by Matt Haig
‘Oh, it’s nothing. It’s just, this bump on my head. I am all over the place.’
‘Dear, that’s terrible. Are you sure you should be here? Shouldn’t you be at home in bed?’
‘Yes, probably I should. After this, I am going home.’
‘Good. Well, I hope you feel better soon.’
‘Oh. Thank you.’
‘Bye.’
She continued downstairs, not realising she had just saved her own life.
I had a key, so I used it. There was no point in doing anything overtly suspicious in case anyone else should have seen me.
And then I was inside his – my – office. I didn’t know what I had been expecting. That was a problem, now: expectation. There were no reference points; everything was new; the immediate archetype of how things were, at least here.
So: an office.
A static chair behind a static desk. A window with the blinds down. Books filling nearly three of the walls. There was a brown-leaved pot plant on the windowsill, smaller and thirstier than the one I had seen at the hospital. On the desk there were photos in frames amidst a chaos of papers and unfathomable stationery, and there in the centre of it all was the computer.
I didn’t have long, so I sat down and switched it on. This one seemed only fractionally more advanced than the one I had used back at the house. Earth computers were still very much at the pre-sentient phase of their evolution, just sitting there and letting you reach in and grab whatever you wanted without even the slightest complaint.
I quickly found what I was looking for. A document called ‘Zeta’.
I opened it up and saw it was twenty-six pages of mathematical symbols. Or most of it was. At the beginning there was a little introduction written in words, which said:
PROOF OF THE RIEMANN HYPOTHESIS
As you will know the proof of the Riemann hypothesis is the most important unsolved problem in mathematics. To solve it would revolutionise applications of mathematical analysis in a myriad of unknowable ways that would transform our lives and those of future generations. Indeed, it is mathematics itself which is the bedrock of civilisation, at first evidenced by architectural achievements such as the Egyptian pyramids, and by astronomical observations essential to architecture. Since then our mathematical understanding has advanced, but never at a constant rate.
Like evolution itself, there have been rapid advances and crippling setbacks along the way. If the Library of Alexandria had never been burned to the ground it is possible to imagine that we would have built upon the achievements of the ancient Greeks to greater and earlier effect, and therefore it could have been in the time of a Cardano or a Newton or a Pascal that we first put a man on the moon. And we can only wonder where we would be. And at the planets we would have terraformed and colonised by the twenty-first century. Which medical advances we would have made. Maybe if there had been no dark ages, no switching off of the light, we would have found a way never to grow old, to never die.
People joke, in our field, about Pythagoras and his religious cult based on perfect geometry and other abstract mathematical forms, but if we are going to have religion at all then a religion of mathematics seems ideal, because if God exists then what is He but a mathematician?
And so today we may be able to say, we have risen a little closer towards our deity. Indeed, potentially we have a chance to turn back the clock and rebuild that ancient library so we can stand on the shoulders of giants that never were.
Primes
The document carried on in this excited way for a bit longer. I learned a little bit more about Bernhard Riemann, a painfully shy, nineteenth-century German child prodigy who displayed exceptional skill with numbers from an early age, before succumbing to a mathematical career and a series of nervous breakdowns which plagued his adulthood. I would later discover this was one of the key problems humans had with numerical understanding – their nervous systems simply weren’t up to it.
Primes, quite literally, sent people insane, particularly as so many puzzles remained. They knew a prime was a whole number that could only be divided by one or itself, but after that they hit all kinds of problems.
For instance, they knew that the total of all primes was precisely the same as the total of all numbers, as both were infinite. This was, for a human, a very puzzling fact, as surely there must be more numbers than prime numbers. So impossible was this to come to terms with, some people, on contemplating it, placed a gun into their mouth, pulled the trigger, and blew their brains out.
Humans also understood that primes were very much like the Earth’s air. The higher you went, the fewer of them there were. For instance, there were 25 primes below 100, but only 21 between 100 and 200, and only 16 between 1000 and 1100. However, unlike with the Earth’s air it didn’t matter how high you went with prime numbers as there were always some around. For instance, 2097593 was a prime, and there were millions between it and, say, 4314398832739895727932419750374600193. So, the atmosphere of prime numbers covered the numerical universe.
However, people had struggled to explain the apparently random pattern of primes. They thinned out, but not in any way that humans could fathom. This frustrated the humans very much. They knew that if they could solve this they could advance in all kinds of ways, because prime numbers were the heart of mathematics and mathematics was the heart of knowledge.
Humans understood other things. Atoms, for instance. They had a machine called a spectrometer which allowed them to see the atoms a molecule was made from. But they didn’t understand primes the way they understood atoms, sensing that they would do so only if they could work out why prime numbers were spread out the way they were.
And then in 1859, at the Berlin Academy, the increasingly ill Bernhard Riemann announced what would become the most studied and celebrated hypothesis in all mathematics. It stated that there was a pattern, or at least there was one for the first hundred thousand or so primes. And it was beautiful, and clean, and it involved something called a ‘zeta function’ – a kind of mental machine in itself, a complex-looking curve that was useful for investigating properties of primes. You put numbers into it and they would form an order that no one had noticed before. A pattern. The distribution of prime numbers was not random.
