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John Henry Constantine Whitehead FRS

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.

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. 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, 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 groups 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 modules is due to him. He also made important contributions in differential topology, 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, J. H. C. Whitehead, On the 3-type of a complex, Proc. Natl. Acad. Sci. USA 36 (1950), 41–48.
  • (published posthumously)

References