They (the senior staff of GCCS) regarded mathematicians as very strange beasts indeed. They required a little persuasion before they believed they could do anything practical or helpful at all.

The people working on Enigma were the celebrated Dilly Knox and a chap called Tony Kendrick, quite a character, who was once head boy at Eton.

There was a slightly bizarre interview with Dilly (Dilwyn Knox) who was himself a bit of a character to put it mildly. He didn't believe in wasting too much time in training his assistant, he gave me a five-minute talk and left me to get on with it.

Turing was certainly unlike anybody the Foreign Office civil servants had ever worked with before. For a start, he was a practising homosexual which made him a security risk. If he was ever caught breaking the law, he was liable to be blackmailed. Whether or not Denniston knew his sexual preferences, some of his colleagues did. Peter Twinn, Turing's assistant, found out one night in London. Returning to their shared hotel room after dinner, Turing asked Twinn whether they should go to bed together. When Twinn said he was not like that, Turing matter of factly made his excuses and got into his own bed alone. Turing was also very eccentric. One of his closest associates suggested that if examined today, he might have been diagnosed to be suffering from a mild form of autism. Perhaps it was Asperger Syndrome, otherwise known as high grade autism, which Isaac Newton is also thought to have had. People with this disorder frequently come up with brilliant ideas which no normal person could have thought of. At the same time, they have no idea how to relate to other people, and cannot understand what other people will think of their behaviour. Asperger Syndrome sufferers are often obsessive about their work, and like to do it alone.

Whether or not Turing had Asperger Syndrome, he certainly had many of its symptoms. He was an isolated loner at work and at play. In 1934, while still an undergraduate studying mathematics at King's College, Cambridge he had "discovered" the so-called Central Limit Theorem, only to be told subsequently that his "discovery" had already been written up twelve years earlier by another mathematician. He had failed to consult the relevant reference books.He admitted that he had only agreed to research Naval Enigma "because no one else was doing anything about it and I could have it to myself".

Peter Twinn, who has died aged 88, was the first mathematician recruited as an Enigma cipher-breaker into the Government Code and Cipher School (GC&CS) before the Second World War; later he was credited with being the first British cryptographer to break an Enigma cipher, something that always embarrassed him and led him to dismiss its significance.

Recruited from Oxford in early 1939, Twinn worked at the GC&CS London headquarters, opposite St James's Park underground station, with Dilwyn "Dilly" Knox, the GC&CS Chief Cryptographer, who was attempting to break the Enigma ciphers.

He then moved to Bletchley Park, the codebreakers' wartime headquarters, working first with Knox and then Alan Turing tackling the German navy's Enigma ciphers.

In early 1942, he took over from Knox as head of the section breaking the Enigma ciphers used by the Abwehr, the German military intelligence service. As such, he played an important role in the Double Cross deception operation that was vital to the success of the D-Day landings.

Peter Frank George Twinn, the son of a senior General Post Office official, was born at Streatham on January 9 1916. He attended Manchester Grammar School and then Dulwich College, before going up to Brasenose College, Oxford, to read Mathematics.

He was in the middle of a postgraduate scholarship studying Physics when he saw an advertisement for a job with the government. "I was a bit unsettled," he remembered. "I'd finished my university degree and I didn't quite know what to do." The advertisement indicated that they were looking for mathematicians, but was unclear about what else was involved.

"They offered me this job at the princely salary of, I think, £275 a year," he said, "which sounded all right to me, and I was taken along on the first day to be introduced to Dilly Knox."

Twinn recalled that until that point GC&CS had been dominated by classicists.

"They regarded mathematicians as very strange beasts indeed, and required a little persuasion before they believed they could do anything practical or helpful at all."

Knox's approach to codebreaking and life in general was "mildly bizarre", Twinn later remembered: "He didn't believe in wasting too much time on training his assistant. He gave me a five-minute talk and told me to get on with it."

The Enigma machine had a keyboard into which the message was typed. Each letter then passed through a series of rotating wheels until the enciphered letter appeared on a "lampboard" above the machine. The British codebreakers had devised systems to break the cipher, but could not work out which letter on the keyboard was wired to which letter on the initial part of the encipherment mechanism.

Twinn said: "Our ordinary alphabet has them in a certain order, but the Germans aren't idiots. When they have the perfect safeguard to introduce to their machine, to jumble it all up would be the sensible thing."

Fortunately, in July 1939, Polish codebreakers, who had managed to break the Enigma ciphers but were now struggling, invited the British to a conference near Warsaw to discuss techniques that could be used to break the ciphers. They told Knox that the Germans had not, in fact, jumbled up the letters. They had wired A to A, B to B and so on, something the British had never thought possible.

"I know in retrospect it sounds daft," Twinn said. "It was such an obvious thing to do, rather a silly thing, that nobody, not Dilly Knox, not Alan Turing, ever thought it worthwhile trying."

When Knox came back, he went immediately on leave, so it fell to Twinn to try out the Polish technique. "The first thing I did when he was on leave was to see if it worked in the machine, and, of course, lo and behold, it did."

It was later pointed out to Twinn that this was the first time that any Wehrmacht Enigma cipher was broken in Britain, but he dismissed it as of no consequence: "It was a trifling exercise, but I repeat for the umpteenth time, no credit to me."

When the codebreakers moved to Bletchley Park, Twinn worked with Knox on Enigma research in the cottage next to the main house before helping Turing to set up the Hut 4 team, which broke the German naval Enigma.

In October 1941, Knox broke the Abwehr Enigma, allowing the codebreakers to ensure that the Germans believed the Double-Cross deception organised by MI5 and MI6. But he soon fell ill with cancer, and Twinn took charge of the Abwehr Enigma section in early 1942.

