The greatest mathematician to never exist - SCP Foundation

Doctor Medes sat in his white wooden chair, staring blackly in front of him. They were coming for him. He could feel it. He knew it. He could tell from the look that Dr. Pitas gave him that morning. Not that he did not expect it. He was certain the moment he started his forbidden journey into the heart of mathematics that this would be the tragic finale. How could he hope to outsmart the Foundation forever? Dr. Medes felt grateful that he had enough time to achieve his incredible results.

And now, his revolutionary discoveries would cost him everything. The Foundation would have probably kept its research and worked on it, improving it. But the public would never know. The amount of knowledge accessible to humankind would remain the same, and his theorems would probably remain conjectures for years to come. And naturally, his name would be erased from history. Once back in the normal world, he could still have a good career as a mathematician, maybe he could even come close to solving Goldbach's conjecture and Riemann's hypothesis without the use of anomalous mathematics. But deep down he had already realized for a long time that he had spent his best and most productive years working at the Foundation and that his mind was slowly but surely deteriorating. And even if he did come to a solution, that would be in reality only a small piece of the entire puzzle, comprised of bears and missing numbers and other oddities.

And yet, despite all of this, he did not feel particularly sad or angry. He felt simple and pure satisfaction, even as he started reminiscing about his life until that point.

Archie Medes was born in a small and uninteresting village. Uninteresting for most people, at least. Archie instead, was incredibly fascinated by his hometown, with its precise geometrical homes, its beautiful leaves full of repeating patterns, and the fresh spring breeze moving his hair in such a chaotic and fascinating way. He was, according to everyone who knew him, a child prodigy. He often visited the small library near him and took home books on biology, chemistry, astronomy, geometry and arithmetics, and even basic algebra. For him, the only thing more interesting than the world around him was trying to understand how and why it functioned in a certain way. He loved to come up with theories and test them out to see if they were correct. Most of the time, they probably were not, but that certainly did not discourage him.

At school, everyone soon realized that he was extremely talented and incredibly intelligent for his age and overall, but that did not stop Archie from making new friends. He had a solar and positive personality, a trait that he kept for all of his life, and classmates and teachers alike could not help but like him, even though he sometimes was a bit aloof and concentrated on his research. After high school, he graduated from Princeton University, where he eventually got his Doctorate. When asked why he chose to study mathematics, he would reply: "Ever since I was a kid, I loved animals, plants, clouds, stars, and numbers. When I grew older, I found out that by studying the latter I could learn more about everything else."

And between all of the branches of maths, one stood out in his mind and piqued his interest: number theory. As previously mentioned, Archie really liked numbers. They were not complicated at all, they were just small and simple lines constantly repeating over and over again. And yet, with those lines, mathematicians could recreate and explain our extremely complex world. And then from those lines questions we did not know the answer to continuously arose. The culprits were often a specific set of lines: primes. Were all numbers the sum of two or three primes? Were primes so close to each other to be called twins infinite? And how were primes distributed? Like so many before him, Archie Medes was determined to finally shed light on these conjectures.

He made significant progress already at a young age, while he was still a teen, and by his early twenties he was already one of the leading experts of the so-called "Queen of Mathematics". At the age of 25, he was awarded the Fields Medal for his "exciting and original ways of tackling Goldbach's conjecture that have helped to uncover some of the deepest truths on natural numbers, the foundation of mathematics".

Soon after, he was contacted by the Foundation. At first, he did not know its purpose, but once he had agreed to work with them under the promise of uncovering mankind's greatest secrets, he came to learn about the anomalous and how it even extended to his beloved number theory. This naturally did not discourage Archie, but it gave him even more motivation. Every day as a junior researcher he kept telling colleagues about the fire burning inside him like never before. He could seem a bit odd at first, but everyone who had the luck to work with him will surely remember him as a lovable person.

