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The third chapter of a novel I wrote last year about drugs, blackmail, and mathematics.

A chapter index can be found here.

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Chapter Three: Progression

“If only I had the theorems, then I would find the proofs easily enough.” – Bernhard Riemann (1826 – 1866)

Anna Platonov stood in the slow moving, ever-increasing queue at Salvin College’s main reception. It hadn’t been her aim to spend her day bogged down in educational bureaucracy, and she felt especially conspicuous in the company of those who stood in line with her. All of the other students seemed so young, like excitable rabbits trapped in the headlights of newfound independence. Anna could not have denied at least a partial envy of these fresh-faced undergraduates, though at the age of 24 she had come to terms with the fact that hedonistic youth was well and truly behind her. She had to keep reminding herself that a combination of a research doctorate and a fresher’s lifestyle would not be a good one.

Right from early childhood Anna had felt like something of an outsider. At the age of four, her parents had emigrated from St. Petersburg to escape a tempestuous family feud that had nearly resulted in her father’s fratricide at the hands of a violent uncle. Her parents had never fully explained the cause of the violence, nor had they ever really explained why of all places on the planet, they chose to move to Sheffield. She knew that her father’s ability to speak English was probably figured in the decision, though as a child she saw images on the television of far more pleasant places, even in the United Kingdom, than the run down steel city. Moreover, her father’s bilingualism was something that Anna didn’t possess, and as such she found her early years of schooling in England difficult. It was in this strange foreign environment, however, that she discovered mathematics. It was something that she embraced and quickly excelled in. There was no need for complex, confusing English grammar, syntax or spelling, just a universal language of numbers and symbols that anyone from any country could easily communicate in. Mathematics was a comfort blanket in an environment that she was unable to fully understand.

When Anna was eleven her primary school, fully aware of the mathematical prodigy she was fast becoming, suggested private secondary schooling to nurture her talent ‘properly’. Anna’s parents were by no means poverty stricken – her father had quickly found employment as a mechanical engineer upon arrival in England and her mother had set up a small business offering her services as a Russian language tutor, having quickly picked up the English language– but they certainly didn’t have the disposable income available to spend on private education. Assured of Anna’s great potential, however, The Sheffield School for Girls offered her an entrance examination, with the promise of a part scholarship for an ‘outstanding’ performance. In the exam she surpassed the expectations of even those that well knew of her precocious talent. After strenuous deliberation her parents decided that the reduced fees, though still costly, were worth it for their little girl, and they took the place that the School offered. However, despite by now having a sophisticated grasp of the English language and finding herself surrounded by new peers and new opportunities to become more extraverted, Anna’s limited social interaction persisted, though ultimately by her own choice. More importantly – in her eyes at least – her academic potential was continuing to be realised. By the age of fourteen, she was capably dealing with A-Level material in a far superior manner than most of the eighteen year olds who weren’t merely tackling topics such as calculus merely for fun as Anna was.

Mathematics, however, wasn’t all that Anna Platonov was learning at the Sheffield School for Girls. Whilst her academic achievements were sources of great pride for her parents and her school alike, her fellow female students found her to be an easy target for derision. And no matter how many times she was told by her teachers, her parents and even her own mind that the girls’ spite was simply a manifestation of jealousy and their own insecurities, their taunts still bothered her profoundly. After a bout of particularly severe ostracism, however, Anna decided to take matters into her own hands – she would use her personal strengths to her advantage in order to exact revenge. Using her greatly superior intellect, she undertook an incredibly subtle war against her assailants. By spreading the occasional poisonous rumour, carefully spilling overheard secrets and using her newly discovered, yet remarkably effective powers of manipulation, she turned the girls against each other, broke friendships and made them as thoroughly miserable as they had attempted to make her. And most perversely satisfying to Anna was the fact that these stupid girls barely knew that it was all of her doing. She couldn’t believe that it had taken her as long as it did for her to discover the power that she often held over them, and she completely loved it. Needless to say, the girls’ taunts soon stopped.

