A key scientific document hand-written by the Enigma codebreaker Alan Turing has been sold at auction in New York for more than $1m. 

The paper, in which he details his work on the foundations of mathematical notation and computer science, was sold for $1,025,000 (£698,000) in a sale of fine books and manuscripts at Bonhams auction house.

Turing, frequently referred to as the father of modern computing and artificial intelligence, is best known for his contribution to cracking the code used by the Germans in their Enigma machines during the second world war when he worked for the government code and cypher school at Bletchley Park in Buckinghamshire.

Cassandra Hatton, a senior specialist in fine books and manuscripts at Bonhams, said the Turing manuscript was among the papers left in his will to his close friend and fellow mathematician, Robin Gandy.

She said it is made up of 56 pages in a simple notebook bought from a stationers in Cambridge and is almost certainly the only extensive autograph manuscript by Turing in existence. It is thought to date from 1942 when Turing was working at Bletchley Park. 

Part of the manuscript reads: “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...”

Hatton said: “This is a wonderful result and a fitting testament to Alan Turing’s impact and legacy. It has been a great privilege to have been involved in this sale and we are immensely pleased that all the people who bid for this unique item and indeed the wider public have recognised Turing’s importance and place in history.”

Turing, whose work cracking the German codes was vital to the British war effort, was convicted in 1952 of gross indecency with a 19-year-old man. He was chemically castrated and two years later died from cyanide poisoning in an apparent suicide.

In 2009, the then prime minister, Gordon Brown, apologised on behalf of the British government for the way Turing had been treated and he was granted a posthumous pardon in 2013. 

Bonhams said a rare three-rotor German Enigma enciphering machine was sold at the same auction for a world record price of $269,000. 

A portion of the proceeds from Bonhams and the vendor will be donated to charity, the auctioneers said.