Movies about mathematicians are rare, the problem being that the real action is all in the head. At first sight, maths doesn’t quite have the cinematic potential of a car chase or a romantic love story.

But The Imitation Game has approached it head on. The remarkable thing about the story it tells is that it is not just about the maths, that scarily incomprehensible abstraction. It is a story so bizarre and intensely moving, you’d have trouble inventing it.

In 1936 a 24-year-old mathematician called Alan Turing wrote a paper on computable numbers. This paper contained something we now call “the Universal Turing Machine”. When working at Bletchley Park in World War II, the machine that Turing designed to crack the supposedly unbreakable German Enigma code: the Turing-Welchman Bombe, was a primitive prototype of the machine he imagined, and of the modern computer. It was not yet “universal”, but it helped the Bletchley Park heroes – almost 10,000 of them – shorten World War II by at least two years.

This is the story at the centre of The Imitation Game, starring Benedict Cumberbatch and Keira Knightley. It’s a film that might finally be making Turing the household name he should be.

Imitation

Director Morten Tyldum set himself a hard task. There’s the double hurdle of accurately portraying somebody’s life, as well as making some sense of the mathematics at the heart of the film; to make it understandable, as well as doing it justice.

It is the scriptwriter Graham Moore who made the director’s task doable. A degree of creative license is essential when making a film that is at once a biopic, an exploration of a key moment of history – and also has complex maths and computing at its heart. And so unsurprisingly, The Imitation Game is already being computed quite differently by individual movie goers and critics.

You might expect me, as a mathematician and Turing champion, to be its harshest critic. But actually it was Turing’s mathematics that helped me understand and appreciate what the film makers are doing. Turing’s mathematics splits information into increasing levels of complexity. This is mirrored in the case of the film where some historical details are added or changed to help us, the viewers, have more insight into the real story.

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So for me, the beauty of the thing is that this kind of imitation is at the root of Graham Moore’s fantastic script. It is present both in Turing’s scientific focus and in his life as a gay man on “the autistic spectrum” – the latter nicely described by Morten Tyldum as “thinking different”. For living and working mathematicians, it is the “neuro-typicals” who are “different”.

This is beautifully shown in a moving scene in which Turing gives his team some apples after having been advised by Joan Clarke (Keira Knightley) that they are more likely to help him in his plan if they like him. This is just part of Alan’s personal imitation game.

This and more makes the film fabulously engrossing, a wonderful creative imitation of the world of Turing that we have left behind us. The brilliant creative team – director, score composer, and some wonderful actors – have astutely accepted that Turing’s mentality has to be at the very centre of the film. The result is a youthful and creative engagement with the Turing story.

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What didn’t happen

There is a need for boldness when dramatising the hidden inner reality of Turing’s amazing mental engagement with the machine and its meaning. To achieve this, the film imports various figures and elements into the story that don’t quite fit the history. Soviet spy John Cairncross is teleported from a quite different hut into Turing’s decrypting team at Bletchley Park, for example, something Turing historian Andrew Hodges has questioned publicly.

To me this made good sense. Using this dramatic device our appreciation of the sheer complexity, pain, and incomputability of the imitation game – and its necessity in wartime Europe – is enriched. Another example is the seeming arrogance and socially abrasiveness of Turing in some scenes; this time dramatically reflecting the undoubted isolating role of originality of thinking and mathematical rationality.

Did Alan ever give his team apples after being advised on the usefulness of being liked? Of course not, but it’s a beautiful and truthful moment in the film. Our amusement is affectionate and – as Graham Moore will have intended – complex. Did Alan ever have a replica of the Bletchley Park Bombe in his final years in the house in Wilmslow, obsessed with the mysteries of the machine called Christopher? Obviously not. But he was busy probing other mysteries (something called morphogenesis), and was sad and isolated. And so that scene is a small but dramatically potent adjustment, one of the most poignant and complex moments of this moving and thought-provoking film.

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It was not until a second viewing that I was fully adjusted to these shifts and additions. I just knew too much. I started out wanting an enormous amount of detail – like that present in the Andrew Hodges’s biography, the inspiration for the film. And I wanted detail explained of the wide spectrum of scientific areas Turing brought his genius to.

But what eventually took hold, powerfully, was the depiction of a very real Turing – and an inner experience of his fundamental thinking on the mathematics, an admirable achievement.

I guess this is not a film for all experts. It’s aimed at the many people who until now have known little or nothing of Turing and his unique contribution to our modern world. The directing and acting – especially from Benedict Cumberbatch and Keira Knightley – is outstanding. And the resulting learning experience is potentially universal. It’s impossible to tell what will emerge from this cinematic playing out of such a poignantly adventurous Imitation Game.