Alan Turing, ‘Solvable and Unsolvable Problems’, in Science News 31, pp. [7]-24 (Penguin Books, Harmondsworth), 1954

112 x 180mm; pp. 137 [1, index of authors for nos 28-31].

Very good condition: pages age-toned; spine slightly faded as always

A masterpiece of science writing: Turing explains his breakthrough 1936 work in lay terms. Considered to be one of the ‘Five Turing Classics’ (Alan Turing: His Work and Impact, p. 339).

This deceptively simple paper contains profound insights into the nature of calculability. Owing to the ambiguous philosophical status of what is known as the ‘Church-Turing Thesis’ (briefly, ‘given any systematic method, we can find a corresponding Turing machine that is equivalent to it’), Turing’s discursive comments in the present paper are, in the words of Turing’s editor Jack Copeland, ‘of outstanding interest’. Here Turing manages to cover his own (and Church’s) thesis on computability, the relationship between the latter and Gödel’s incompleteness theorem, and much else concerning the nature of puzzles and mathematical proofs, all in his typical playful and admirably clear prose.

This is Turing’s final completed essay before his death in June 1954. Turing’s short career was one of the most brilliant in the whole history of science.