By the time she turned seventeen, she might as well have gone straight into university education. Sixth form and A-Levels provided no challenge. Moreover, and quite under the noses of all who knew her, Anna was flourishing into a markedly attractive young woman. She inherited her mother’s Slavic good looks, the skin hewn of translucent porcelain, and green eyes permanently guilt with an endearing mischief. It hadn’t been until her time in sixth form when the boys’ and girls’ schools combined their students that her appearance had garnered her any real attention. She dismissed most of her peers’ leering glances and continued to focus on her studies, even though she knew extra study was somewhat superfluous – there were no extra marks to be gleaned beyond 100%. During the entirety of her adolescence she had found herself drawn to, a single shy individual, a boy who had also possessed a penchant for mathematics, if not quite as much so as Anna. He had even taken Russian for a term, though he was patently inept and only took the classes, Anna deduced, in order to spend more time with her. It was cute in a way – she had to admire anyone who was willing to punish themselves by learning the Cyrillic alphabet, just to be in her presence for three set hours a week. Despite the initial development of a promising friendship, his advances were hopelessly clumsy and Anna gradually tired of him just as she assumed she eventually would.

 In the December of her upper sixth year, she earned herself an interview at Oxford University. Upon her first visit, the city instantly blew her away. It was so far removed from the steel and concrete of her northern English hometown; the quaint colleges, chapels and their pristine grounds that she explored at length during her time there were like something from a film, one in which she had to play the lead. She felt an instant love for Oxford – certainly one that she had not felt for any clumsy boy – and told herself that she would spend her university life nowhere else. By now moreover, Anna had realised that she had the ability to achieve anything that she desired to, and although the entrance interviews were certainly the greatest test of her calibre up to that point, she knew that she had done more than well enough before the letter of acceptance had even been posted.

 “Hello, can I help you?” the homely looking receptionist behind the desk called, snatching Anna’s attention back from her daydreaming. She had finally reached the front of the queue.

“Oh hello, I have these, I think I need to give them to you?” Anna dropped a clutch of loose papers onto the desk in front of her.

“Do you now…” the receptionist replied under exasperated breath, gathering the pages up into a single bundle and looking through them in turn. After about two minutes of making sure that they were correctly filled in, she looked back up at Anna, “These all seem to be in order, wait here a second please,” The receptionist scurried off through a door into an office behind her desk and returned with a different, pre-filled out paper form and a plastic ID card baring the university’s logo and a profile shot of Anna, who even managed to look good in passport photos. Having been instructed to report to the Mathematics department coordinator, some Ms. J. Sasco, to confirm her attendance, Anna made her way back down Salvin Street, which the main reception backed on to. Although not quite as intensely busy as it had been during the first week of term, the street still possessed a tangible buzz that emanated from the busy host of students walking along it. Salvin College certainly didn’t enjoy the charming beauty of Oxford, Anna thought, though she assumed that no other place ever would. The occasional building here was undeniably pleasant, but for every such beautiful construction, a concrete tower block next door would restore architectural karma. She had been slightly disappointed to discover that the mathematics department was housed in one such ugly tower, though she knew that the study that went on within its walls was beautiful. She pushed her way through the revolving front door and looked around for some kind of reception or main office. Eventually, after outwardly appearing more than a little lost, a passing professor pointed her in the direction of a room just off to the left of the main entrance foyer where she was stood. She tapped lightly on the window.

“Yes, come in,” Jacqueline Sasco barked from inside. Anna entered the room, immediately noting the immaculate filing operation that Jacqueline was running. It was certainly not something that Anna could have maintained herself – being neither an organised nor especially tidy individual. Anna’s living spaces were perpetually disordered and cluttered, the floor covered in a carpet of clothes and the desk always stacked high with textbooks, papers and stationary. She even harboured suspicions of people as structured as this woman before her seemed to be.

“How can I help you then?” Jacqueline asked in a new, softer tone,

“My name’s Anna Platonov, I think I’m supposed to give you these,” she explained, handing over the papers that she had just been given at the main reception,

“Ah, Anna, yes, of course,” Jacqueline wheeled an about turn on her swivel chair and plucked a file from a low shelf behind her. “We had ever so much fun with your application,”

“What do you mean?” asked Anna, confused by the woman’s irony. Jacqueline stopped thumbing through the file and looked back up. She had to remind herself that strangers were not necessarily accustomed to her brand of acerbic wit.

