A Method for the Calculation of the Zeta-Function(122 views)
Description: FIRST EDITION of Turing’s work outlining a method (which he hoped could be performed by a machine) to solve one of mathematics’ most perplexing issues: the calculation the zeros of the Riemann zeta-function. Having worked on the zeta-function since his Ph.D.-thesis but never having published anything directly on the topic, Turing began working as chief cryptanalyst during the Second World War and thus postponed this important work till after the war. Thus, it was not until 1943 that he was actually able to publish his first work on this most important subject, namely the work that he had presented already in 1939, the groundbreaking A Method for the Calculation of the Zeta-Function, which constitutes his first printed contribution to the subject (Andrew Hodges). The Turing archive contains a sketch of a proposal, in 1939, to build an analog computer that would calculate approximate values for the Riemann zeta-function on the critical line. His ingenious method was published in 1943... Although he received a grant to build a special-purpose analog computer using his electromechanical relays to compute values of the Riemann zeta function, [he] never completed this project. (Downey, Turings Legacy; Modern Mathematics). Turing not only designed a machine to calculate the zeros of the zeta function, but did his own engineering work [and] hence, got involved in all the fine details of constructing this machine. He planned on eighty meshing gear wheels with weights attached at specific distances from their centers. The different moments of inertia would contribute different factors to the calculation, and the result would be the location of and an enumeration of the zeros of zeta. Visitors to Turings apartment would be greeted by heaps of gear wheels and axles and other junk strewn about the place. Although Turing got a good start cutting the gears and getting ready to assemble the machine, more pressing events (such as World War II) interrupted his efforts. His untimely death prevented the completion of the project (Krantz, Mathematical Apocrypha Redux). IN: Proceedings of the London Mathematical Society, Series 2., Vol. 48., Part 3., December 15, 1943, pp. 180-197. London: C.F. Hodgson & Son, Ltd., 1943. Tall octavo, modern three quarter red cloth over linen boards, original wrappers bound-in. A beautiful, fine copy with full margins and no institutional stamps. RARE.
Artist or Maker: TURING, ALAN