His talent was certainly uncommon and he quickly rose the ranks. By the time he was 27, he was one of the leaders of the Mathematics Department, officially known as the Department of Studies of Anomalous Mathematics, Logic and Computer Science (DSAMLCS). He had the habit of saying the full name whenever he met a new researcher. He said it gave him an aura of importance. He used to make a lot of similar jokes. In reality, he never cared about fame and was certainly a humble individual. When he was little, he was ostracized and sometimes ridiculed by others for being too good, and too unreachable. That's why, even though he could usually always add several observations during talks and meetings, he remained quiet most of the time. That is if the subject was not number theory.

Two anomalies interested Dr. Medes more than any immortal lizard or creepy old man: SCP-033 and SCP-1313. They were natural numbers, the bricks of math, what he had been studying for years! Most importantly, they could have been puzzle pieces, missing pieces that could have helped him in completing his masterpiece: demonstrating Goldbach's conjecture. There were just two problems: bureaucracy and interests.

Researching in a conceptual and non-experimental field such as mathematics, where there is no physical and tangible boundary to an experiment is extremely restrictive. The amount of time you are allowed to study a specific anomaly is fairly short and the objective needs to be clear, achievable, and typically not particularly ambitious. This is because there is always the risk of unknown properties causing great damage either to researchers, to the Foundation, or mathematics as a whole. Unfortunately, this has indeed happened before, and ever since the Foundation has been overly cautious, taking away a good deal of freedom from the MD. All because, as Archie would put it, mathematics is not a science enslaved by glass containers, by cells, or by the limits of the Universe. Its only limitation is in the head of us mathematicians.

Moreover, the Foundation tends to search for explanations not on how an anomaly can be useful, but on how it works. Of course, it makes sense, since the "C" stands for "Contain". But in our field, it spells more like "Limit". Instead of encouraging researchers to ask "How can an equation that creates a bear be integrated and used in studies and theorems?", the Foundation often forces us to try to understand why that particular equation produces a bear and how. Finally, solving problems such as the twin primes or Goldbach's conjectures was not a priority nor was it advised. On the contrary, these were seen as unimportant distractions, obstacles that prevented mathematicians working at the SCP Foundation from giving total attention to their job: study the anomalous.

These reasons, while without a doubt strong enough to discourage anyone else, did not affect Archie Medes. He would not have spent his whole career chasing bears or staring at vanishing papers. That was not why he became a mathematician. All he wished for was to walk in a park one day with the knowledge that no matter how many flowers bloomed around him, he always could have found 2 or 3 prime numbers that when added together would have given him the number of flowers. He became a mathematician because he wanted to advance the knowledge of humankind so that when he was older, he could look at his wrinkly face and tell himself: "You did well. Thanks to you, everyone is a bit smarter."

On the day of his 28th birthday, he decided what he would do: he would become the scientist he always sought to be. He started researching in secret, on his own, in his free time. Every day, after returning home, he would take his dairy and continue where he left off. He did not care for the consequences of his actions and he knew that being an esteemed researcher and a reserved person, suspicions would not arise for some time, maybe even years. So without any hesitation, he began exploring and learning about SCP-033 and SCP-1313.

His initial research on SCP-033 was not very fruitful: sure, he knew the two whole numbers before and after the anomaly, but he could not deduct much from so little information. The "Bear Equation", on the other hand, was easier to study: first of all, a bear could be represented as a square, and possibly be a centered octagonal number. Further research in the field of bear topology and bear packing confirmed his theory. Since Archie was pretty keen on not getting mauled by a bear, he analyzed each logical step of the equation separately. He discovered some curious things:

1. The square root of a bear was a Sophie Germain prime, so the number after its double was also prime;

2. The square root of a bear was not a Mersenne prime, so it was not one less than a power of 2;

3. The square root of a bear was a Pythagorean prime, so it could be written as the sum of two squares;

4. The square root of a bear was a twin prime.

5. The number after a bear was a multiple of 24, like for every square of a prime.

Then, three months later, the first big discovery. While he was observing a typical appearance of SCP-033, he looked at some of the symbols and started to think about them. Then all of a sudden he started gasping, afterward he became serious once again, as if he was deeply reflecting on something, followed by a series of smiles and a joyous laugh. He forgot about everything: his concerned colleagues, the point of the experiment, what he was going to have for lunch. Nothing else mattered. He had found a connection between the two anomalies he was studying, a way to express one using the other. He rushed home and started to work on what that implied: he now knew where all of the anomalous numbers were on the natural number line. Every single one of them. He felt like a Renaissance explorer, discovering and mapping incredible jungles in South America, or encountering animals straight out of his wildest dreams in Africa.