There were gasps when Riemann – mid panic attack – announced this to his smartly dressed and bearded peers. They truly believed the end was in sight, and that in their lifetimes there would be a proof that worked for all prime numbers. But Riemann had only located the lock, he hadn’t actually found the key, and shortly afterwards he died of tuberculosis.
And as time went on, the quest became more desperate. Other mathematical riddles were solved in due course – things like Fermat’s Last Theorem and the Poincaré Conjecture – which left proof of the long-buried German’s hypothesis as the last and largest problem to solve. The one that would be the equivalent of seeing atoms in molecules, or identifying the chemical elements of the periodic table. The one that would ultimately give humans supercomputers, explanations of quantum physics and interstellar transportation.
After getting to grips with all this I then trawled through all the pages full of numbers, graphs and mathematical symbols. This was another language for me to learn, but it was an easier and more truthful one than the one I had learnt with the help of Cosmopolitan.
And by the end of it, after a few moments of sheer terror, I was in quite a state. After that very last and conclusive ∞, I was left in no doubt that the proof had been found, and the key had turned that all-important lock.
So, without so much as a second’s thought, I deleted the document, feeling a small rush of pride as I did so.
‘There,’ I told myself, ‘you may have just managed to save the universe.’ But of course, things are never that simple, not even on Earth.
A moment of sheer terror
ξ(1/2+it)=[eŖlog(r(s/2))π-1/4(–t2–1/4)/2]x[eiJlog(r(s/2))π-it/2ζ(1/2+it)]
The distribution of prime numbers<
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I looked at Andrew Martin’s emails, specifically the very last one in his sent folder. It had the subject heading, ‘153 years later . . .’, and it had a little red exclamation mark beside it. The message itself was a simple one: ‘I have proved the Riemann hypothesis, haven’t I? Need to tell you first. Please, Daniel, cast your eyes over this. Oh, and needless to say, this is for those eyes only at the moment. Until it goes public. What do you reckon? Humans will never be the same again? Biggest news anywhere since 1905? See attachment.’
The attachment was the document I had deleted elsewhere, and had just been reading, so I didn’t waste much time on that. Instead, I looked at the recipient: [email protected].
Daniel Russell, I swiftly discovered, was the Lucasian Professor of Mathematics at Cambridge University. He was sixty-three years old. He had written fourteen books, most of which had been international bestsellers. The Internet told me he had taught at every English-language university with an intimidating enough reputation – Cambridge (where he was now), Oxford, Harvard, Princeton and Yale among others – and had received numerous awards and titles. He had worked on quite a few academic papers with Andrew Martin, but as far as I could tell from my brief research they were colleagues more than friends.
I looked at the time. In about twenty minutes my ‘wife’ would be coming home and wondering where I was. The less suspicion there was at this stage the better. There was a sequence of doing things, after all. I had to follow the sequence.
And the first part of the sequence needed to be done right now, so I trashed the email and the attachment. Then, to be on the safe side, I quickly designed a virus – yes, with the help of primes – which would ensure that nothing could be accessed intact from this computer again.
Before I left, I checked the papers on the desk. There was nothing there to be worried about. Insignificant letters, timetables, blank pages, but then, on one of them, a telephone number 07865542187. I put it in my pocket and noticed, as I did so, one of the photographs on the desk. Isobel, Andrew and the boy I assumed to be Gulliver. He had dark hair, and was the only one of the three who wasn’t smiling. He had wide eyes, peeping out from below a dark fringe of hair. He carried the ugliness of his species better than most. At least he wasn’t looking happy about what he was, and that was something.
Another minute had gone by. It was time to go.
We are pleased with your progress. But now the real work must begin.
Yes.
Deleting documents from computers is not the same as deleting lives. Even human lives.
I understand that.
A prime number is strong. It does not depend on others. It is pure and complete and never weakens. You must be like a prime. You must not weaken, you must distance yourself, and you must not change after interaction. You must be indivisible.
Yes. I will be.
Good. Now, continue.
Glory
Isobel was still not back, on my return to the house, so I did a little more research. She was not a mathematician. She was a historian.
On Earth, this was an important distinction as here history was not yet viewed as a sub-division of mathematics, which of course it was. I also discovered that Isobel, like her husband, was considered to be very clever by the standards of her species. I knew this because one of the books on the shelf in the bedroom was The Dark Ages, the one I had seen in the bookshop window. And now I could see it had a quote from a publication called the New York Times which read ‘very clever’. The book was 1,253 pages long.
A door opened downstairs. I heard the soft sound of metal keys being rested on a wooden chest. She came up to see me. That was the first thing she did.
‘How are you?’ she asked.
‘I’ve been looking at your book. About the Dark Ages.’
She laughed.
‘What are you laughing at?’
‘Oh, it’s that or cry.’
‘Listen,’ I said, ‘do you know where Daniel Russell lives?’
‘Of course I do. We’ve been to his house for dinner.’
‘Where does he live?’
‘In Babraham. He’s got a whopping place. Can you seriously not remember? It’s like not remembering a visit to Nero’s palace.’
