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The confluence of ideas in 1936. (English) Zbl 0689.01010
The universal Turing machine, a half-century survey, 55-111 (1988).
[For the entire collection see Zbl 0648.00002.]
The author puts in evidence the almost simultaneous appearance in 1936 of several independent characterizations of the notion of effective calculability. He examines the historical aspects from Babbage (1830) and he insists on the decision problems and on the significance of Turing’s work. In this paper the author tries to answer the following questions (see Introduction): What was in the air in the early 1930’s? What connections are there between the abstract work in the papers cited and actual mathematical calculation (by hand or by machine)? The problems dealt with in the 1936 papers largely arose from the work of Hilbert and his school at Göttingen; why did that school contribute so little to their solution? Eventually Turing’s work has proved to be of greater mathematical and philosophical significance than that of the other authors; why?
The essay is divided into fourteen paragraphs.
Reviewer: P.Freguglia

MSC:
01A60 History of mathematics in the 20th century
68-03 History of computer science