TURING,ALAN AND THE CENTRAL-LIMIT-THEOREM

Although the English mathematician Alan Mathison Turing (1912-1954) is remembered today primarily for his work in mathematical logic (Turing machines and the ''Entscheidungsproblem''), machine computation, and artificial intelligence (the ''Turing test''), his name is not usually thought of in connection with either probability or statistics. One of the basic tools in both of these subjects is the use of the normal or Gaussian distribution as an approximation, one basic:result being the Lindeberg-Feller central limit theorem taught in first-year graduate courses in mathematical probability No one associates Turing with the central limit theorem, but in 1934 Turing, while still an undergraduate, rediscovered a version of Lindeberg's 1922 theorem and much of the Feller-Levy converse to it (then unpublished). This paper discusses Turing's connection with the central limit theorem and its surprising aftermath: his use of statistical methods during World War II to break key German military codes.