Archie soon came to realize that some problems that had puzzled mathematicians for centuries were not inherently hard, but what truly made them difficult was the fact that they were playing unfairly: humans simply lacked the tools and knowledge to completely understand them. It was as if every attempt to reach the top of the mountain did not have the final, crucial rope. This was the final crucial rope. Within the span of half a year, Dr. Medes had solved the longest-standing problem in number theory: there were indeed infinite twin primes. Certainly an important and very exciting result, but not Archie's end goal. He was the type of person to not brag about anything. In fact, him doing something appeared to strike him as a drawback or an unfortunate event. After solving a problem, although he did not deny the importance of it, he would minimize the importance of solving it. So, after some joyful months of celebration, he embarked once more on his quest.

Contrary to the twin prime problem, Goldbach's conjecture was still a tough nut to crack. Despite his best efforts, its solution continued to be only one of his dreams, his most cherished. He most definitely tried: in his notebook, some days there were written down 10 separate approaches, not just quick ideas, but fully developed hypotheses that often led to him reaching impressive results in numerous fields. And yet, Goldbach's conjecture kept on fighting back. With his confidence starting to shatter, the cheerful, friendly researcher transformed into a secluded, lonely man, caught up in his own personal struggle. He started to hate his job, hate the Foundation, hate mathematics, hate the world for which he had fought for.

Then one day, on 2nd December, he brushed his teeth as always and noticed he was bleeding from the mouth. What shocked him was that he had just remembered that the same thing had happened a year and a half ago, and then again three months prior. He had not cleaned his mouth for three months. His nails were long and dirty, his hair was an untidied mess, his face looked tired, and long deep wrinkles had appeared on it. He was ugly. Not unattractive or bad-looking. Ugly. His face, and most of all his sad expression looked so ugly. He hated it. It was so ugly that he started crying. He glanced at the calendar and realized he had been neglecting his life for three years. For three years, following his first great discovery, he had been a slave, a zombie, a non-living being. This was not life. He did not want this. Never. Never again.

On that day, Archie Medes made his greatest finding: he was not only a mathematician, he was also a human. First and foremost. He wrote this phrase down with the title "The Axiom of Life". The next day, he arrived early at the site he worked in, well dressed, cleaned, and smiling.

Naturally, he kept on wanting to study math. All he wished for was to run away from Goldbach's conjecture. Far, far away. He did not want to talk about it, or even mention its name. For a little while, he focused only on his official duties as a Foundation researcher. In the meantime, he started to talk about other notorious problems with his colleagues, especially with his best friend, Dr. Delph. Jack Delph was considered by many the leader of the MD. He was a charismatic, organized, middle-of-the-road mathematician, who had the great luck to meet a charming and unordinary person like Dr. Medes. On multiple occasions, he would discuss with Archie Riemann's Hypotheses, one of the most stubborn and challenging problems ever. Solving it would mean reaching a near-total understanding of prime numbers, the building blocks of number theory.

"There is no connection with Goldbach's conjecture, right?" "Not that I heard of." After this conversation, Archie got up with a smile—the smile of someone about to do something reckless.

Unlike many may think, working on this new problem was not nearly as stressful for Archie. For him, this was a recreational activity, something to distract his brain with, a game. Some people like to keep their minds fresh and active by playing chess or solving puzzles. Archie kept his mind active by trying to solve Riemann's Hypotheses. It was a long game, a fun game, as he stated in his diary. The game challenged him out of his comfort zone, into branches of math he had paid very little attention to. At the same time, he read books about his puzzle, finding out the beauties that made it the greatest problem of mathematics, and the most beautiful.

It was, without a doubt, a magnificent game. But all games must come to an end, resulting in either the loss or the triumph of the player. And in Archie's case, it was a resounding victory.

