Some people’s lives drive you into a rage. Alan Turing’s is one. In The Man Who Knew Too Much David Leavitt unexpectedly compares him to Alec Guinness playing Sidney Stratton in The Man in the White Suit. Like Stratton, who invented a suit that would never wear out, Turing was a brilliant scientific deviant, interested in ‘welding the theoretical to the practical, approaching mathematics from a perspective that reflected the industrial ethos of the England in which he was raised’. And, like Stratton, he was ‘hounded out of the world’. But Stratton was playing an Ealing comedy. The injustice done to Turing makes you want to spit at someone. Snow White and the Seven Dwarfs was Turing’s favourite film. He was especially fond of a scene in which the Wicked Queen coats an apple in poison to give to Snow White.

Turing’s first great mathematical contribution followed shortly after Gödel’s Incompleteness Theorem and used similar unseemly mathematical techniques. Gödel proved that no mathematical system can ever be shown to be consistent or complete. Turing, by imagining a room filled with strange machines that could analyse every possible mathematical equation, showed that no mathematical system can provide a general method for testing the truth or falsehood of its theorems. With Gödel and Turing, the certitude of mathematics disappeared. Leavitt spends 40 pages describing straightforwardly how Turing managed to prove this thesis. They should be reread two or three times, and mulled over like a good puzzle. How could something that begins so simply turn out so destructive to mathematical divinity? I’m on my fourth reading, and still don’t quite get it.

In 1939, under the guise of joining ‘Captain Ridley’s Shooting Party’, Turing reported secretly to Bletchley Park to lead the team working on cracking the German Enigma codes. These were not just mathematicians. Other members of the team included the British chess champion, winners of a speed crossword competition in the Telegraph and Malcolm Muggeridge. Together they built a machine more than six and a half feet high and seven feet wide, using more than ten miles of wire, that simulated 30 Enigma machines working at once. Turing’s startling mathematical analyses, taken straight from the once-considered practically useless field of mathematical logic, were helped by the fact that the Germans tended to be sloppy, the operator repeatedly choosing, for example, ‘the first three letters of his girlfriend’s name’ for part of the information instructing the receiver how to set his decoding machine. Sometimes the RAF would help by deliberately planting mines where the Germans could find them. In such cases, the crew at Bletchley could crack the day’s code because they already knew part of the text of the location reports that the joyful Germans sent back to base when the mines were discovered.

Turing was famous for what Leavitt, too politely, calls his ‘literal-mindedness’. At one point, he joined the Home Guard. ‘Do you understand that by enrolling in the Home Guard you place yourself liable to military law?’ asked the application form. ‘No,’ answered Turing. He completed the training, became a ‘first-class’ marksman, then stopped appearing at parades. When his officer threatened him with hellfire, Turing merely replied that he was not a soldier. He had answered ‘no’ to that question, therefore was not subject to military law and under no obligation to attend parades. Leavitt does not say what happened next. If the sergeant had had any sense, he would have clapped the pedantic little monster in irons.

But there was courage in his ‘literal-mindedness’ too. Turing never hid his homosexuality. Leavitt suggests that, as a logician, ‘he simply accepted it and assumed (wrongly) that others would as well’. It’s difficult to believe. It makes his character at odds with his unfettered, almost whimsical approach to mathematical problems and the sharpness of his letters to his mother that Leavitt quotes. Throughout The Man Who Knew Too Much there is a mischievous, bloody- minded, somewhat smug and loveless figure stumbling forward.

Turing’s final years are a disgusting indictment of something, though I can’t quite fix on what. Our judiciary? Our sexual f***ed-upness? The whole of postwar Britain? In 1952 Turing was arrested for ‘gross indecency’ with another man and sentenced to submit to a course of oestrogen treatments — chemical castration — to ‘cure’ him of his homosexuality. He grew breasts. Two years later, humiliated and mad, the man who devoted so much time to protecting his people and hastening the end of the war, committed suicide by eating an apple dipped in cyanide.

Leavitt’s own conclusion is nicely done, and with a mildness I can’t share after reading The Man Who Knew Too Much. I feel sick. But Leavitt manages to see something past this visceral response.

Perhaps what chills us is that in taking his own life Turing actually chose to camp it up a bit... yet in all the pages I have read about Turing — and there are scores of them — no one has yet mentioned what seems to me the most obvious message. In the fairytale the apple into which Snow White bites doesn’t kill her; it puts her to sleep until the Prince wakes her up with a kiss.