Its work was of particular importance during the Fortitude deception operation that helped to ensure the success of the D-Day landings.

After the war, Twinn worked in several government departments, including the Ministry for Technology in which, during the late 1960s, he was Director of Hovercraft under the then Labour Technology Minister, Tony Benn.

He subsequently became Secretary of the Royal Aircraft Establishment, Farnborough. During this period, he developed an interest in entomology, gaining a PhD in the subject from London University.

His doctorate was on the jumping mechanism of the click beetle, which he studied using the ultra-high-speed cameras available at Farnborough.

On one occasion, while attempting to collect click beetles at the edge of the Farnborough runway, he was arrested by an MoD police officer who was highly embarrassed to discover that his prisoner was in fact the RAE Secretary.

In 1999 Twinn published, with PT Harding, a study of the distribution of the longhorn beetle, A Provisional Atlas of the Longhorn Beetle (Coleoptera Cerambycidae) of Britain; it records the present and past distribution of 63 species and is to be found on the desks of many entomologists.

Twinn was a keen musician who played the viola and clarinet and wrote a number of pieces of music. It was this shared interest in music, and the concerts performed to entertain the other Bletchley Park codebreakers, which led to his meeting Rosamund Case, who worked in the registry and played the cello. They married in 1944.

Peter Twinn, who died on October 29, is survived by his wife Rosamund, and by a son and three daughters.

Peter Twinn, who has died aged 88, was the first mathematician recruited by British intelligence before the second world war to attack German ciphers. He was also the first person to break open a signal encoded by an Enigma machine.

Decryption skills painstakingly developed in Room 40 of the old Admiralty building, where throughout the first world war naval intelligence had brilliantly exploited a captured German naval codebook, were allowed almost to wither away after 1918. But under the aegis of the Foreign Office, a handful of Room 40 veterans set up, on a shoestring, a Government Code and Cipher School (GC&CS) in Victoria. In wartime, its HQ moved to a requisitioned Victorian villa at Bletchley Park in Buckinghamshire, scene of extraordinary expansion. After the war, GC&CS developed into the current Government Communications Headquarters.

After a failure to achieve anything against Italian ciphers during the 1936 Abyssinian crisis, a revived GC&CS cut its teeth during the Spanish civil war on German naval traffic, which was intercepted by British naval eavesdroppers and passed on by the navy's fledgling Operational Intelligence Centre (OIC). GC&CS set up a separate naval section which moved into Hut 4 in the grounds of Bletchley Park.

The Munich crisis of 1938 prompted the creation of secure teleprinter and telephone links between OIC, naval and RAF commands and GC&CS, the basis of a massive, successful interception and penetration of enemy ciphers that by the end of the war drew in some 10,000 people: decrypted Enigma messages were the basis of Ultra intelligence, perhaps the most closely guarded secret of the war.

Before 1939, GC&CS personnel were a few decidedly unmilitary individuals, chiefly classicists, of whom Alfred Dilwyn ("Dilly") Knox was regarded as the most brilliant. Knox, whose eccentricity stood out even in this context, was the first Briton to tackle the Enigma cipher. Only as war approached did GC&CS consider recruiting crossword fiends, chess players, mathematicians and other lateral thinkers.

Twinn was born in Streatham, south London, the son of a senior Post Office administrator. He went to school at Manchester Grammar and Dulwich College, and read mathematics at Oxford, winning a scholarship for a higher degree in physics but with no clear idea of a career.

As the international climate chilled after Munich in 1938, cryptic advertisements began appearing in Britain. Early in 1939 Twinn answered one that sought mathematicians without revealing reasons. The result was an interview in Victoria and the offer of a modestly paid position as assistant to Dilly Knox; "training" was a five-minute briefing by Knox.

The Enigma machine had a typewriter keyboard and a "lampboard" in the same pattern. Between them lay a maze of wires passing through two circuit-boards and three geared wheels, each imprinted with the alphabet. The operator pressed the keys and wrote down the apparently random letters they lit up.

The device had been on file at the British patent office well before the war. The problem was not the workings of the machine so much as the manner in which the operator randomly set his wheels before encipherment. Prompted by Polish work on Enigma, Twinn experimentally assumed that the first circuit board did not substitute another letter for the letter that had been typed, though the wheels and the final circuit-board both did so.

This educated guess helped him to decipher a two-month-old Wehrmacht message at the end of 1939. He always modestly downplayed the importance of this breakthrough. It was followed early in 1940 by the penetration of a message on the day it was sent. In May 1940 GC&CS took delivery of the first "bombe" (because it ticked), a machine developed by the mathematical genius Alan Turing to speed up the trial-and-error decipherment process. The crucial, day-to-day value of Ultra was its use by OIC to pinpoint U-boats while helping convoys to avoid them.

Twinn assisted Turing in organising Hut 4's assault on naval Enigma (each major German command used different ciphers) while Knox turned to the Abwehr, German military intelligence. When Knox fell ill with cancer, Twinn took over the Abwehr operation, which underpinned the elaborate allied disinformation campaign that successfully masked the plans for the invasion of Normandy in June 1944 (Churchill's "bodyguard of lies").

At this time he married Rosamund Case, a GC&CS colleague who shared his love of music and played the cello.

After 1945 Twinn remained in government service, notably with the Ministry of Technology, where he became director of Hovercraft, before his appointment as secretary of the Royal Aircraft Establishment.

His impressive intellectual versatility included musical composition, virtuosity on the clarinet and the viola, and an interest in insects; to photograph them he borrowed the RAE's special cameras. He studied part-time for a PhD in entomology from London University, helping to produce a standard work on beetles.

His wife, three daughters and a son survive him.

Peter Frank George Twinn, mathematician, born January 9 1916; died October 29 2004