J. H. C. Whitehead
Encyclopedia
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.
, 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, where he co-founded the The Invariant Society
, the student mathematics society. After a year working as a stockbroker, he started a Ph.D. in 1929 at Princeton University
. His thesis, titled The representation of projective space
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. 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
.
In the late 1950s, Whitehead approached Robert Maxwell
, then chairman of Pergamon Press
, to start a new journal, Topology
, but died before its first edition appeared in 1962.
es 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 product
is an operation in homotopy theory. The Whitehead problem
on abelian group
s was solved (as an independence proof) by Saharon Shelah
. His involvement with topology and the Poincaré conjecture
led to the creation of the Whitehead manifold
. The definition of crossed module
s is due to him. Whitehead also made important contributions in differential topology
, particularly on triangulations
and their associated smooth structure
s.
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and was one of the founders of homotopy theory. He was born in Chennai
Chennai
Chennai , formerly known as Madras or Madarasapatinam , is the capital city of the Indian state of Tamil Nadu, located on the Coromandel Coast off the Bay of Bengal. Chennai is the fourth most populous metropolitan area and the sixth most populous city in India...
(then known as Madras), in India, and died in Princeton, New Jersey
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
, in 1960.
Life
J. H. C. (Henry) Whitehead was the son of the Right Rev. Henry WhiteheadHenry Whitehead (bishop)
The Rt Rev Henry Whitehead, DD was an eminent Anglican clergyman in the last decade of the 19th century and the first quarter of the 20th.He was born on December 19, 1863 and educated at Sherborne and Trinity College, Oxford. Ordained in 1879 his first post was as a preacher at St Nicholas, Abingdon...
, Bishop of Madras
Bishop of Madras
The Bishop of Madras was the Ordinary of the Anglican Church in Madras from its inception in 1835 until the foundation of the Church in India, Pakistan, Burma and Ceylon in 1927; and since then head of one of its most prominent Dioceses.-External links:*...
, who had studied mathematics at Oxford, and was the nephew of Alfred North Whitehead
Alfred North Whitehead
Alfred North Whitehead, OM FRS was an English mathematician who became a philosopher. He wrote on algebra, logic, foundations of mathematics, philosophy of science, physics, metaphysics, and education...
and Isobel Duncan. He was brought up in Oxford
Oxford
The city of Oxford is the county town of Oxfordshire, England. The city, made prominent by its medieval university, has a population of just under 165,000, with 153,900 living within the district boundary. It lies about 50 miles north-west of London. The rivers Cherwell and Thames run through...
, went to Eton
Eton College
Eton College, often referred to simply as Eton, is a British independent school for boys aged 13 to 18. It was founded in 1440 by King Henry VI as "The King's College of Our Lady of Eton besides Wyndsor"....
and read mathematics at Balliol College, Oxford, where he co-founded the The Invariant Society
Oxford University Invariant Society
The Oxford University Invariant Society, or 'The Invariants', is a university society open to members of Oxford University, dedicated to promotion of interest in Mathematics. The society regularly hosts talks from prominent British mathematicians such as G. H. Hardy on wide ranging topics from the...
, the student mathematics society. After a year working as a stockbroker, he started a Ph.D. in 1929 at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
. His thesis, titled The representation of projective space
Projective space
In mathematics a projective space is a set of elements similar to the set P of lines through the origin of a vector space V. The cases when V=R2 or V=R3 are the projective line and the projective plane, respectively....
s, was written under the direction of Oswald Veblen
Oswald Veblen
Oswald Veblen 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.-Life:...
in 1930. While in Princeton
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
, he also worked with Solomon Lefschetz
Solomon Lefschetz
Solomon Lefschetz was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.-Life:...
.
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
Elizabeth Fry , née Gurney, was an English prison reformer, social reformer and, as a Quaker, a Christian philanthropist...
and a cousin of Peter Pears
Peter Pears
Sir Peter Neville Luard Pears CBE was an English tenor who was knighted in 1978. His career was closely associated with the composer Edward Benjamin Britten....
; they had two sons. During the Second World War he worked on operations research
Operations research
Operations research is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations...
for submarine warfare. Later, he joined the codebreakers at Bletchley Park
Bletchley Park
Bletchley Park is an estate located in the town of Bletchley, in Buckinghamshire, England, which currently houses the National Museum of Computing...
, and by 1945 was one of some fifteen mathematicians working in the "Newmanry
Newmanry
The Newmanry was a section at Bletchley Park, the British codebreaking station during World War II. Its job was to develop and employ machine methods in Cryptanalysis of the Lorenz cipher. The Newmanry was named after its founder and head, Max Newman...
", a section headed by Max Newman
Max Newman
Maxwell Herman Alexander "Max" Newman, FRS was a British mathematician and codebreaker.-Pre–World War II:Max Newman was born Maxwell Neumann in Chelsea, London, England, on 7 February 1897...
and responsible for breaking a German teleprinter
Teleprinter
A teleprinter is a electromechanical typewriter that can be used to communicate typed messages from point to point and point to multipoint over a variety of communication channels that range from a simple electrical connection, such as a pair of wires, to the use of radio and microwave as the...
cipher using machine methods. Those methods included the Colossus machines
Colossus computer
Not to be confused with the fictional computer of the same name in the movie Colossus: The Forbin Project.Colossus was the world's first electronic, digital, programmable computer. Colossus and its successors were used by British codebreakers to help read encrypted German messages during World War II...
