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1939

Turing's Zeta Function Machine

Riemann zeta cogs

This blueprint for an elaborate gear-driven mechanical calculator to compute approximate values for the Riemann zeta function on the critical line was drawn up by Alan Turing's friend and student engineer Donald MacPhail in 1939.

Turing's Zeta Function Machine

In 1937, Alan Turing became interested in the Riemann hypothesis. In March 1939, he both submitted a paper to the London Mathematical Society (which was not published until 1943) and applied to the Royal Society for a grant for the construction of an elaborate gear-driven mechanical calculator to compute approximate values for the Riemann zeta function on the critical line. A £40 grant was awarded, and Turing's Canadian student engineer and friend Donald MacPhail drew up an actual blueprint on July 17, 1939. A table in the blueprint contains the ratios needed for mechanical linkages, though as prepared, the table contains a number of calculation errors. In any case, the Second World War intervened and the machine was never built. No parts survive.

Artifact format

1 item

Artifact origin

University of Cambridge

Current artifact location

University of Cambridge

Timeline

Primes timeline The Sieve of Eratosthenes Cataldi's Divisor Table Guldin's Factor Table Van Schooten's Prime Table Turing's Zeta Function Machine SWAC Computes New Mersenne Primes

Interactive Content

Computational Explanation

Other Resources

Additional Reading

  • Casselman, B. "Blueprint for a Turing Machine: About the Cover...and a Bit More." Notices of the American Mathematical Society, Vol. 53, No. 10, cover and pp. 1186–1189, 2006.
  • Hejhala, D. A. and Odlyzko, A. M. "Alan Turing and the Riemann Zeta Function." Unpublished (?) manuscript, 2011. [link].
  • Hodges, A. Alan Turing: The Enigma, rev ed. Princeton, NJ: Princeton University Press, pp. 196–199, 2014.
  • Turing, A. M. "A Method for calculation of the Zeta function." Proceedings of the London Mathematical Society, Vol. 48, pp. 180–197, 1943.
  • Welch, P. D. "Turing’s Mathematical Work." In Proceedings of the 6th Congress (6 ECM) held at the Jagiellonian University, Kraków, July 2–7, 2012 (Ed. R. Latała, A. Ruciński, P. Strzelecki, J. Świątkowski, D. Wrzosek and P. Zakrzewski). Zürich, Switzerland: European Mathematical Society, pp. 763–777, 2013.

Image Credits

King's College Library, Cambridge. AMT/C 2 Blueprint of the zeta function machine