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.

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.