The Fields Medal and the Millennium Prize
Switzerland, a federal republic in Central Europe, has no official capital under its constitution, yet Bern serves as the de facto capital, hosting the Federal Assembly and numerous international organizations. The largest city, however, was Zurich, where Yoo Jae-won and his party had just arrived. They landed in the evening, ate a light meal, and retired early for their first night. Everyone dined together. His parents, exhausted from the journey, headed straight to their hotel rooms, but Yoo Jae-won and Tiffany, still brimming with youthful energy, ventured into the city for an evening stroll through foreign streets.
Even in the city, Jae-won's camera never rested. They took turns photographing each other, and Greg, their bodyguard, captured several shots of the couple. They roamed Zurich until dusk, indulging in the kind of affectionate displays that would make onlookers blush. Yet their time outdoors proved shorter than expected. In most European countries, shops and restaurants close within an hour or two after sunset, leaving the streets nearly deserted. Jae-won and Tiffany had heard the stories but still felt a pang of disappointment at how abruptly the evening wound down. With little left to do in the darkened streets, they returned to the hotel and turned in early, looking forward to the next day's schedule.
The following morning, Yoo Jae-won's official itinerary in Switzerland began. Several public engagements awaited him. The first was a meeting with the President of Switzerland. Jae-won had not initiated the request. While some ID Group subsidiaries had expanded into Europe, none had entered Switzerland, and he had no particular demands of the Swiss government. When the schedule first appeared, he had assumed the Swiss side might be seeking investment. Instead, it turned out to be a banquet hosted by the Swiss government in honor of the International Congress of Mathematicians. High-ranking officials, including the President and the Speaker of the National Council, would attend alongside Fields Medal laureates and the President of the International Mathematical Union.
It was there that Jae-won met the other laureates for the first time. Among them, he shone brightest. Interestingly, the mathematicians reacted far more enthusiastically than the Swiss officials. Their excitement stemmed, of course, from his proof of the Poincaré conjecture. While ordinary people might grasp only that a century-old problem had finally been solved, the laureates present had each attempted the problem at least once. As mathematicians who had personally wrestled with it, the impact of its resolution struck them with far greater force.
The questions directed at Jae-won all centered on how he had solved the Poincaré conjecture and how he had managed to present the proof with such remarkable clarity. Had he merely transcribed the solution from his Memory Palace without true understanding, he would have been left stammering. But because he had internalized both the problem and its solution, he answered every question with ease. Once their curiosity was satisfied, the mathematicians wore the contented expressions of cats that had drunk their fill of milk, and the conversation finally moved on.
“Chairman Yoo, will you be tackling the next unsolved problem as well?”
“Could you tell us which problem currently interests you?”
The follow-up questions remained firmly rooted in mathematics.
“Of course! I fully intend to try.”
Jae-won nodded firmly, meeting the hopeful gazes of the mathematicians with bright eyes.
“But not right away. My current responsibilities are overwhelming, and carving out the necessary time is difficult.”
His answer fell short of their full expectations. After all, his primary role was that of a businessman.
“Haha! Simply knowing that someone of your caliber continues to hold an interest in mathematics is reassuring enough.”
Nevertheless, the Fields Medalists and the IMU President brightened visibly. Jae-won was still in his teens; his prime years lay ahead. If his passion for mathematics endured, they had no doubt he would bring tremendous progress to the field.
“Now that one of the seven problems has been solved, shouldn’t we add another? Calling them the six problems would feel rather odd.”
Perhaps it was the relief of having that particular concern addressed, but IMU President Jacques-Louis Lions offered the remark lightly. Seven did carry a more satisfying ring than six.
“Then, Chairman Yoo, would you care to recommend a replacement problem?”
“That would be ideal. Any problem you designate would undoubtedly draw far greater public attention.”
Once again, every eye turned to Jae-won. The original seven problems had been assembled largely as a publicity device to spark interest in mathematics. Countless other unsolved problems existed, yet selecting the most difficult ones and branding them as the seven had naturally drawn attention, encouraging students to pursue mathematics. Jae-won, whose mind overflowed with good ideas on the subject, spoke up.
“How about this?”
Mathematicians and even the Swiss President and Speaker leaned in.
“In a few years we’ll enter a new millennium. The ‘seven problems’ label already feels dated. Let’s rename them the Millennium Problems to mark the occasion. And let’s attach a substantial prize to each one.”
It had always struck Jae-won as unfortunate that the seven problems carried no monetary award; they had simply been grouped together because of their difficulty.
“Oh! An excellent idea.”
Jacques-Louis Lions slapped his knee in delight. The shift from one millennium to the next was a momentous calendrical change. Branding the problems as Millennium Problems would lend them genuine distinction. The mention of large prizes, however, gave him pause. The IMU, a nonprofit funded solely by donations, lacked the resources to offer sums large enough to capture the public imagination. Even the Fields Medal, mathematics’ highest honor, carried a prize of only fifteen thousand dollars.
“If it’s not too presumptuous, I would be willing to fund the prizes myself. How does one million dollars per problem sound?”
When Jae-won finished speaking, silence fell. Then—
“Good heavens!”
The scale of the offer had been so unexpected that its reality took a moment to register.
“A million dollars for each Millennium Problem…”
President Lions felt an overwhelming urge to rise and embrace Jae-won on the spot. He was already profoundly grateful that Jae-won’s solution had advanced mathematics so dramatically and inspired countless children to take an interest in the subject. Now Jae-won was not only elevating the seven problems to Millennium Problems but also underwriting a million-dollar prize for each. Nothing could have been more welcome.