‘Yes. I can, I can. It’s just that there are things which are still a bit hazy. I think it’s the pills. That was a blank, so that’s why I asked. That’s all. So, I’m good friends with him?’
‘No. You hate him. You can’t stand him. Though deep hostility is your default setting with other academics these days, Ari excepted.’
‘Ari?’
She sighed. ‘Your best friend.’
‘Oh, Ari. Yes. Of course. Ari. My ears are a bit blocked. I didn’t hear you properly.’
‘But with Daniel,’ she said, speaking a little louder, ‘if I dare say it, the hatred is just the manifestation of an inferiority complex on your part. But superficially, you get on with him. You’ve even sought his guidance a few times, with your prime number stuff.’
‘Right. Okay. My prime number stuff. Yes. And where am I with that? Where was I? When I last spoke to you, before?’ I felt the urge to ask it outright. ‘Had I proved the Riemann hypothesis?’
‘No. You hadn’t. At least, not that I knew. But you should probably check that out, because if you have we’ll be a million pounds richer.’
‘What?’
‘Dollars, actually, isn’t it?’
‘I—’
‘The Millennium Prize, or whatever it is. Proof of the Riemann hypothesis is the largest remaining puzzle that hasn’t been solved. There is an institute in Massachusetts, the other Cambridge, the Clay Institute . . . You know this stuff backwards, Andrew. You mumble this stuff in your sleep.’
‘Absolutely. Backwards and forwards. All the ways. I just need a little reminding that is all.’
‘Well, it’s a very wealthy institute. They obviously have a lot of money because they’ve already given about ten million dollars away to other mathematicians. Apart from that last guy.’
‘Last guy?’
‘The Russian. Grigori something. The one who turned it down for solving the Whatever-it-was Conjecture.’
‘But a million dollars is a lot of money, isn’t it?’
‘It is. It’s a nice amount.’
‘So why did he turn it down?’
‘How do I know? I don’t know. You told me he was a recluse who lives with his mother. There are people in this world who have motives that extend beyond the financial, Andrew.’
This was genuinely news to me. ‘Are there?’
‘Yes. There are. Because, you know, there’s this new groundbreaking and controversial theory that money can’t buy you happiness.’
‘Oh,’ I said.
She laughed again. She was trying to be funny, I think, so I laughed, too.
‘So, no one has solved the Riemann hypothesis?’
‘What? Since yesterday?’
‘Since, well, ever?’
‘No. No one has solved it. There was a false alarm, a few years back. Someone from France. But no. The money is still there.’
‘So, that is why he . . . why I . . . this is what motivates me, money?’
She was now arranging socks on the bed, in pairs. It was a terrible system she had developed. ‘Not just that,’ she went on. ‘Glory is what motivates you. Ego. You want your name everywhere. Andrew Martin. Andrew Martin. Andrew Martin. You want to be on every Wikipedia page going. You want to be an Einstein. The trouble is, Andrew, you’re still two years old.’
This confused me. ‘I am? How is that possible?’
‘Your mother never gave you the love you needed. You will for ever be sucking at a nipple that offers no milk. You want the world to know you. You want to be a great man.’
She said this in quite a cool tone. I wondered if this was how people always talked to each other, or if it was just unique to spouses. I heard a key enter a lock.
Isobel looked at
me with wide, astonished eyes. ‘Gulliver.’
Dark matter
Gulliver’s room was at the top of the house. The ‘attic’. The last stop before the thermosphere. He went straight there, his feet passing the bedroom I was in, with only the slightest pause before climbing the final set of stairs.
While Isobel went out to walk the dog I decided to phone the number on the piece of paper in my pocket. Maybe it was Daniel Russell’s number.
‘Hello,’ came a voice. Female. ‘Who’s this?’
‘This is Professor Andrew Martin,’ I said.
The female laughed. ‘Well hello, Professor Andrew Martin.’
‘Who are you? Do you know me?’
‘You’re on YouTube. Everyone knows you now. You’ve gone viral. The Naked Professor.’
‘Oh.’
‘Hey, don’t worry about it. Everyone loves an exhibitionist.’ She spoke slowly, lingering on words as if each one had a taste she didn’t want to lose.
‘Please, how do I know you?’
The question was never answered, because at that precise moment Gulliver walked into the room and I switched off the phone.
Gulliver. My ‘son’. The dark-haired boy I had seen in the photographs. He looked as I had expected, but maybe taller. He was nearly as tall as me. His eyes were shaded by his hair. (Hair, by the way, is very important here. Not as important as clothes obviously, but getting there. To humans, hair is more than just a filamentous biomaterial that happens to grow out of their heads. It carries all kinds of social signifiers, most of which I couldn’t translate.) His clothes were as black as space and his T-shirt had the words ‘Dark Matter’ on them. Maybe this was how certain people communicated, via the slogans on their T-shirts. He wore ‘wristbands’. His hands were in his pockets and he seemed uncomfortable looking at my face. (The feeling, then, was mutual.) His voice was low. Or at least low by human standards. About the same depth as a Vonnadorian humming plant. He came and sat on the bed and tried to be nice, at the start, but then at one point he switched to a higher frequency.