also called cellular complex or cell complex) is a kind of a topological space that is particularly important in algebraic topology. It was introduced by J. H. C. Whitehead (open access) to meet the needs of homotopy theory. This cla ...

es 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 Algebraic ''K''-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called ''K''-groups. These are groups in the sense ...

. 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 In group theory, a branch of abstract algebra, the Whitehead problem is the following question: Saharon Shelah proved that Whitehead's problem is independent of ZFC, the standard axioms of set theory. Refinement Assume that ''A'' is an abel ...

abelian group In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commut ...

s 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 In the mathematics, mathematical field of geometric topology, the Poincaré conjecture (, , ) is a theorem about the Characterization (mathematics), characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dim ...

led to the creation of the

Whitehead manifold In mathematics, the Whitehead manifold is an open 3-manifold that is contractible, but not homeomorphic to \R^3. discovered this puzzling object while he was trying to prove the Poincaré conjecture, correcting an error in an earlier paper where ...

. The definition of

crossed module In mathematics, and especially in homotopy theory, a crossed module consists of groups G and H, where G acts on H by automorphisms (which we will write on the left, (g,h) \mapsto g \cdot h , and a homomorphism of groups : d\colon H \longrightarro ...

s 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 structure In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function. In particular, a smooth structure allows one to perform mathematical analysis on the manifold. Definition A smooth structure on a manifold M is ...

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, 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