For Jae-won, the arrangement was equally advantageous. Seven million dollars was a negligible sum against ID Group’s massive cash flow, and the tax benefits would reduce the actual burden even further. Moreover, the gesture would enhance the group’s global reputation, making it a worthwhile investment in publicity.
The banquet, which had filled both stomach and spirit, came to an end. After a brief rest, the afternoon brought the official opening of the International Congress of Mathematicians, culminating in the highlight: the Fields Medal ceremony.
“The first recipient of the 1994 Fields Medal is Chairman Yoo Jae-won of ID Group.”
At the announcer’s voice, Jae-won rose from his seat among the other laureates and walked forward. He did not forget to offer a small wave to his parents and Tiffany, who sat in the front row applauding enthusiastically. The Swiss President, presenting the award, handed him the large gold medal bearing the likeness of Canadian mathematician John Charles Fields and shook his hand. Cameras from the assembled media captured the moment. Notably, Korean press outlets—absent from the previous congress in 1990—had arrived in force. This time, with a Korean laureate, networks had dispatched not only correspondents but full film crews. Jae-won posed graciously for them as well, offering the standard remarks about the honor and his commitment to continued effort. The audience’s response was the warmest of all.
Once the ceremony concluded, the media began to disperse, assuming the remaining program would lack further interest. Yet the evening was not over.
“We now have a major announcement from the President of the International Mathematical Union.”
IMU President Lions stepped onto the stage. There he revealed that the seven problems would be rebranded as the Millennium Problems, each carrying a one-million-dollar prize sponsored by ID Group, and expressed his gratitude for Jae-won’s extraordinary generosity. The surprise announcement proved dramatically effective. That evening, the Millennium Problems led news broadcasts around the world—an extraordinary occurrence for a mathematical achievement. The promise of a million-dollar reward for solving any one of the problems captured global attention. Questions immediately arose about which problems would be selected, but no decisions had yet been made. Interest intensified, however, when it became known that one of the problems would be chosen by Yoo Jae-won himself. Many believed that any problem selected by the brilliant young businessman and mathematician would be exceptionally difficult.
Jae-won offered no comment to the persistent reporters. He already had a problem in mind—one whose study, even without a solution, would significantly advance humanity’s intellectual capabilities. It concerned a core algorithm related to artificial intelligence. He intended to announce it at the appropriate time.
“It’s not actually solid gold, is it?”
“Honestly, even at this size, a solid-gold medal would be far too heavy to lift comfortably.”
Jae-won’s parents passed the Fields Medal back and forth, marveling at it with exaggerated awe. The medal, roughly the size of a palm, would not have been impossibly heavy even if made of pure gold, but their pride and delight were unmistakable. While they were proud of the fortune he had built through his company, seeing their son receive an award from the Swiss President before a worldwide audience filled them with a different, deeper joy.
Tiffany felt the same. As an engineering student, she understood the weight of the Fields Medal better than his parents. Having always recognized Jae-won’s extraordinary talent, she had applauded more fervently than anyone, and the cameras had caught her unrestrained enthusiasm.
“Jae-won, your mother shared some fascinating stories with me.”
Tiffany, it seemed, had found something even more intriguing than the medal itself. Kim Mal-sook spoke no English, and Tiffany’s Korean was still rudimentary after less than a year of study, yet the two women had evidently communicated well enough to share many stories.
“Oh? What kind of stories?”
“She told me all about when your genius with computers first appeared! Apparently you learned piano on a computer and even predicted the rankings for the ’88 Olympics. I was amazed. Do you still have that program?”
Jae-won’s mouth went dry. The memory of 1988 remained vivid—how he had written a simple BASIC program to predict Olympic results and bolster his credibility with his parents. Once they accepted his computer aptitude, they had never again questioned the hours he spent at the keyboard, allowing him to lay the foundation for ID Group. The problem was the program’s actual sophistication. His parents might have been fooled, but Tiffany would immediately recognize that the outputs had been prearranged.
“That was years ago. Between multiple reformats and hardware upgrades, nothing from back then survived.”
Jae-won scrambled for an explanation. His computer had indeed progressed far beyond the 286 model he had used at the time.
“I suppose that makes sense. What a shame.”
Tiffany accepted the explanation readily, having performed similar upgrades herself.
“I would have loved to see how you made the predictions.”
Her disappointment was plain.
“I can still explain the method later. I remember the algorithm.”
“Really?”
“Of course. I’ll tell you sometime. Just don’t expect anything too impressive.”
“Got it!”
Confident in his knowledge of various predictive algorithms, Jae-won felt certain he could describe the approach convincingly without code.
“We’ll be arriving in Basel shortly.”
Kim Dae-seok’s announcement from the driver’s seat rescued Jae-won from further interrogation. Their business in Zurich had concluded with the Fields Medal ceremony; now they were traveling to Basel for the more leisurely portion of their trip.
Switzerland’s three great prides were said to be the Alps, Federer, and watches. Within Switzerland, the center of watchmaking was Basel. Every major brand was represented there, along with the highest concentration of independent watchmakers who signed their own work. Jae-won had always considered the precise time displayed on a mobile phone superior to any mechanical watch, so he had arrived in Basel with no intention of shopping. His plans, however, had changed. They intended to shop with enough enthusiasm to exhaust everyone by an early bedtime. At the same time, he would purchase watches for his parents and ask them to keep the more outlandish stories of his childhood to themselves. Those tales, already stretched beyond belief, might be manageable with Tiffany, but if they spread further the exaggerations would become unpredictable. Keeping them as family secrets seemed the wisest course. He would also buy gifts for friends, colleagues, and respected teachers while he was at it.