The Royal Road
Yoo Jae-won's hand moved without the slightest hesitation across the Royal Road. With every stroke of the chalk, elegant equations appeared on the green blackboard. The notoriously difficult problem was being resolved in a manner no one had ever considered. At this point, the professors' faces naturally filled with shock. Their reactions varied. Professor Conner of the Applied Mathematics Department stood with his mouth agape, unaware that chalk dust was flying into it. Professor Daniel Camen, who regained his composure first, began erasing the blackboard in advance, worried there might not be enough space to complete the proof.
"A camera! Someone get a camera!" one of them shouted. In this era, a camera was essential for capturing historic moments. Fortunately, the laboratory was equipped with various experimental devices, so finding a camera with spare film was not difficult. The only issue was that it was a disposable camera rather than one with a high-quality interchangeable lens. They usually used disposables for simple photographs to attach to reports. Since capturing the moment was the priority, the professor framed the shot with Yoo Jae-won at the center while he was still writing, making sure to include the professors craning their necks like meerkats toward the blackboard, and pressed the shutter. A historic scene was being recorded on a humble disposable camera.
"...And thus, that space can be transformed into a sphere." Amid the professors' varied reactions, Yoo Jae-won calmly finished the proof, adding the final equations. He wanted to toss the chalk dramatically, but refrained because the professors were still absorbed in studying the equations. There was no applause or cheers. After all, everyone present stood at the pinnacle of the sciences. None of them failed to grasp the symbolic weight of solving one of the seven Millennium Prize Problems. Precisely because they understood its importance, they were now frantically verifying whether Yoo Jae-won's solution was correct. Verification, however, could not be completed in an instant. While a simple division could be checked by reversing the calculation, Yoo Jae-won's proof compressed highly advanced mathematical techniques; even with computers, it would take weeks to verify.
The verification process itself would yield tremendous value. It contained layer upon layer of new-dimensional techniques born from the fusion of the twenty-first century's mathematical pinnacle and an enormous-scale artificial intelligence. Yoo Jae-won was confident that even grasping half of it would allow the current mathematical community to advance several dimensions further. That was why a small part of him wondered if he had gone too far. Still, he felt no regret. The Poincaré Conjecture would only find practical application once humanity's manned space exploration extended beyond the solar system. It formed the theoretical foundation for verifying the stability of navigation systems used in space travel, ensuring the safety of passengers. Progress in mathematics was difficult for ordinary people to feel in their daily lives. Instead, enormous changes would occur in places invisible to the public eye.
Having completed such a monumental proof, Yoo Jae-won found himself sidelined. Some professors were taking photographs, others were transcribing the equations from the blackboard, and still others stood staring blankly at the ceiling as they performed mental calculations. Every professor was absorbed in digesting Yoo Jae-won's proof in their own distinctive way, paying him no attention whatsoever.
"Ah, well... I'll be heading out now. If any errors or questions arise, please contact me at this number. It's a mobile phone, so you can reach me anytime." Not knowing whom to address, Yoo Jae-won spoke loudly to Professor Conner, who happened to be closest. Judging by the professor's waving hand, he seemed to have understood. Yoo Jae-won gave a slight bow and turned to leave.
"Wait! Let's all gather for a group photo!" It was the professor holding the disposable camera. At his words, the professors clustered around the blackboard glanced back once before returning to their work. Not everyone ignored the request, however. Several who understood the importance of documentation moved toward the camera. Yoo Jae-won, who had been about to go eat, did the same. Once a group had assembled, the remaining professors could no longer continue their individual activities. They took several group photographs together.
From that moment, Stanford's School of Engineering began to buzz with activity. The Electronic Engineering laboratory where Yoo Jae-won's proof remained became a pilgrimage site for engineering professors. Even though the proof had already been organized into documents and photographs, many came in person to transcribe the equations directly from the blackboard. The fact that it spanned only three A4 pages made transcription easier than photographing it. Naturally, when professors moved, graduate students followed. The scene resembled a religious pilgrimage. Countless mathematicians had challenged this problem, only to be blocked by its immense wall. It was not something that could be solved through sheer effort alone; it required a flash of insight and the ability to apply that insight to the problem. Even those hailed as mathematical geniuses from a young age and who had produced remarkable achievements had repeatedly tasted bitter defeat when attempting the Millennium Prize Problems. That Yoo Jae-won had solved one in a single stroke naturally threw Stanford University into an uproar.