The puzzle was complete, and the secret of the distribution of prime numbers was uncovered. Riemann, poor Riemann, who perhaps had already reached this conclusion, was right all along.

Medes wrote in his diary: "I believe that if there is a Heaven for mathematicians, it should include a library, full of books, with all past, present, and future theories, conjectures and theorems. Dear Riemann, if you are in such a Heaven, I'm sure you have already seen it. The answer to your greatest question, the completion of your greatest achievement, the most splendid theorem of all time: the solution to your hypotheses. It's beautiful, isn't it? It's the most beautiful thing I have ever seen. I hope one day to stand by your side, in this Heaven, and marvel with you at the beauty of our theorem. Forevermore."

In the following days, Archie was extremely cheerful. He kept saying to everyone that he had met up again with an old friend. "Who?" everyone would ask. "Rie, man." Nobody would laugh. He was horrible at making jokes. He had several adventures at the Foundation that don't regard our story. Once he tried to express SCP-682 as an equation and entered into a fierce battle with the "Adaptive Equation". He neutralized it in the end. His father died a few weeks after his 35th birthday. He dedicated one of his many secret theorems to him. Sometimes he would ask to Delph to go for a smoke and cry a bit in my arms. He never smoked and drank rarely. He was however addicted to coffee and though he wasn't a playboy, he enjoyed women's company. He ended up marrying a janitor. That's a story for another day.

As I mentioned before, Archie hated slacking off. So, after around one year completely focused on his occupation, he felt like he was ready to fight one more time against his best friend and his worst enemy: Goldbach's conjecture. The knowledge he had obtained on his journey to solve Riemann's Hypotheses proved crucial. He soon realised that the solution was there. He hadn't reached it, but he knew it existed and that it was within reach. It's as if he could feel like it was behind a wall of fragile rocks and he had a scalpel in his hands. All he had to do was push forward.

It was for this observation, that some may regard as arrogance, that his second attempt caused him significantly less stress than his first despite being just as difficult. He challenged the conjecture with much more serenity and peace. He never was obsessive, though he surely was determined. Sometimes he would pull all-nighters. Not too many, since his wife would often drag him to bed. He never was someone who didn't enjoy life. He often made Dr. Lambert, the Head of the MD, furious because he would take several vacations and he would always send to everyone postcards to everyone and souvenirs to his best friends. He had a kid just before his 36th Christmas. Andrew. Claire immediately forbade her husband to introduce him to two things: the Foundation and math.

On his 37th birthday, we had a great party for him, despite Dr. Lambert's objections. Some colleagues made a cake with the first digits of π, others brought alcohol and we all played a drinking game in which the slowest one at solving a problem would drink a shot. Archie looked at the problems of others, solved them and then his problem, then changed his answer to his problem so that he would have to drink. Over and over again. Towards the end of the day, he pushed me to the side, a bit drunk, and told me: "Jack…I'm so happy… GC is no more…I did it…I helped the world…Dad…I helped the world…" He cried a bit and I carried him to his car. Claire was also tipsy, so I drove them home. When he went inside, he looked at me with a serious expression, the same expression my mother gave me three days before dying.

"Thank you, Jack. For everything. Please remember me."

He knew it was a matter of time. When you know about the Foundation and you know something that they don't, you can be sure that, sooner or later, they'll find out. You never really understand how they manage. They just…do. Simple as that. And Archie knew that too. He wrote as much in his notebook, adding: "The fact that after a decade, the Foundation still hasn't found out about this is probably one of the most flattering compliments the world has given me."

13th of May. It was a pretty hot day. Summer was close. He was talking with Dr. Delph. He told me he wanted to go on a trip to Africa in July. He talked about Andrew. About Claire. He wanted a daughter. We discussed the idea of a pet Komodo dragon. And of course, we had a conversation about mathematics. He said the heptagon was better than the hexagon—a clear provocation. Our debate dragged on as we entered the MD wing of the site. Out of nowhere, a hand appeared on Archie's shoulder. It was Lambert. He looked at him dead in the eyes, an expression of anger, compassion, concern, sadness. He merely said: "Tonight. 6 pm." Archie became a bit pale, but still found the strength of smiling a bit. "I understand. Thanks." He dodged my questions regarding what had happened. Before our meeting started, he put a USB in my pocket. "The data you asked for." He said with a gentle grin.