“Nothing dear, its just we don’t normally receive such…” She chose her words carefully, “Unusually timed – shall we say – applications as yours,” she pulled a single sheet of paper from a plastic wallet. “But how could we turn this one down?” Anna said nothing, still not knowing quite what to make of the woman in front of her, “Though, between you and me,” Jacqueline continued in a hushed tone, “I had to do a little… persuasion, to get the powers that be to look at your application at all. Having seen it myself there was no way I was going to let you get away!”

“Thank you, how good of you,” Anna replied almost sycophantically through a forced smile,

“Obviously you’re going to need to see and meet regularly with your supervisor. Having reviewed your interests and areas of mathematical study, I’ve assigned you to Professor Matthew Quinn, for reasons that should become apparent once you meet him. You’d probably find his work quite engaging. People around here certainly think that he’s quite wonderful,”

“Oh, well that sounds good,”

“Yes. Anyway he’s so wonderful, in fact, he hasn’t come in to Salvin at all today. But I’ll let him know that you were here and you’ll be able to come and see him tomorrow afternoon?”

“Okay, thank you. So is there anything else that I need to do? No more paperwork?” Anna asked, sincerely hoping that she was finished with the day’s bureaucracy.

“No, not a thing. Just be sure to enjoy the last day off you’re going to have for a good long while.”

* * *

The Professor had decided that he was no longer to able to put off reconvening with Neil Parry. Although Matthew mentally praised himself for taking the proactive decision to meet his prospective paymaster, the recent deluge of emails – each displaying a further deteriorating temper from the last – had been his primary motivation. As per usual they had agreed to meet on neutral ground, this time in a small pub that they both knew, tucked away on a small back street leading off of The Strand in central London. It was a quarter past midday, and the place was almost empty, save for a clutch of lost tourists. Matthew had arrived a little early to give himself time to settle down. The air hung dark and stale in this place, whilst the sky outside was dark and foreboding, the atmosphere uncharacteristically humid for a late October day. An uneasy feeling throbbed – a feeling like the next half-hour was going to be thoroughly vexing.

And then, staring out of the translucent stained window, the undeniable silhouette of a tall, purposeful man could be seen marching towards the front doors. It was, just as Matthew suspected, Mr. Parry, who gestured a “Hello,” from the other side of the room and walked straight to the bar, and quickly ordered a pint of real-ale. He moved over to the table where Matthew was sat and pulled a chair out from underneath it, taking a seat.

“Not a bit early on a Monday for that?” Matthew said, pointing to the full glass that was firmly placed down upon the table.

“No, sir, it is not. Can I assume that you’ve been exceptionally busy then, Professor?” Neil asked in his sly tone, which Matthew had almost forgotten the sound of.

“I certainly have,” replied Matthew, trying not to sound nervous, “The start of the academic year’s always a little hectic,” he added. Neil appeared quite disinterested.

“I’m sure it is,” He took a sip from his glass. “The question that I’m going to ask – that I expect you can predict with some ease – is a simple one. What progress have you made in finding our golden algorithm since we last met?” There was an extended pause that Matthew could physically feel becoming awkward. “Has there been any progress at all?” Neil knowingly continued.

“May I be perfectly frank,” Matthew replied,

“Of course,”

“Well then I can tell you that there has been progress. A lot of progress in fact,” Neil narrowed his eyes and raised his brow. It was not the response that he had been expecting.

“Your decision to keep any such ‘progress’ from me is a little misguided, don’t you think?”

“Perhaps, though I should of course clarify that the progress I have made recently has been… more narrowing down my potential leads more than anything else, shall we say?”

“You mean you’ve been hitting a lot of dead ends?” Neil swiftly replied, seeing straight through Matthew’s flimsy mesh of elaborate words. Another silent pause ensued.