News of the proof of the Poincaré Conjecture spread rapidly. The equations once written on the blackboard were compiled into an IDW file and uploaded to Stanford's intranet and internet bulletin boards, quickly disseminating across the web. Most who saw the title refused to believe it. Moreover, because ID Word Processor was not yet perfect at handling complex equations, large portions had been written out in words, leading many to misunderstand the content. As a result, professors from other universities relatively close to Stanford—and in competitive relationships with it—began making pilgrimages to the site. Professors from the California Institute of Technology, UCLA, and UC Berkeley arrived. The number of such distinguished visitors from prestigious institutions grew steadily. Eventually, the scale became so large that it resembled a massive mathematics conference hosted by Stanford. Every one of them visited the laboratory as if on pilgrimage and saw the proof written on the blackboard with their own eyes. Their reactions were largely the same. Though many were taciturn and showed little change in expression, they were astonished that a proof spanning only three A4 pages could exist.
A considerable number of reporters also arrived after hearing the rumors. The professors made extra efforts to maintain their expressions, but instinct could not be suppressed. Faced with such an elegant proof, their mouths fell open in awe.
"Who did you say solved this?" asked a man whose face was lined with wrinkles.
"A student named Yoo Jae-won," Professor Daniel Camen answered respectfully. His eyes were filled with reverence for the questioner. After all, the man who had asked was none other than the legendary John Nash. He had presented his doctoral thesis in 1950 on non-cooperative game theory, which later became known simply as game theory and was widely applied across the social sciences, particularly economics. He was a genius of the rarest kind, and simultaneously an unfortunate one. He too had been a challenger to the Millennium Prize Problems, and that was where his troubles began. Among the seven problems, the most famous was the Riemann Hypothesis. It stood as a colossal barrier blocking the very edge of humanity's mathematical knowledge, defeating every challenger and turning them into failures. John Nash was one of those failures. No—he was perhaps the most famous failure of all. After all, he was an authority who had left an enormous mark on mathematics by founding game theory. Yet his obsession with solving the Riemann Hypothesis had ultimately triggered schizophrenia. He had been receiving treatment for thirty years. Fortunately, through sheer mental fortitude, he had managed to separate delusional thoughts from rational thinking and had barely returned to a normal state.
"Yoo Jae-won. The name sounds familiar."
"Yes. He was already famous before even enrolling. He is the chairman of ID Group, which created the Android operating system, acquired Microsoft, and unified the PC operating system market."
Even while recuperating, John Nash remembered seeing Yoo Jae-won's name in the newspapers. However, only the name surfaced in his mind; no specific details came to him.
"Would it be possible for me to meet this protagonist before the verification is complete?" John Nash's curiosity was only natural. There was something else he wanted to ask as well.
"Yes, I will arrange a meeting as soon as possible." Professor Daniel Camen answered politely, recalling Yoo Jae-won's mobile phone number. At the same time, he was already thinking of ways to insert himself into that meeting. It was a gathering of two extraordinary geniuses. Nothing might come of it, but something monumental could also emerge. Professor Daniel Camen desperately wanted to be present.
John Nash's name alone was enough to stir the entire United States. The fact that the reclusive John Nash had visited Stanford University was already major news, and the reason being the solution to one of the Millennium Prize Problems made it a story that would shock the world. What had been a topic of conversation only in San Francisco and California quickly spread nationwide through broadcast news. Since an American scoop was effectively a global scoop, the news instantly spread from the United States to Europe and Asia.
-Shock! The Poincaré Conjecture, One of the Seven Millennium Prize Problems, Fully Proven!
-Massive Shock! The Solver of a Millennium Prize Problem Is a 16-Year-Old Stanford Freshman!
-Massive Shock! The 16-Year-Old Stanford Freshman Turns Out to Be the Chairman of ID Group!
