Chapter 81: A Gift of Congratulations-Back Before the College Entrance Exam, I Became a Sensation in the Science Community(Flowing waters fill the goblet.)

The second problem was a game, but this game required far more brainpower than ordinary ones: she was to prove that the final box would contain 2010^2010^2010 gold coins. Intrigued by the question, Wu Tong set about her solution with great interest. She wrote out her thought process, established the operational conditions according to the problem statement, set the directional requirements, deduced the number of operations... and finally, through a finite number of steps, arrived at the result: all other boxes were empty, and the sixth and final box contained 2010^2010^2010 gold coins.

The third problem, once again a high-difficulty watershed question, was a deep sequence problem that showcased the IMO's usual strategy of combining geometry, algebra, and number theory, all competing to take the stage.

Without pause, Wu Tong’s mind extended forward. She completed the complex proof for the last problem in one smooth, unbroken flow. With her concluding remarks written, her conclusion established, she checked her work, closed her pen, and raised her hand to submit her paper. All within an hour, Wu Tong left the examination room.

Outside, the natural light was bright, and the temperature was little changed from when she had entered. The IMO competition had now reached a perfect conclusion. Her backup plan, prepared with early university admission in mind, also seemed to have come to a satisfactory end.

As Wu Tong emerged, Professors Cheng and Li—now freed from their isolation—stood by the window, basking in the warm sunlight and savoring the rich aroma of coffee. Both had spent years abroad and, as representatives of the youthful new era, had far more appreciation for coffee than Wu Tong, who was stepping out of her home country for the first time and still had the air of a country girl.

“Congratulations, Wu Tong! You’ve broken the IMO record for fastest completion!” Professor Li smiled, raising his cup to her in salute. “Come, sit here. I ordered you some pastries and pistachio yogurt ice cream. They were just delivered!”

Wu Tong’s timing remained as precise as ever. They had known she wouldn’t take more than an hour. With Professor Li there to translate the exam questions, Wu Tong hadn’t had to handwrite them herself today.

“The score will depend on the committee’s evaluation,” Wu Tong replied with a relaxed smile. She was confident in the correctness of her answers, but the precise score would depend on whether the committee nitpicked her work.

“Hahaha, don’t worry! As long as your process is solid and your answers are correct, if they try any tricks, our country won’t back down. None of the teachers here are pushovers!” Li Yisheng’s exuberant confidence shone through. As team leaders, they had grading rights; no one could dock their students’ scores without reason.

Wu Tong’s achievements spoke for themselves. The committee would trust her work and wouldn’t dare make trouble.

Over sweets, they exchanged thoughts: from initial discussions of the last three IMO problems, they delved further into geometry, number theory, and algebra. Wu Tong engaged effortlessly, her logic rigorous, her thinking powerful and ingenious, her analyses deep—prompting both professors to praise her profound knowledge.

It should be noted that these two were considered mainstays of Peking University, having devoted over twenty years to mathematics. They would not claim exceptional genius, but they could say their knowledge was solid—worthy of their titles and their students. Yet, seeing the ease with which the underage Wu Tong conversed with them, they could not help but feel that the new generation was overtaking the old, the waves of the Yangtze forever pushing forward.

When k=1, for all natural numbers k, there exist infinitely many pairs of prime numbers (p, p + 2k).

Staring at the pistachio-studded, uniquely beautiful ice cream before her, Wu Tong suddenly fell into contemplation. The conditions of the twin prime conjecture leaped to her mind. The ice cream was no longer just a dessert, but a series of marvelous mathematical formulas.

The right Lambda function? Vinogradov’s three-prime theorem? The infinite expanses of topology...

Suddenly, inspiration struck Wu Tong. She instinctively took out pen and paper from her bag and began a series of calculations, completely absorbed in her own world. Mathematics flowed from her pen in a storm of formulas, her mind expanding in boundless thought, stirring up an endless mathematical tempest.

p1, p2, ..., pn; let N=p1×p2×...×pn. If N+1 is prime, then N+1 must be greater than p1, p2, ..., pn.

...5×7×11×13...p×3×5×7×11×11×17...(p-2)/p...

The breeze gently drifted in through the window, yet at that moment, Professors Li and Cheng found themselves no longer in a state of leisure.

“What is this...” Professor Cheng thought back to rumors he’d once heard, looking at Li Yisheng in disbelief.

Li Yisheng merely shrugged and spread his hands with a wry smile. He was familiar with this state. As expected, they were once again witnessing a moment of inspiration from their young prodigy.

Had they been discussing anything special just now? Were they even in the same dimensional space as her?

Why were they the same people as before, with not a hint of inspiration, while the young girl across from them was, right before their eyes, launching an assault on the twin prime conjecture?

The small round table was not large, and without moving, they could see what Wu Tong was writing. The familiar formulas made them recall Wu Tong’s longstanding interest in the twin prime conjecture.

All they could say was that their minds and a genius’s mind were truly different. For a genius, the breeze, the shape of drifting clouds, even the patterns in an ice cream swirl—everything was an extension of mathematics.

At this point, neither professor dared to make a sound. They enacted a silent pantomime. Li Yisheng smiled wryly but couldn’t hide the excitement in his eyes. He was both anxious for his own mind and thrilled that such a child belonged to China, to their university—even, if he could be so bold, to say, to his own tutelage.

With renewed focus, Professors Li and Cheng surveyed the surroundings, ready to prevent any disturbance that might interrupt Wu Tong’s inspiration and break the miracle unfolding before them. They carefully gathered and preserved each sheet of her drafts laid out on the table—these might one day be priceless treasures.

Wu Tong continued her calculations until the exam ended, only then lifting her head to stretch her shoulders and neck, meeting the eager, expectant gazes of the two professors.

“Professor Li, Professor Cheng, what is it?” She was nearly startled.

“Wu Tong, did you... did you prove it?” Li Yisheng and Professor Cheng lowered their voices, speaking in veiled tones. This wasn’t their own country—they could not be too cautious.

Wu Tong shook her head. “Not all the way yet, of course. It’s not that simple!”

Oh, that was a relief. Professors Li and Cheng let out a small breath. Even this much progress was impressive. They were just about to comfort Wu Tong, to tell her there was no need to rush—her breakthroughs were already remarkable.

But then Wu Tong paused and added, “Fortunately, I’ve found the general direction. I think I’ll be able to give myself the proof as a birthday present!”

(End of chapter)