“You’re a very perceptive man,” said Matthew, blindly attempting flattery. Neil said nothing and didn’t look especially impressed. Matthew attempted to explain himself. “Look Neil, I am honestly sorry that I can’t bring you better news, but this isn’t like some kind of construction project with a readymade blueprint and a definite schedule to stick to. Any progress that I’m making is erratic and completely unpredictable. I sit down and after some thought, something new is suddenly there, or as is more often the case, it is not. These new discoveries can’t just ‘happen’ as I please. And it’s not as if I don’t want to make these discoveries,”

“What worries me though Matthew, is that I gifted you a whole year to work on this; a whole year of nothing but time to focus on finding your golden algorithm, and yet we sit here now and you’re telling me we are no where nearer to it?”

“Well that isn’t strictly true to be fair. For a start, I was initially convinced that such an algorithm definitely didn’t exist at all,” Matthew explained. Neil still looked surly, supping slowly on his drink. “Okay, perhaps I should provide a quick summary of where exactly we are?”

“Very well,” Neil flatly replied,

“So we now definitely know that the golden algorithm exists. I have proved beyond equivocal doubt that it is definitely out there somewhere, so we know for sure that this isn’t going to descend into some academic wild goose chase,”

“Continue,” said Neil, sipping his beer.

“I also think that I have the specific type of algorithm that can produce our unbreakable code. I say ‘I have’, I actually discovered it myself some time around June, which was good progress in itself let me tell you,”

“What do you mean, type? Any algorithm is just an algorithm, surely?”

“Not exactly. It’s all to do with the method used to generate the code itself. Secure online bank transfers, for example, use combinations of enormous randomly generated prime numbers and their associated properties; it’s a complex process, and one that works very well. But it produces a code that can be broken, theoretically at least. So that type of algorithm is no good to us. There are many other algorithms that use other methods,”

“So is this leading us to a solution, to our golden algorithm that you are so sure exists?”

“Well it’s difficult to say. Because what I’m dealing with is completely new mathematics, there are still many things that I don’t know about it. And it’s these new, unknown properties that I’m trying to discover and learn about. If my inclination is correct, however, then an ability to output an indestructible cypher should be one of them,”

“Well, hang on a second Matthew,” interrupted Neil, “If you know so little about this new area of mathematics that you claim to have discovered, then how can you even be sure that you haven’t already stumbled across the golden algorithm and falsely disregarded it?”

“Because it’s intrinsically much easier to disprove something than it is to prove something. If I want to prove that a particular algorithm that I’ve come up with really is the one that we’re looking for, then I would have to show that it works for every possible input. There are tricks to do this, though trying out every possible input in turn would obviously be impossible since there are infinitely many possible inputs. If I take that same algorithm, however, and I want to show that is not the right one, then I only have to find one code for which it doesn’t work. That input would be what we call a ‘counter-example’, and it’s a completely watertight way of telling me that the algorithm is wrong,” Matthew continued, “I can assure you that after this long, I have become a past master at finding counter-examples.” Neil took this new information carefully in as he leaned in over the table.

“Matthew, I’ve listened to what you’ve had to say, and I fully appreciate the problems that you have had, but your year for working on this is over. Now you’re back working at the university again how much time are you going to get to continue serious research on the golden algorithm? You know I can’t spend any more money on the mere promise that you’re going to deliver the solution eventually? We could be talking another decade here for all I know”

“Don’t worry, I can still take this on. Look, my responsibilities at Salvin College needn’t take up that much of my time. I have the occasional seminar to preside over, yes, as well as the odd public lecture and a few PhD students. I can easily set aside time for my research,” The heat of the exchange and the taverns thick air were becoming suffocating. Neil was fast approaching the end of his tether.

“Look, Professor Quinn, there is a serious risk of this becoming tiresome. So I’m going to give you incentive beyond that of finance. I’m going to give you until the end of the year to see this through. If you don’t have an answer by then, then we will end this,” with this final statement Neil finished his pint, in suitably dramatic fashion. “Is that understood?”

“Perfectly well, Neil,” Matthew retorted, not wholly appreciating Neil’s abrasive tone.

“Good. I don’t have to send Miss Sasco a hundred emails to get the message across then, do I?”

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