The first chapter of a novel I wrote last year about drugs, blackmail, and mathematics.
A chapter index can be found here.
CHAPTER ONE: SOLUTIONS
“Number rules the Universe.” – Pythagoras (570 BC – 495 BC)
The plain white pages spread out on the wide glass desk, decorated with scrawls of black, blue and red. The colours bled together. The symbols danced, unintelligible and erratic. Each additional statement became ever less logical, making ever less sense. Intensity swelled inside the writer, head in hands, body hunched right over the table, sweating palms running through short dark brown hair. Thoughts and ideas swelled and exploded like great bubbles inside the skull, which by now was unknowingly bouncing up and down on the glass surface. There was only one conclusion that could be drawn; simply, this was going nowhere. With a regained calm, the blanket of papers was swept up into folded arms and released out of the adjacent open sixth floor window. The author of the air born sheets reveled in watching the fruitless musings take flight, an ironic celebration of yet another day’s failure. The paper flew especially well today – the vigorously swaying trees dotted in the street below indicated that some pages could make it as far as the South Bank of the Thames, the author thought.
Though an author, strictly speaking, Professor Matthew Quinn was not. Rather, he was a senior faculty member of the prestigious Salvin College University, London. The Professor was a mathematician, and one held in high regard by all who knew and worked with him. The whole ten years of his employed life had been spent at the university that he had graduated from, in which time he had made significant – if often totally intangible – discoveries that had seen him rise through the academic ranks faster and further than many of his peers. Far from being the awkward, introverted stereotype often assigned to his discipline, Matthew was outgoing and an adept public speaker, a shrewd cynic and an adroit intellectual. He was also blessed with a self-assessed, above average appearance, which he complimented with a carefully executed dress sense, something the majority of his colleagues didn’t do. Looking up at his reflection in the glass pane before him, the re-constriction of the pupils of his dark brown eyes indicated that he was coming down. Leaning against the sill of the open window, however, it took longer than it should have done for him to notice that the backdrop to the city scene before him was a deep blue on the western horizon and dark charcoal grey everywhere else, the distant foreboding clouds stained with orange light pollution. The evening had melted away faster than he had realised, and even though the long days of summer was drawing to a close, Matthew estimated that it couldn’t have been earlier than half nine. He turned from the bay window, slammed it shut and walked back to the desk to collect his belongings. His office wasn’t exactly enormous, but had more than ample space for his desk, a stack of plastic chairs and a whiteboard mounted on a portable frame that were used for seminars, which he occasionally held with students in the room. Every square inch of the large wall opposite the window, adjacent to the office’s frosted glass door, was covered floor to ceiling in ageing, well-used whiteboards. They were covered in dense scrawls not dissimilar to those that had adorned the pages that were by now drifting through the streets of central London. There was a significant difference between the two sets of work however; namely the fact that he had verified that the mathematics written on the walls was all completely correct. Other members of the departmental staff had nicknamed these particular whiteboards “The Boards of Truth”; a grandiose term mocking Matthew’s almost paternal protection towards them, though it was a moniker that he ultimately took a shine to, and now even used himself. Unfortunately for the Professor however, none of the statements garnishing the boards of truth were at all recent revelations. Indeed, Matthew had not made a single addition to them in the last two months, over which time the summer sun that poured in through the large south facing window had bleached the marker pen, causing shadowy outlines of the characters to be left on the board whenever they were rubbed off with an eraser. He felt the last of the illegal substance draining from his blood stream. Standing, he stared right at the board in front of him, willing some flash of sweet inspiration to jump out. As before however, nothing did. He wiped the edge of his credit card clean, dabbing the resultant white residue on his fingertips onto the lining of his trouser pocket. He donned a jacket and left the room frustrated, locking the frosted glass door behind him as he did so.
