Chapter 179: This Pancake, Big and Round

The owner of the poster announcing the proof of the Goldbach Conjecture was a gaunt German man who looked as if he hadn't slept properly in days; two blackboards beside him were covered in formulas.

Most passersby glanced once and lost interest instantly.

Xu Xu Qingzhou stood before the blackboards with a strange expression, carefully examining every formula on both boards.

Three minutes later, he finished.

The man's eyes burned brightly: "Hey, Chinese?"

"Hello." Xu Xu Qingzhou nodded.

The man, as if finding a kindred spirit, grabbed Xu Xu Qingzhou and said: "Since you're Chinese, your math must be excellent. Look here—I've adjusted Chen's weighted sieve method from your country, making it smoother than before."

Pure mathematical exchange—Xu Xu Qingzhou sat in the last row, listening intently, gaining new insights into L-functions; unfortunately, he had no need for analytic continuation—the current L-functions already sufficed for his research.

Read! {

By 8:30 a. m., most people had arrived; everyone was busy exchanging ideas or displaying their work—two blackboards, a few people gathered around each, forming small discussion circles.

"Although the L-function was originally defined for σ > 1, through analytic continuation, we can extend its definition to the entire complex plane—except possibly for poles or essential singularities."

Xu Xu Qingzhou had rehearsed this question many times—he answered without hesitation: "Here, we must first define the ratio between the gap between consecutive primes and the square of the natural logarithm of the prime."

To many foreigners, Chinese people were all math geniuses.

Look at this pancake—it's big and round.

"Thank you, I agree," Xu Xu Qingzhou said, fully acknowledging his own appearance.

Xu Xu Qingzhou greeted her while observing the girl—she looked about twenty-five or twenty-six, with blonde hair, blue eyes, and a dusting of freckles on her cheeks; she was very attractive.

"Rather than listen to your compliments, I'd rather know how you arrived at the adjacent iterative expression for the function of prime gaps when proving Cramér's theorem."

"Wait—I'll find the materials. Believe me, I'll solve it soon!" The man took a deep breath and rummaged through his bag.

"Xu Xu Qingzhou?"

"Interested in collaborating? Don't doubt it—in the near future, you'll witness the birth of a miracle!"

In the classroom, everyone else shook their heads, thinking this young Chinese guy was too naive to actually take it seriously.

At the entrance of Conference Hall 2.

Professor Darte bowed to the audience, offered no small talk, then picked up a piece of chalk and wrote a row of formulas on the board: L(s, χ) = ∑_{n=1}^∞ χ(n)/n^s = χ(1) + χ(2)/2^s + χ(3)/3^s + "A year ago, my assistant and I were studying class number formulas and Galois representation theory, and found Dirichlet L-functions insufficient for our needs."

The man froze, staring at the point Xu Xu Qingzhou had pointed out.

"Call me 'Kathleen.'"

At this moment, the lecture hall was bustling—every seat was filled.

At 9:00 a. m., the first lecture officially began.

A figure entered from outside the auditorium, walking quickly straight toward the podium; as the man stepped in, the hall erupted in loud applause.

He was a middle-aged man with a beard, wearing an old jacket.

Kathleen said: "I studied Cramér's theorem, but after a week, I gave up."

The sixty-minute lecture passed in a flash.

Soon, she finished writing, tore off the paper, and handed it to Xu Xu Qingzhou with a light smile: "If you want someone to show you around here, call me."

Kathleen didn't delay—she walked toward the hall exit, but after two steps, she suddenly turned back, stopped before Xu Xu Qingzhou, opened her notebook, and wrote something. As soon as she left the lecture hall, she said to Xu Xu Qingzhou: "Xu, I'm afraid I must leave now—I'd hoped to continue our discussion."

"My pleasure."

"Thank you."

Xu Xu Qingzhou immediately realized this was the owner of the blue pickup truck; he smiled and extended his hand: "Miss Mills, it's a pleasure to meet you."

"Then, use the circle method to prove that every sufficiently large odd number can be expressed as the sum of three primes."

"Let p be prime, i and j positive integers—this set includes 1, all primes and their powers; although even numbers are rare, there are still infinitely many here—how did you derive x log x?"

Xu Xu Qingzhou smiled helplessly and pointed to one step on the blackboard:

After Professor Darte finished, the Q&A session began.

Kathleen apologized: "Sorry—I planned to ask you next Tuesday, but you know, curiosity is hard to suppress."

"A fascinating field," Xu Xu Qingzhou praised. In discrete mathematics—graph theory, set theory, logic, etc. —his Cramér conjecture had already drawn on graph theory.

Xu Xu Qingzhou smiled and shook his head, then turned and walked away, leaving the man with a face full of frustration; though cruel, a proof ignoring a necessary condition was meaningless—and adding that condition would lead to a dead end.

Someone always wants to make a splash here.

Kathleen felt this Chinese man was different—not as excessively humble as others. "Let's go sit inside; otherwise we won't find seats." They entered and found seats near the center.

This man was Benji Darte.

Every year at this conference, one or two people go off the deep end. Last year, someone claimed to have proven the Riemann Hypothesis; the year before, it was the Twin Prime Conjecture.

Kathleen smiled gently and added: "I majored in prime number theory for my master's; now I'm working with my advisor on discrete mathematics."

He turned around—standing behind him was a girl, curiously studying him.

"No problem, next time." Xu Xu Qingzhou nodded.

Xu Xu Qingzhou said nothing, listening as he shared his findings.

After the lecture ended, many scholars approached Professor Darte to exchange ideas; Xu Xu Qingzhou exhaled, then walked out of the hall with Kathleen.

"Hello?"

!.

The girl extended her hand: "I'm Kathleen Mills—pleased to meet you, Xu."

"Xu, you're better-looking than in the photo," Kathleen complimented.

"Does Miss Mills specialize in number theory?"

As Xu Xu Qingzhou was about to enter, a voice behind him called out—clearly calling his name.

Xu Xu Qingzhou chuckled—he hadn't expected her to return for this; the note contained Kathleen's phone number and email.

"Goodbye."

"Goodbye."

After parting with Kathleen, Xu Xu Qingzhou wandered the lecture hall but found no topic worth discussing; he returned directly to the hotel, ate lunch on the second floor, then went to his room and plunged into calculations on the Twin Prime Conjecture.

(End of Chapter)