Chapter Fifty-Five: Number Theory-Back Before the College Entrance Exam, I Became a Sensation in the Science Community(Flowing waters fill the goblet.)

“Whenever you feel like going out for a change of pace, just let me know in advance,” Professor Li Yisheng said warmly, “I’ll arrange a little guide to accompany you around the capital, and you can come to my home for a family meal as well!” Considering Wu Tong had just arrived in the city and was unfamiliar with her surroundings, Professor Li made this special invitation. Since the young student treated him with the respect due to a teacher, he felt it was his duty to look after her thoroughly. After all, one couldn’t stay on campus all the time; going out for a walk would be a good way to refresh her mind.

“There’s a little rascal at my house who can’t sit still whenever school’s out,” he added with a laugh, thinking it would be good for his son to spend more time with Wu Tong and perhaps catch some of her natural talent by association.

He was, after all, a graduate of the prestigious Peking University with both bachelor’s and master’s degrees, and had earned a doctorate from Stanford in the United States. His wife was also a Stanford PhD in economics. With such backgrounds, they could be considered geniuses or at least top scholars. Yet their only son had inherited little of their brilliance. The world’s mathematical conjectures remained unsolved by him, and at home, there was this troublesome son he couldn’t figure out either. Sometimes, the thought of it was enough to make him feel utterly defeated—life was indeed difficult!

Only when he saw these gifted children did he regain hope for the world.

“It’s been a long day. Get some rest early. If you need anything, call me. We’ll meet again soon!” With winter not yet departed, night fell early. After giving Wu Tong these instructions, Professor Li left the dormitory building.

After seeing Professor Li off, Wu Tong called her family for a chat and took the opportunity to sort her luggage.

From afar, Teacher Jin Yu guided Wu Tong on the details of independent living: what to eat, what to wear, how to get around… With her child out of sight, she wanted to share every piece of advice she could think of. In her past life, Wu Tong had found such words nagging, but now, in a different context, they felt heartwarming. She would never again bear the regret of wanting to care for her parents when it was already too late.

Having just arrived, Wu Tong didn’t fuss much that night; she familiarized herself with her surroundings and rested.

The next morning, as usual, Wu Tong began her day before sunrise with morning exercises on her small balcony. Her dormitory was well situated—the balcony faced the east, unobstructed by other buildings, offering a broad view and the first rays of the morning sun.

She had come to deeply appreciate the wonders and benefits of the Morning Radiance Qi Method over the past months. Her health improved steadily; her complexion glowed with vitality, she was full of energy, and no matter how intensely she worked her mind or body, she never seemed to run out of steam. Her hair remained thick, black, and silky as ever.

There was an added bonus—her physical strength was also increasing. Though she hadn’t measured it exactly, her keen sense for numbers told her that lifting a hundred pounds or so was no burden at all.

She had once tried quietly lifting Jin Xin while he was asleep—one-handed, without much effort. He was six foot one and weighed about one hundred fifty pounds. It was a remarkable discovery, and a useful secret skill for self-defense.

By six o’clock, the sun was fully risen. Wu Tong finished her morning routine, changed clothes, and set out to explore—starting with breakfast at the cafeteria. Unfamiliar with the university’s meals, she opted for two steamed buns and a cup of five-grain soy milk—a safe, basic choice.

After breakfast, Wu Tong went straight to the university library. Professor Li had already told her where to find it and given her a library card. She could either study there or borrow books to read back in her dorm.

Strolling down the university’s winter avenues, Wu Tong didn’t have a poet’s sensibility; she simply surveyed her surroundings, mainly to get her bearings and become familiar with the environment. Following Professor Li’s clear directions, she stepped into the vast library. The sheer size, facilities, and quality of the collection were a revelation to someone from a small county town.

The library was rich in resources, meticulously organized, with clear signage and dedicated study areas.

With everything she needed, Wu Tong found the mathematics section—a comprehensive collection of research materials, textbooks, and handwritten papers. She located her target books, settled into a nearby seat, and launched into study, completely at ease and content.

To Wu Tong, who was growing increasingly obsessed with mathematics, this place was a treasure trove beyond compare.

Thus began her official academic life at Peking University, her days revolving between the library, the cafeteria, and her dormitory, rarely setting foot outside campus.

Even the library staff soon became familiar with Wu Tong.

She didn’t necessarily visit every day, but whenever she did, she would either arrive early to seek out specific books and study in the reading room until noon before borrowing them and returning to her dorm to continue, or she would research thoroughly in her room first, then visit the library for new materials, studying there until closing time.

Wu Tong’s total immersion and focus left her oblivious to the outside world; it was usually the librarians who had to remind her when it was time to close.

The rotating librarians couldn’t help but marvel. In all their years at Peking University—a place brimming with talent—they rarely saw someone so utterly absorbed in study as Wu Tong.

Here, those who approached a near-maniacal state over their work were rarely nameless drudges. After all, this was Peking University, a gathering place for the gifted; sheer grind was what was truly rare here.

Time slipped quietly by as Wu Tong’s daily routine repeated itself. She absorbed knowledge like a sponge, ravenous for the rich resources around her. Her mathematical knowledge tree grew rapidly, expanding and filling out at an astonishing rate.

Her eyes grew deeper, gleaming with the radiance of knowledge as she studied.

This was the Polignac conjecture: for every natural number k, there exist infinitely many pairs of primes (p, p + 2k). When k = 1, it becomes the famous twin primes conjecture.

Wu Tong scribbled a few formulas on her scratch paper:

Let y be the y-th prime number, P(y) its value, and P(y)^2 its square, representing the range within which primes can be determined.

P(y)^2 - P(y-1)^2P(y) = 11,
P(y)^2 = 121,
L(5) = (1/2)*(2/3)*(4/5)*(6/7)*(10/11) = 16/77,
U(5) = (1/2)*(1/3)*(3/5)*(5/7)*(9/11) = 27/154,
P(5)^2 - P(5-1)^2 = 72.

The mathematical world was vast and boundless, and her first deep exploration led her to number theory.

Number theory was a magical field, enchanting countless souls who could not bear to awaken from its charms.

Its threshold was low; many formulas and theorems could be understood by middle school students. It had produced countless folk scientists—every year, the Chinese Academy of Sciences was flooded with letters from amateur mathematicians claiming to have solved the famous Goldbach conjecture.

These enthusiasts were convinced they had proven the world’s greatest puzzles, only to find, unfortunately, that their knowledge often didn’t even meet the Academy’s basic entry requirements.

Clearly, number theory was an area where innate talent was absolutely critical. The reality was harsh: without a solid foundation and extraordinary gifts, it was nearly impossible to achieve anything in this field.