Rebecca Bonfield reclined on a deep red leather sofa, toying with a diamond ring in her left hand. She looked at the living room wall across from where she was lying. The framed photograph hanging above the disused hearth exhibited her smiling in the arms of a well dressed, dark haired man with an above average appearance. Her first encounter of Matthew Quinn had been some twelve years ago whilst she had been reading English Literature at Salvin College. It was far from a case of ‘love at first sight’ like the kind that she had come across so often in many of the works that she had studied. And whilst there had been something intangibly appealing about this man, it had just been a friendship that developed – not a romance. Indeed, it wasn’t until a year after their respective graduations that the line between those two states had blurred, and it was a further eight years into their relationship before Matthew had proposed to her. Having returned home from work, Rebecca had been in the house alone for the last five hours. It was something that she was becoming reluctantly, but increasingly used to. She had accepted that Matthew’s mathematical work was extremely important for all manner of reasons, even if she had long since resigned herself to the fact that she would never understand a single sentence of it. Her line of sight remained fixed upon the mounted photograph. The woman depicted in it was attractive to a certain degree, though it was a bookish kind of beauty, one that had appreciated with time. She possessed wavy black hair cropped at the shoulders – a little shorter than it was now – a fair complexion and a quite perfectly defined nose, upon which rested black thick framed glasses that she sometimes interchanged with contact lenses, depending upon how her morning mood took her. She also wore a long sleeved shirt, which covered a scar that would have otherwise been visible on the top of her right arm. The blaring message tone from her phone snapped her attention back away from the photograph. She opened it, and it contained precisely the words that she wanted to read. Her fiancé was on his way home at last.
After letting himself through one of the many turnstiles beyond the entrance of the station, Matthew Quinn descended the escalator into the depths of the London underground. Warm waves of stale air washed upwards through the tunnels, trying to escape to the surface. Having boarded a train he sat himself down and rocked his head back against the window, exhaling loudly. The last day of September marked the last day of his university’s summer break. It also marked the end of his sabbatical year, a period of time in which he had been solely dedicated to research, a time as it transpired, that was dedicated to one sole problem whose solution still eluded him. It had been nearly eleven months since Matthew had jointly delivered a public lecture at Salvin College discussing advancements and discoveries made by the university’s mathematics department. His research had been dedicated to the mathematics of algorithms, codes, and cryptography, though as his speech was being delivered to a general audience, the Professor had to stay clear of any dense mathematical language and skirt around a lot of hugely complex detail. Even so, he was still able to unambiguously present his motivations.
“Ladies and Gentleman; the globe is shrinking,” he started, perched behind the branded lectern on the wide stage, “It is shrinking at a truly alarming rate… I am of course, speaking figuratively,” he added, noting more than a couple confused expressions amongst the audience. “When you go home this evening, you can see and talk to a friend that you have in Australia… You can buy shares from the NIKKEI markets in Japan, purchase a book in America and even order it to arrive on your doorstep by Saturday evening. None of us in here need telling that the Internet is the most important invention of the last 50 years. And up until a few years ago, we were all in agreement that the home computer was the perfect conduit for it’s awesome potential. And then look what happened,” Matthew pulled an expensive smartphone from his jacket, “I can now do all of what I just described on something that I can comfortably carry around in my back pocket. And I can even make calls to my mother on this thing…” He looked down into the crowd, immediately picking out Rebecca who had come to watch her fiancé in action, her eyes apparently captivated by what he was saying – if unimpressed by his attempts at humour. He continued, “Despite the wonder and sheer possibility of all this technology however, there is still something completely and fundamentally wrong with it. Allow me to present you with some background knowledge. When you click the button of a mouse, strike a key, tap on a touchscreen or send a message, it isn’t just ‘magic’ that happens beneath your fingers. The electronic codes that are used to send your messages and commands are, as you would imagine, incredibly complex. You might be thinking that this all sounds as if this speech should be being delivered by a computer scientist, however as a mathematician, it fills me with a certain sense of pride to tell you that their generation, transmission and delivery use sheer, pure mathematics,” he paused, “My kind of mathematics to be precise… the mathematics of algebraic coding, and their algorithms. Put in layman’s terms, an algorithm is like a machine. Your computer takes your message built from letters, numbers, pictures, sound waves – whatever it happens to be – then puts it through an algorithm. This then generates the ‘code’ in the form of a computer language such as binary. It is this code that actually gets sent across the Internet to another device that then takes the code, and by using the same algorithm in reverse, outputs whatever it was that you sent in the first place. There are of course many, many different variations on these algorithms depending on what you’re sending and what you’re sending it to and from. It’s all quite brilliant, and it all happens in fractions of seconds without you even thinking about it.
