Chapter 439: He Ultimately Gave Up

Xu Xu Qingzhou wasn't stubborn; he pulled out all his old manuscripts, reorganized them, and also compiled the revision suggestions he'd received on the Riemann-Siegel zero problem, uploading the second version to arXiv.

When he had time, he'd take out even earlier materials and take a look.

The next day, the mathematics community grew lively again as another research group made progress on the Riemann Hypothesis.

In Princeton, Steven Jell and Grace Aiheti built upon Professor Maynard's work, optimizing the multidimensional sieve and successfully improving the large value estimates of Dirichlet polynomials.

Better than the results from Jianqiao.

"These two people look familiar."

Xu Xu Qingzhou browsed the news feed and quickly remembered who they were.

He had interacted with them during a lecture at Jin Ling University, discussing the distribution of primes and upper and lower bounds.

He read the papers they had posted on arXiv.

Though still slightly less accurate than his own, their approach was novel, employing analytical techniques developed for missing-digit primes.

"I can only proceed slowly."

Xu Xu Qingzhou wasn't in a hurry to upload his paper. Since beginning work on the Riemann Hypothesis, he had accumulated over two hundred pages of manuscript that needed time to sort through.

Organizing papers, reviewing materials, cooking for Song Yao.

Xu Xu Qingzhou lived this leisurely life for three days; on Sunday morning, he received a call from Professor Roberts.

"Xu, the second approach works—we introduced a discriminator to force the model to focus on tail features, dynamically generating interest vectors using users' historical click sequences. CTR has increased by 20%, GMV by 10%."

"Congratulations."

Xu Xu Qingzhou sipped his coffee in celebration.

Song Yao lay on the sofa, the novel *The Castle* resting on her stomach, scrolling her phone for travel destinations.

Professor Roberts laughed on the other end: "No, your contribution was huge—you gave me and Hoern inspiration. We're still busy; the celebration will likely be moved to next month."

"I'm glad I could help. I've also learned many interesting things."

Xu Xu Qingzhou replied modestly.

Professor Roberts didn't linger; he got straight to the point: "Xu, how's your progress on the Riemann Hypothesis?"

"All I can say is, we'd all live more comfortably if we didn't study this thing."

Gazing out the window at the Charles River, Xu Xu Qingzhou sighed helplessly: "I think next month I'll need to consider my next topic."

"Hoern and I both agree. We've both spent 'hard times' because of it—even fallen into despair."

"Yes."

They exchanged a few brief words and hung up.

Office.

"He gave up?" Hoern paused his calculations.

Professor Roberts nodded. "Undeniably, he's the most brilliant young mathematician I've ever seen—but the Riemann Hypothesis? I guarantee, even God would be helpless."

"I thought I'd witness the birth of a great proof," Hoern sighed.

"Not solving it now doesn't mean it won't be solved later."

Professor Roberts remained optimistic. Strictly speaking, Xu Xu Qingzhou is only twenty-one—barely the beginning for a mathematician. Infinite possibilities lie ahead.

"Indeed, mathematics seems to be entering an explosion—or a revolution. In recent years, problems that plagued people for decades, even centuries, have been solved one after another."

To be honest, both felt a pang of regret.

The Riemann Hypothesis is like a mountain peak. Countless mathematicians have labored day and night on its slopes; ninety percent could only gaze at the mist-shrouded summit and turn back.

Xu Xu Qingzhou is unquestionably the one most likely to reach the summit.

On the other end, Xu Xu Qingzhou finished his coffee in a few gulps and went to tug at Song Yao's long legs.

"Next month, let's visit the town of Plymouth."

Song Yao was looking up hotels and restaurants in Plymouth; she hooked her foot around his clothes. She'd mentioned it before, but they'd never had time.

Xu Xu Qingzhou nodded: "Sure. Since February, we haven't taken a proper trip."

Having legs to play with wasn't boring at all.

Squeezing her clean, pale feet, he opened Weibo and found many topics related to him.

"Xu Shen, Jianqiao and Princeton both made major breakthroughs. What's your progress?" This was the most-liked Weibo post.

Clearly, everyone was concerned about his progress.

"Xu Shen: Don't ask. Ask again and it's rude."

"Don't get your hopes up. Xu Xu Qingzhou has been busy with the Riemann-Siegel zero problem. He probably hasn't done much direct research on proving the Riemann Hypothesis."

Someone asked: "Isn't the Riemann-Siegel zero problem harder than these two?"

The blogger explained: "Hard to say. Both the Riemann-Siegel zero problem and zero-density estimates are only extensions of the Riemann Hypothesis. I think the former mainly supports its validity; the latter directly proves it."

Song Yao was still researching where to go when she felt her foot lift—she turned to see the man who had just been squeezing her leg now standing before his manuscript, pulling out a sheet and snapping photos.

"What are you doing?"

"Stabilizing morale." Xu Xu Qingzhou returned after taking the photos and began typing again.

Song Yao looked puzzled, curious what he was up to, and leaned over to see he had already composed his Weibo post.

Xu Xu Qingzhou: Hold steady.

Attached was a photo.

The photo contained nothing extra—just a brief formula.

0.48≤re(s)≤0.51

o＞1/15=0.067

By now, Xu Xu Qingzhou had over 2.6 million followers. The moment he posted, comments flooded in.

"Someone explain what this is."

"If I'm not mistaken, this is an estimate of nontrivial zeros. Simply put, the Riemann Hypothesis claims all nontrivial zeros lie on the line re(s)=0.5. If we prove the zero density approaches zero—or equals zero—in regions outside 0.48≤re(s)≤0.51, the Riemann Hypothesis holds."

"Can you make it simpler?"

"Even simpler? —Xu Shen is awesome!"

Someone else explained: "Jianqiao's zero estimate range is 0.45≤re(s)≤0.515; Princeton's is 0.46≤re(s)≤0.512."

"Bro, stop. This stuff's too advanced. I'll just stick to the program—Xu Shen is awesome!"

"o＞1/15=0.067 means Xu Shen is nearly there. The Riemann Hypothesis requires o＞0—this is infinitesimally close."

"But… I follow Xu Shen's arXiv. He hasn't uploaded a paper yet."

"Me neither."

"You're all so technical. Am I the only one here who's just a fanboy?"

"Sis, +1."

(End of Chapter)