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Time to Reinspect the Foundations?

By Jack Copeland, Eli Dresner, Diane Proudfoot, Oron Shagrir

Communications of the ACM, Vol. 59 No. 11, Pages 34-38
10.1145/2908733

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The theory of computability was launched in the 1930s, by a group of logicians who proposed new characterizations of the ancient idea of an algorithmic process. The most prominent of these iconoclasts were Kurt Gödel, Alonzo Church, and Alan Turing. The theoretical and philosophical work that they carried out in the 1930s laid the foundations for the computer revolution, and this revolution in turn fueled the fantastic expansion of scientific knowledge in the late 20th and early 21st centuries. Thanks in large part to these groundbreaking logico-mathematical investigations, unimagined number-crunching power was soon boosting all fields of scientific enquiry. (For an account of other early contributors to the emergence of the computer age see Copeland and Sommaruga.9)

The motivation of these three revolutionary thinkers was not to pioneer the disciplines now known as theoretical and applied computer science, although with hindsight this is indeed what they did. Nor was their objective to design electronic digital computers, although Turing did go on to do so. The founding fathers of computability would have thought of themselves as working in a most abstract field, far from practical computing. They sought to clarify and define the limits of human computability in order to resolve open questions at the foundations of mathematics.

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