, early digital electronic computers.
From 1947 to 1960 he was the Waynflete Professor of Pure Mathematics at Magdalen College, Oxford
Magdalen College, Oxford
Magdalen College is one of the constituent colleges of the University of Oxford in England. As of 2006 the college had an estimated financial endowment of £153 million. Magdalen is currently top of the Norrington Table after over half of its 2010 finalists received first-class degrees, a record...
.
He became president of the London Mathematical Society
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
(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
Whitehead Prize
The Whitehead Prize is awarded yearly by the London Mathematical Society to a mathematician working in the United Kingdom who is at an early stage of their career. The prize is named in memory of homotopy theory pioneer J. H. C...
; the second a biennially awarded Senior Whitehead Prize
Senior Whitehead Prize
The Senior Whitehead Prize of the London Mathematical Society is currently 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 resident in the United Kingdom on 1 January of the...
.
In the late 1950s, Whitehead approached Robert Maxwell
Robert Maxwell
Ian Robert Maxwell MC was a Czechoslovakian-born British media proprietor and former Member of Parliament , who rose from poverty to build an extensive publishing empire...
, then chairman of Pergamon Press
Pergamon Press
Pergamon Press was an Oxford-based publishing house, founded by Paul Rosbaud and Robert Maxwell, which published scientific and medical books and journals. It is now an imprint of Elsevier....
, to start a new journal, Topology
Topology (journal)
Topology is a mathematical journal publishing scholarly articles related to topology and geometry. It was founded by J. H. C. Whitehead in 1962 and is published by Elsevier....
, but died before its first edition appeared in 1962.
Work
His definition of CW complexCW complex
In topology, a CW complex is a type of topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory. This class of spaces is broader and has some better categorical properties than simplicial complexes, but still retains a combinatorial naturethat allows for...
es 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
Algebraic K-theory
In mathematics, algebraic K-theory is an important part of homological algebra concerned with defining and applying a sequenceof functors from rings to abelian groups, for all integers n....
. The Whitehead product
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 .- Definition :Given elements f \in \pi_k, g \in \pi_l, the Whitehead bracket...
is an operation in homotopy theory. The Whitehead problem
Whitehead problem
In group theory, a branch of abstract algebra, the Whitehead problem is the following question:Shelah proved that Whitehead's problem is undecidable within standard ZFC set theory.-Refinement:...
on abelian group
Abelian group
In abstract algebra, 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 their order . Abelian groups generalize the arithmetic of addition of integers...
s was solved (as an independence proof) by Saharon Shelah
Saharon Shelah
Saharon Shelah is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and Rutgers University in New Jersey.-Biography:...
. His involvement with topology and the Poincaré conjecture
Poincaré conjecture
In mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere , which is the hypersphere that bounds the unit ball in four-dimensional space...
led to the creation of the Whitehead manifold
Whitehead manifold
In mathematics, the Whitehead manifold is an open 3-manifold that is contractible, but not homeomorphic to R3. Henry Whitehead discovered this puzzling object while he was trying to prove the Poincaré conjecture....
. The definition of crossed module
Crossed module
In mathematics, and especially in homotopy theory, a crossed module consists of groups G and H, where G acts on H , and a homomorphism of groups...
s is due to him. Whitehead also made important contributions in differential topology
Differential topology
In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds.- Description :...
, particularly on triangulations
Triangulation (topology)
In mathematics, topology generalizes the notion of triangulation in a natural way as follows:A triangulation of a topological space X is a simplicial complex K, homeomorphic to X, together with a homeomorphism h:K\to X....
and their associated smooth structure
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....
s.
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. Nat. Acad. Sci. U. S. A. 36 (1950), 41–48. (published posthumously)
See also
- Simple homotopy
- Spanier–Whitehead duality
- Whitehead groupWhitehead groupWhitehead group in mathematics may mean:* A group W with Ext=0; see Whitehead problem* For a ring, the Whitehead group Wh of a ring A, equal to K_1...
- Whitehead linkWhitehead linkIn knot theory, the Whitehead link, discovered by J.H.C. Whitehead, is one of the most basic links.J.H.C. Whitehead spent much of the 1930s looking for a proof of the Poincaré conjecture...
- Whitehead theoremWhitehead theoremIn homotopy theory , the Whitehead theorem states that if a continuous mapping f between topological spaces X and Y induces isomorphisms on all homotopy groups, then f is a homotopy equivalence provided X and Y are connected and have the homotopy-type of CW complexes. This result was proved by J....
- Whitehead torsionWhitehead torsionIn geometric topology, the obstruction to a homotopy equivalence f\colon X \to Y of finite CW-complexes being a simple homotopy equivalence is its Whitehead torsion \tau, which is an element in the Whitehead group Wh. These are named after the mathematician J. H. C...