Logic at Cambridge and Princeton
Turing entered King’s College, Cambridge, in 1931 and later became a fellow. His interests moved from probability toward logic and decidability: what procedures count as effective calculation? At Princeton he worked under Alonzo Church, completed a doctorate in 1938, and returned to Britain with a developing account of formal computation.
Abstract machines and computational limits
His computable-numbers paper, completed in 1936, described calculation using a tape, finite states, and explicit rules. A universal machine could simulate machines specified by input descriptions, while certain decision tasks admitted no general procedure. This separated questions about computation’s possibilities from the construction details of any particular physical device.
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Cryptanalysis and electronic computing
During the Second World War, Turing joined the collective effort against Enigma at Bletchley Park. Afterward he proposed the ACE computer at the National Physical Laboratory and worked on computing in Manchester. Mathematical ideas and engineering met in this career, alongside the contributions of colleagues, intelligence sources, and other technical teams.
Machine intelligence and biological form
In “Computing Machinery and Intelligence” in 1950, Turing used an imitation game to frame discussion of machine intelligence through interaction. His subsequent work turned to biological pattern and form, with a morphogenesis paper in 1952. His research thus joined formal limits on computation with mathematical modeling of questions arising from living systems.