From this point on, sensational breaking news headlines began pouring out. Not just "shock," but "massive shock." Thanks to this, Yoo Jae-won received an excited phone call from home for the first time in a while. He had intended to explain things appropriately to his parents, but they, now surrounded by capable staff, already knew everything. There was no longer any need for Yoo Jae-won to explain things himself. Instead, they were already drinking imaginary celebratory kimchi soup, convinced he would win a Nobel Prize, so he had to calm them down. Solving a Millennium Prize Problem was certainly a tremendous achievement. However, there was no mathematics category in the Nobel Prize, so it was impossible to receive one. Instead, there existed the Fields Medal, mathematics' equivalent of the Nobel Prize, and he told them there was a very high probability he would receive it.
In Korea, Yoo Jae-won's name once again soared to new heights. They briefly explained the Poincaré Conjecture before moving on, focusing instead on Yoo Jae-won, the solution of a Millennium Prize Problem, and the Fields Medal, often compared to the Nobel Prize. However, because Yoo Jae-won had already become widely known through ID Group, most ordinary people simply thought he had done something impressive again without fully understanding the significance of that achievement. That did not mean there were no changes in daily life.
"Boss, we're on Level 1 alert today as well." At Greg's words as he waited in front of the house, Yoo Jae-won returned the electric bicycle he had brought out back inside. Level 1 meant situations like events in crowded areas. In other words, the road to the university was filled with reporters. There were far more reckless American journalists who would charge forward without hesitation just to get a single word. Fortunately, Yoo Jae-won's security team had anticipated this media frenzy early and prepared thoroughly. The electric bicycle would not be used for the time being, and the number of bodyguards had been increased several times over. Since money was no object when it came to ensuring safety, no unpleasant incidents like those from his previous life occurred. Cars carrying bodyguards guarded the front, rear, and even the sides of the vehicle Yoo Jae-won rode in, fundamentally preventing paparazzi from approaching.
Some professors and classmates worried that it might seem excessive, but everyone understood.
"It's Jae-won!"
"Really? Where's a pen and paper?"
"Yoo Jae-won! Can I get your autograph?"
Of course, not everyone reacted that way. Some classmates had not suddenly turned into paparazzi, but they had become like rock star fans. That had started a few days ago, and it was still the same now. Yoo Jae-won knew Americans tended to have big gestures and enthusiastic reactions. He had expected the surroundings to be noisy for a few days. Yet even after several days, the intensity of the commotion showed no sign of decreasing. He felt as though he had already signed over a hundred autographs, but every day on the way to school, more papers would appear from somewhere. Writing the same signature repeatedly was extremely tedious, but whenever he had time, Yoo Jae-won smiled and signed his name.
"Hey! How dare a lowly commoner block the path of Stanford Engineering's hope, the chairman of ID Group, and the solver of a Millennium Prize Problem, Yoo Jae-won! Shoo, shoo! Stand aside!"
Moreover, whenever students began bothering Yoo Jae-won, Jonathan would somehow appear and drive them away. Yoo Jae-won wished he would stop calling him "hope" or "chairman," but with Jonathan's massive frame waving his hands, the crowd scattered instantly.
"Thanks!"
"Heh heh, dealing with these nerds is nothing." Jonathan tilted his head up proudly. Then, as if remembering something, he turned back to Yoo Jae-won.
"Are you free after three?"
After three? He had no classes scheduled. Even if he did, it would not matter. It was as if he had already secured a fast-track pass; attendance requirements would no longer hinder his graduation. However, the reason there were "no classes" was because the verification process was still ongoing. Since Millennium Prize Problems were extremely difficult, verification naturally took a long time as well.
"Of course!"
At any rate, Yoo Jae-won was hoping Jonathan might be arranging some kind of meeting.
"Great. Professor Camen wants to see you at COHO."
As expected, Yoo Jae-won had been drinking imaginary kimchi soup. COHO was a restaurant and café on Stanford University's campus. It served simple meals, coffee, and drinks at very low prices from morning until evening, making it a popular meeting spot for students and faculty. There was no way the department head would call him to COHO for an introduction or blind date. It was undoubtedly about the Poincaré proof.
"How do you do? I'm John Nash."
Yoo Jae-won's expectations were pleasantly upended. Sitting beside Professor Camen, who was waiting for him at COHO, was the legendary John Nash.
