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NEW YORK, NY - APRIL 09: The 1942 56-page notebook belonging to codebreaker Alan Turing is displayed at Bonham's auction house on April 9, 2015 in New York City. The notebook, along with a working Enigma cipher machine that the math genius used, are to be auctioned on in New York on Monday. the notebook alone is expected to go for $1 million. Turing's life and work were recently brought to life in the 2014 blockbuster "The Imitation Game", which drew eight Oscar nominations. Spencer Platt/Getty Images/AFP == FOR NEWSPAPERS, INTERNET, TELCOS & TELEVISION USE ONLY == Image Credit: AFP

A handwritten notebook by British Second World War code-breaking genius Alan Turing is expected to bring at least $1 million (Dh3.67 million) at auction in New York.

The 56-page manuscript was written at the time the mathematician and computer science pioneer was working to break the seemingly unbreakable Enigma codes used by the Germans throughout the war. It contains Turing’s complex mathematical and computer science notations, and is believed to be the only extensive Turing manuscript known to exist, according to Bonhams, which is offering the manuscript for sale on Monday.

The story of how Turing and a team of cryptanalysts broke the code was portrayed in the 2014 movie, The Imitation Game, starring Benedict Cumberbatch in the role of Turing.

The notebook dates from 1942, when they were at Britain’s Second World War code and cypher school Bletchley Park. In one entry, Turing writes about a complex calculus notation.

“The Leibniz notation I find extremely difficult to understand in spite of it having been the one I understood the best once! It certainly implies that some relation between x and y has been laid down eg, y=x2+3x.”

The sale also includes a working German Enigma enciphering machine. The three-rotor device was manufactured for the German military in July 1944. It’s estimated to sell for $140,000 to $180,000.

Turing was prosecuted for being gay at a time when it was illegal in Britain. He was convicted of indecency in 1952 and agreed to undergo hormone treatment as an alternative to imprisonment to “cure” his homosexuality.

He died in 1954 of cyanide poisoning. It was ruled a suicide although his family and friends believed it might have been accidental. The notebook was among the papers he left in his will to friend and fellow mathematician Robin Gandy.

Gandy gave the papers to The Archive Centre at King’s College in Cambridge in 1977. But he kept the notebook, using its blank pages for writing down his dreams at the request of his psychiatrist. Bonham describes Gandy’s entries as highly personal; the notebook remained in his possession until he died in 1995.

At the beginning of his journal, Gandy writes: “It seems a suitable disguise to write in between these notes of Alan’s on notation, but possibly a little sinister; a dead father figure, some of whose thoughts I most completely inherited.”

In a statement through Bonhams, Turing scholar Andrew Hodges said the notebook sheds more light on how Turing remained committed to free-thinking work in pure mathematics.”

The Imitation Game, which also stars Keira Knightley, is based on Hodges’ book Alan Turing: The Enigma.

Bonhams said the seller wished to remain anonymous. Part of the proceeds will be donated to charity.