“But this brings us on to a much, much more important point, because it isn’t just you or I who use this technology on a daily basis. Think bigger… much bigger. Think Governments, militaries, multinational companies and people in high places with dangerous secrets… if their messages and secrets are going to remain… well, secret then these codes have to be totally impenetrable, because it’s much easier than you might imagine for agents to intercept these messages and decode them for themselves. Right now the algorithms are good, in fact they’re better than just ‘good’; the most modern of these codes are actually near impossible to crack. But as long as the condition ‘near’ remains, that isn’t good enough, because the technology at the disposal of these people who wish to steal these secrets is formidable, and is becoming increasingly more so. As a consequence, the parties that I spoke of earlier, the companies, governments and the like are spending vast sums of money on the study and research of algorithms; millions upon millions of pounds. Their mathematicians have convinced themselves that it’s out there, that ‘golden algorithm’, that special set of instructions that will produce an immaculate, unbreakable cypher. And believe me, if they do find it then it will have been worth every single penny. For all manner of reasons. It is a leading school of thought – and indeed one that I subscribe to myself – that an algorithm constructed using pure mathematics can be proven to be unbreakable for every single possible input, if the algorithm in question is indeed ‘golden’. After some degree of research however, it is my opinion that these companies are in fact wasting their time. I believe that this golden algorithm that produces a code that cannot be broken simply doesn’t exist…”
It hadn’t been more than a week after the lecture that Matthew had first received correspondence from Neil Parry, in the form of a letter addressed to the mathematics department at the university. The sheet of paper bore the letterhead of SL-Tech, a company that Matthew was entirely unfamiliar with and one that Internet searches shed scant light upon. It requested a personal meeting and an expressed interest in the Professor’s work, and though it wasn’t explicitly stated, it didn’t need to specify that the subject of conversation was likely to be Matthew’s research on algorithms. Intrigued, Matthew responded and the next evening found himself at an office just south of the River Thames. It was a small and thoroughly innocuous building; indeed the company itself only seemed to occupy the basement floor. Neil Parry had made an instant impression. He was an incredibly imposing figure, being at least six and a half feet tall with short thinning blonde hair and a handshake that about took Matthew’s arm clean off. Despite a slightly daunting first impression, Matthew concluded that there was something essentially placid about Neil, he seemed like a man in absolute control of everything that he needed to be in control of. They sat either side of a thick set oak desk in Neil’s office that contrasted starkly with Matthew’s. Whereas the Professor’s workspace was clean cut and minimalist, with its glass desk and whiteboard walls, Neil’s was rather more old-fashioned – stuffy even. Aside from the wooden desk, which was far too big for the office that it occupied, there were mismatched wooden filing cabinets spanning the length of the walls, each one topped with a trite painted landscape scene that hung on subtly patterned wallpaper. One got the impression that the place had not seen renovation in a very long time, and that Neil was making the best of a bad lot with his attempts at decoration. Being one level below ground, only a small amount of late autumn sun fell through roof windows situated on one side of the room opposite where they were sat, whilst harsh artificial light glared from a number of non-matching lamps spread across the room, as well as a bare strip light that was mounted at an odd angle on the ceiling, neither parallel nor perpendicular to the walls.
“It was a colleague of mine that brought you to my attention, Professor Quinn,” Neil started in a tone that wasn’t quite as deep as Matthew had expected, “After spending vast sums for her daughter to study at your institution, I suppose she wanted a flavour of what exactly she was paying for at Salvin. She doesn’t really care for mathematics. And normally, nor do I to be perfectly frank,”
“Well, feel free to be precisely that,”
“What I really care about, however,” Neil quickly continued, “|s what you talked about in that lecture… I don’t assume that you know an awful lot about my company and what we do?”
“You would be right to make that assumption, yes,”
“Allow me to fill the gaps in your knowledge then. SL-TECH works… closely with many different types of companies and organisations. You surely know the word ‘solutions’ in a – how shall I say – business sense?”
“Of course, I know it. And thoroughly hate it, may I add,” Matthew replied through a wry smile,
“Oh yes well that goes without saying, everybody does, it just happens to be an easy word to describe services that are… a little vague in nature.” Neil stood up and retrieved a file from one of the many cabinets behind him. “The thing that you, and anyone who might have heard SL-TECH’s name in passing may not appreciate though, is that we have… fingers in a lot of pies,” He threw the file in his hand onto the desk. “A lot of big, important pies; this for example is a report from the Government of Spain on the subject of leaked sensitive information,”
“Spain certainly is a big shiny pie, Mr. Parry” Matthew said, unsure of how to react,
“Please don’t be quite so off-handed Professor, this is important,” Neil shot back stoically, casting another, larger file down, “This is from HSBC,” and another, “News International,” and one further folder, bright scarlet in colour and quite considerably more substantial than the others, Neil paused dramatically before announcing, “The MoD”.
