One side of the Alan Turing document that sold for £35,000 at Bonhams.

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A set of calculations which set out to analyse a problem in n-dimensional geometry that had been handwritten in ink by Alan Turing (1912-54) on two pages of mathematical paper proved one of the main attractions of a March 29 sale held by Bonhams (27.5/26/20/14.5% buyer’s premium).

Sold above high estimate at £35,000, they were found among the papers of Rolf Noskwith (1919-2017).

As a young cryptographer, Noskwith worked closely with Turing on German naval codes from June 1941 until, in the autumn of the following year, the latter left for the US, where he was to assist the US Navy’s codebreakers.

Problem solvers

In the words of Prof Jack Copeland, director of the Turing archive for the history of computing, these calculations offer “ excellent example of the recreational mathematics that went on at Bletchley Park”.

Turing’s extensive contributions in this line also included work on computerised chess, mechanised learning and other aspects of what he called “machine intelligence”.

They also served to demonstrate the pervading culture of intellectual enquiry and collaboration.

Turing and his colleagues had a deep-rooted interest in problem solving and puzzles and their leisure time was in part an extension of their intellectual interests. Noskwith writes of his colleagues’ reluctance to leave work at the end of a long shift, so engrossed were they in the challenges of the day.

There were, however, many other activities at Bletchley to occupy their time – among then tiddlywinks, table-tennis, rounders, tennis and cricket. Musical and dramatic societies also existed, along with chess and bridge clubs.

A separate lot of papers from the collection of Noskwith related to his time at Bletchley Park, together with further family correspondence, personal and business papers, sold above estimate for £2200.