He arrived home at 4 pm and started writing down his thoughts and impressions. He didn't seem sad. Sure, he would have liked to work at the Foundation for all his life, and leaving his colleagues and friends and the fact that he would forget about everything that he had accomplished, that he had made the world slightly better… ok, maybe he was a bit sad. But he accepted it. He had accepted this fate since the very beginning. He simply hoped that the people he had met and known throughout the best years of his life would remember him fondly and perhaps pass down his memory to their children, so that maybe, just maybe…someone would remember him. Not just as a mathematician, but also as a person.

Four men knocked at his door. He opened up to them and immediately followed them without putting up a fight. He later said to me that the only thing he asked them was to be gentle with his wife. He had told her everything two months after they had gotten married. They had left Andrew with Claire's brother. Their memory erasure was scheduled to be performed a week later. Lambert fought with all the might an old man could have to have him prepare a specific amnestic that would only cancel his memories about the Foundation. During one of his many fights with the Site Director, I heard him scream: "I can take away the achievements of the greatest mind of my field, but I refuse to take his life!" In the end he succeeded.

20th May, 10 am. From the setup, he looked like a death row inmate who was about to be lethally injected. The whole Mathematics Department watched from a glass. Before they brought him inside the room, he looked at me and giggled softly, then he whispered softly: "I had to." I looked him in the eye, trying to smile weakly.

They strapped him down and prepared the amnestic. They asked if he had any last words. He looked at the ceiling and smiled. 7 lights. He turned slightly towards us and said:

"I'm sorry I was too human. I will never regret it. Thank you and… farewell."

They injected him. He closed his eyes.

He was still smiling.

There was a second USB in my pocket. It was his notebook transcribed. I stored it away for years. I didn't want the Foundation to take it from me.

He, Claire and Andrew were reintroduced into society after all the necessary precautions. They didn't get their names changed. The last favor Dr. Lambert insisted to be given to his former colleague. Whenever someone mentioned Archie, he would always say that he was an idiot, that if he had told the Foundation from the start they would have surely let him study the anomalies as he pleased. I'm more skeptical than he was.

He moved to Europe and often visited Africa. I always kept myself updated on what he was doing. I visited him sometimes, as a fellow mathematician. He was still as cheerful as ever. Of course. Nothing had happened. At least according to him. He had two daughters, Luise and Emma. Andrew now has a son called Jack. Oh, fate, you twisted beast. Archie Medes passed away at the age of 63 from throat cancer. In the eyes of mathematicians, he was a great mind. In the eyes of the world, he never existed. Claire gave me a copy of his new notebook. Among many things, there was the start of a solution to Goldbach's conjecture that used a group of numbers he had hypothesised, the "anomalous numbers". He thought that no one would pay this result any mind, since no one else would accept those numbers.

"My mind gives me no reason why these numbers should exist, but my heart keeps screaming that they do. Perhaps a better mathematician will translate in brain waves my palpitations."

And now, even after all of these years, thinking back to my whole life and to those moments I spent with him, I can't help but cry a bit. I gave my everything for the Foundation and I keep telling myself that I did good, that I helped humanity, that I protected the world. And yet, despite all this, I can't help but feel like my talent, my passion, the very desire that led me to study mathematics, my one true love, I just can't help thinking that it all was… wasted…that I could have spent my time better, that I could have been greater, better…happier.

I often wish I had Archie's resolve. He knew how to be a mathematician and a man. He explored and understood the universe of numbers better than everyone else, and yet that didn't stop him from being a just and honest man, a man who enjoyed real life to its fullest and wanted all the people he cared about to do the same.

The world had forgotten him, but he never forgot the world.

He managed to live in harmony and happiness in two places simultaneously.

That's why, to me, among all mathematicians and friends…

He was the greatest.