"Ah, yes! I'm Yoo Jae-won!"
Yoo Jae-won was well aware of John Nash's reputation. He had become so immersed in proving the Riemann Hypothesis that he developed schizophrenia, overcame it through superhuman mental strength, returned to academia, and later met an untimely death in an accident. That rough outline of his life story immediately came to mind. Although he had not studied it as diligently as IT technology, there had been a period when he had spent several weeks carefully studying John Nash's game theory as well.
Soon after, the coffee they ordered arrived, and the conversation continued. Through it, Yoo Jae-won learned that this meeting had been requested by John Nash, not Professor Camen. There was one question he wanted to ask seriously. A question from a legend. Yoo Jae-won was extremely tense. Could there have been an error in the equations he had transcribed onto the blackboard?
"So, what do you plan to challenge next?"
John Nash's actual question was completely different from what Yoo Jae-won had expected.
"The verification isn't even finished yet."
"Of course. But you already believe the proof is complete, don't you? I, too, didn't feel even the slightest sense that such beautiful equations could contain an error."
That was John Nash for you. Because of that, Yoo Jae-won began speaking honestly without trying to dress up his feelings.
"Are you hoping I'll challenge another Millennium Prize Problem? I'm sorry, but I have no intention of doing so right now." Solving another Millennium Prize Problem would not be particularly difficult for Yoo Jae-won. Unlike the Poincaré Conjecture, the others were things he would need to retrieve from his Memory Palace. It would be troublesome, and consecutively solving multiple problems carried a high risk of causing issues. What was unexpected was John Nash's reaction. As a mathematician, Yoo Jae-won had thought John Nash would be disappointed to hear he would not challenge another Millennium Prize Problem. Instead, he smiled.
"As expected, my worry was unfounded."
Worry?
"I've seen many geniuses like you. I, too, pride myself on being different from others. That's why I was greatly concerned you might attempt the Riemann Hypothesis. If a shining existence like you were to waste time on a problem with no end in sight, what a tremendous loss that would be. And if, by some chance, you developed a mental illness like I did, that would not be your sorrow alone, but a tragedy for all of humanity."
Listening to John Nash's continued words, Yoo Jae-won finally understood his feelings. He was right. Although the seven problems were called Millennium Prize Problems because they were problems of the century, there was clearly a difference in difficulty among the seven. Naturally, the final boss among the Millennium Prize Problems was the Riemann Hypothesis. Countless people had come to grief attempting to solve it. John Nash, sitting right in front of him, was living proof of that.
"Thank you for your concern. I am interested in the Riemann Hypothesis, but it doesn't seem like a problem humans can solve. Besides, I only solved a Millennium Prize Problem to obtain a fast-track pass. I'm not particularly interested in mathematics. I'm far more interested in semiconductor design."
It was a problem that could not possibly be solved by human intellect alone, which was why even an artificial intelligence of tremendous capability had been brought in. Even then, no answer had been found. When he observed the organizations that had run artificial intelligence for the Riemann Hypothesis, it seemed they had definitely achieved some results. However, since they had not made it public, Yoo Jae-won was ultimately back at square one. He would challenge the Riemann Hypothesis someday, but he had no intention of doing it himself. Instead, he planned to entrust it to artificial intelligence, just as a massive internet company had done.
"I see. I agree. But you said you're not interested in mathematics?"
He had been too honest. After all, who would believe someone who had just artistically proven the Poincaré Conjecture a few days ago when they claimed to have no interest in mathematics? Yet Yoo Jae-won's words were the unvarnished truth. He had chosen the Electronic Engineering Department to accelerate IT technology development beyond his previous life by focusing on semiconductor design and materials.
"Why don't you take an interest in mathematics as well? Simply solving one Millennium Prize Problem is an achievement that will shine for eternity. Your future path will be equally solid because of it."
"I'm sorry." Yoo Jae-won refused outright. Disappointment spread across John Nash's face. He seemed to be saying that an existence that could become a supernova in mathematics had fallen into the wrong field. Even though he was grateful for John Nash's suggestion, the answer was still no. Yoo Jae-won was already walking a path far more solid and brilliant than what John Nash had proposed. It was a path no one in history had ever walked before—a golden Royal Road.