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In any case, it was enough to focus the little professor’s attention. Even if he suspected all of this, he didn’t know it and he wouldn’t be likely to want to test the thing out. He had been warned, flattered and warned. He was short, and Red Queen was tall. He was sitting on a low sofa without a table in front of him, and Red Queen was sitting upright behind a desk. He was as ready as he’d ever be.

‘OK,’ Red Queen continued. ‘Banacharski. The organisation I work for has been very interested in Nicolas Banacharski for several years…’

Professor Hands, as Red Queen knew, was a number theorist with a very strong interest in Banacharski’s work. And Red Queen knew, too, most of the basic facts of Banacharski’s life.

‘Well, ehm, Banacharski was a prodigy. Born in Germany. Father was a Russian Jew, died in the camps. He won the Fields in the sixties – you know, the big mathematical medal?’

‘I know.’

‘Amazing work. Very, very high levels of abstraction. He more or less invented – well, completely reshaped – the field I work in. The Fermat solution wouldn’t have been possible without his work. But he’s barely been heard from since the early nineties. I don’t know where he is. Nobody does.’

‘Presumably he knows where he is,’ said Red Queen.

‘I wouldn’t bet on it. He’d be in his eighties now, and he – you know – went mad.’

Hands scratched the back of his neck. He still looked a little uneasy.

‘Banacharski had – well, they started as strong convictions. He was in Paris for ’68 and he started to become more and more political. There’d been a chair created for him at the Sorbonne. He’d worked there for a decade or so, perfectly normally. Then he threw it up in 1972 on the grounds that his chair was partly funded by the military. He was a pacifist.’

‘That’s what was said.’

‘It’s the only explanation. He was still working at this stage, but he was getting crankier. Started claiming there was going to come some sort of scientific apocalypse by the end of the century if the physicists weren’t kept in check. Then he upped and off.’

‘Off?’

‘Vanished.’ The mathematician was starting to forget his surroundings and enjoy his story. ‘He was living in communes, going Buddhist, vegan, some people said – stopped using beds for a bit. There were stories that he went round trying to sell buckets of his own faeces to farmers as fertiliser. He turned into a mad monk. He was notionally attached to the University of Toulouse, but -’ he blew air out between his lips and shrugged ‘- he was doing his own thing. Proofs, papers – he mostly just wrote thousands of pages of what he called “meditations”. There’d be fragments of proofs in them, amazing proofs – some of them are in libraries. But he was cracked. That’s how the story goes.

‘One morning in the early nineties his girlfriend returned home to find he’d had a kind of manuscript bonfire in her garden. He was never seen again.’

‘Literally never seen again?’

‘More or less. These letters go out, though – of the long and rambling sort. People in the community, you know – they try to piece together what he’s doing. He claims to have given up on math. He’s living by himself and working something like twelve hours a day on mad material – some huge manuscript about the physics of free will.’

‘That’s where we come in,’ said Red Queen. ‘We know about the letters. We were keeping an eye on them. Does the name Isla Holderness mean anything to you?’

‘Yes,’ said Hands, and there was a moment before something dropped into place behind his eyes. Red Queen looked expressionlessly at him. ‘Uh, yes. She’s a mathematician in my field. She’s one of the last people who saw Banacharski. She went to look for him in the Pyrenees.’

Red Queen exhaled. ‘You know the story.’

‘ “What is a metre?” ’

Red Queen nodded in recognition. ‘What is a metre?’ Banacharski’s weird riddle: the last communication with Holderness before he disappeared for the final time.

‘OK. We’re on the same page. We know a bit more than you about some of it. But I’ll lay it out. Our organisation is called the Directorate of the Extremely Improbable. It’s a silly name, but it’s always been called that, and the silliness acts as a sort of camouflage. We could just as easily have brought you here in a green helicopter, and had you picked up by men wearing clear eyeglasses and button-down shirts from Gap. As it is, we don’t sound like what we are. That is the idea.

‘Our job is to assess threats to national security that we don’t know exist, using methods that we don’t know work. This produces results that we generally can’t recognise as results, and when we can recognise them as results, we don’t know how to interpret them.’

Red Queen continued to look at him levelly.

‘It’s frustrating work. Here.’

Red Queen fished in a desk drawer, pulled something out, and lobbed it across the room to the little mathematician, who caught it. ‘This is a souvenir from the days when we used to have our own memorabilia.’

He turned it over. It was a bronze medallion. Engraved on it was the pyramid-and-eye logo from the dollar bill. Above it, a scrollwork banner carried the initials ‘DEI’. Curving below, a scroll carried the words ‘Ignota ignoti’.

‘Unknown unknowns,’ Red Queen said. ‘That’s what we do. We deal with things we don’t know we don’t know about. Once we know we don’t know about them we hand them over to the CIA, who -’ Red Queen sighed ‘- generally continue not to know about them.

‘Predecessors of the DEI have existed as long ago as the Salem witch trials. We had operatives in the Culper Ring during the Revolutionary War. This, at least, is how the story within the organisation goes – but there’s no real evidence for any of it.

‘We were shut down for reasons nobody within the organisation understands after the Kennedy assassination, but then, come the run-up to the second Gulf War, certain senior members of the administration became very interested indeed in the sort of paranoid X-Files material that was traditionally associated with the Directorate. Donald Rumsfeld, as Secretary of Defense, reinstated our work. Our off-books budget suddenly reappeared. It got big.

‘Below where we’re sitting this compound goes twelve storeys down. There are tea-leaf readers, distance seers, chaos magicians and tarot tellers. Dicemen. Catatonics. Psychokinetics, psychic healers, lunatics. Haruspices. Illuminati. Idiot savants. Hypnotists. Bearded ladies. Oracles. All drinking the same coffee, and all paid for by the American taxpayer.’

Red Queen didn’t seem entirely sold on the tea-leaf readers, it occurred to Hands, but it didn’t seem his place to point it out.

Instead, he said: ‘So, ah, what is your interest in our mad genius?’

‘Banacharski?’ Red Queen said. ‘We don’t think Banacharski was mad. We think Banacharski was trying to build a weapon.’

Chapter 5

Alex didn’t know what made him stop in Atlanta.

He’d been rebooked onto an onward flight to San Francisco, after the hurricane, but he had never gone to the airport. He had sat on the bed in his motel looking at the clock, his suitcase packed on the bed beside him.

The time when he had planned to leave for the airport had passed. Then the time when he’d need to leave to have a hope of making the flight. Then the time that the gate would have closed. Had he looked out of his window he’d have been able to watch his flight lift into the air. He thought about the empty seat on the plane, carrying a ghost of him to San Francisco, another reality peeling off this one and heading its own way.