“Okay, I think I’m starting to see where you’re taking this,”
“This, Professor Quinn, is the evidence for the assertions that you made in that lecture. Hackers, cyber criminals and spies plague these organisations. It is costing them money. And in some cases,” he pointed to the thick red folder on the desk in front of him, “It is costing them lives, and severely jeopardising national securities.” Neil sat himself back behind his desk. “SL-TECH is very, very good at providing ‘solutions’, Professor. We are whom companies and governments turn to for ‘solutions’. But this solution, the ability to provide absolutely watertight electronic security, well… it’s one that we are having trouble with,” Neil pointed slowly but purposefully at the Professor, “So imagine our surprise when one of the UK’s leading authorities in exactly this field tells his expectant audience that this solution – an algorithm that produces infallible, unbreakable codes – will not, and can not ever be found.” Matthew held back a second, narrowing his eyes. The tone of his reply was sincere,
“On the assumption that you are referring to me, then yes, it is a conjecture that I believe in,” Neil lowered his hands to the desk. And spoke firmly, staring Matthew straight in the eyes.
“Well, Professor, I believe that you are wrong.” Matthew was rather taken aback by the delivery of this statement.
“How can you be so certain, Mr. Parry?” He calmly retorted, “You said it yourself; this area of mathematics is, you know, kind of ‘my thing’… What are you basing these bold assertions on?” Neil was slow in forming a response.
“A strong hunch, Professor, shall we say?”
“A strong hunch? You’re joking, surely?”
“Absolutely not. I’d even go as far as to say that we’ve nearly solved the problem. Very nearly, indeed.”
“With respect, Mr. Parry, to a mathematician, and especially with regards to this particular problem, ‘nearly solved’ might as well be ‘nothing near solved’. Two times two ‘very nearly’ equals five, but it never actually can.” Matthew continued, somewhat bemused by this man’s bullish claim. Neil looked away and inhaled slowly.
“Matthew, this solution could very well be the greatest ‘solution’ that our company has ever provided-”
“You’re still assuming that this solution exists,”
“Let me finish, Professor, because further to that, the discovery of an algorithm that can make an unbreakable code – this ‘golden algorithm’ as you apparently like to call it – would almost certainly be the greatest mathematical discovery that you will ever make.” Matthew still looked skeptical, though Neil continued on anyway. “Look, I know you mathematical types tend to not care for cash, but I can tell you one thing; this one solution is worth more to us than a combination of any other million solutions that we could ever provide. So I’m going to make you an offer. If you take on this problem and succeed in providing us with the solution, then I will give you a cheque for ten million pounds.”
Neil was right; Matthew didn’t particularly care for money. But the figures involved in the deal that Neil Parry offered were outrageous. As well as the ‘grand prize’ for discovery of the golden algorithm, he was offered £50,000 for agreeing to take the problem on in the first place, plus the wages to be paid to Salvin College that were needed to cover a sabbatical year in order for Matthew to give the problem his full attention. And so, after short deliberation, Matthew agreed to take it on. Yet, here he was, the sabbatical year drawing to a fruitless climax. There had been some progress. The most significant development coming some time during February, when Matthew proved beyond doubt that an unbreakable code, and a golden algorithm in order to encode it, definitely did exist, though apart from its definite existence he still knew very little about it. In mathematics the difference between discovering the existence of something and actually finding the thing itself is vast. Since then, he had tried many methods to try and coax life back into his pursuit of an answer, the cocaine being a highly unorthodox one. He had cut the powder – that he had been assured was of a high purity – with a not impotent cholinergic cognitive enhancing drug of his own. It was an unreliable study aid, certainly, but he still thought it one with a degree of potential. Breathing in the vile powder though a nostril was initially unpleasant and the chemical drip that ran down his soft palette and onto the back of his throat was truly terrible, but within minutes of doing so his mind would split wide open, ideas and buzzing trails of thought would spill out onto the paper with a flow he was sure that he’d never otherwise have achieved. One time, these ideas were bound to make logical sense when read back the following day, or so he thought. Taking the mixture of drugs wasn’t something he did often; it required absolute solitude for one thing, which he seldom got. Besides, the increasingly frequent nosebleeds caused by the abrasive powder had started to arouse suspicion. Risking his whole professional career was something he was becoming increasingly uncomfortable with.
The automated voice announced that the tube train had arrived at Angel, Islington, which was Matthew’s home station. He made his way through the short underground tunnels and ascended the escalator to the surface; the escalator that he would always tell visiting friends was the longest in the whole of London. He was quite sure of this fact’s validity, and though he had never bothered to check no one ever picked him up on it. He quickly walked the ten-minute journey back to the three-storey Georgian terraced house that he shared with his fiancée, Rebecca, whom Matthew found lying sound asleep on the red leather living room sofa.