Disagreement

"In the coming period, I hope that Shen Qi and Mary can concentrate on revising the problem of the Riemann zeta function ζ(2n+1). Solving this problem is of great significance to the Riemann Hypothesis," Muller said. In his mind, Shen Qi was no longer an ordinary graduate student, but an award winner capable of undertaking important academic research projects.

"Okay, I have no problem." Shen Qi nodded.

"I have no problem either." Mary glanced at Shen Qi had clearly become the backbone of the team.

"If..." Jonas, who had been drinking coffee in silence, suddenly spoke up.

The other three looked at Jonas.

Jonas poured himself a cup of coffee and smiled brightly, "I mean, it would be great if I could have another one."

"No, Jonas, that's not what you meant." Shen Qi shook his head. He could clearly sense that Jonas wanted to talk about some academic issues.

Mary had the same feeling. She knew Jonas's level of expertise. She had previously consulted Jonas with the first draft of "The Problem of Riemann zeta function ζ(2n+1)," but Jonas ignored her.

Muller said to Jonas, "Jonas, you published a paper when you were a graduate student. You assumed that the Riemann Hypothesis was true and obtained a corollary for any positive number ε. It was because of this paper that I chose you as my doctoral student."

"Why not just prove Riemann's fifth conjecture directly, instead of wasting time proving the two recurrence formulas of the Riemann zeta function ζ(2n+1)?" Jonas said, at which point he abandoned his detached, Buddhist-like attitude and became serious and earnest.

"All of Riemann's six conjectures are interconnected; we should consider them from a global perspective. The two recursive formulas for the Riemann zeta function ζ(2n+1) are essential, Jonas." Muller disagreed with Jonas on academic matters.

"Okay, perhaps Professor Muller is right, but I stand by my point of view." Jonas is usually quite easygoing and doesn't care about anything, but he is very stubborn when it comes to academic issues.

This was the first time Shen Qi had seen Jonas so serious. Sure enough, Jonas was quite capable; otherwise, he wouldn't have been able to become a PhD student in the Princeton Mathematics Department.

"So Jonas, the topic you've been researching is to directly prove Riemann's fifth conjecture?" Shen Qi asked.

"It's quite a challenging thing, isn't it, Shen Qi?" Jonas stopped arguing and looked at Shen Qi with a smile, hoping to get Shen Qi's support.

"Jonas, I admire your courage, but on the RH issue, I agree with Professor Muller's view: consider the overall picture and proceed step by step." However, Shen Qi is aligned with Professor Muller and Mary on the RH issue.

This disappointed Jonas, who reverted to his Zen-like demeanor, shrugging indifferently and saying, "Why not?"

Riemann published only one paper related to number theory in his lifetime, in which Riemann proposed a total of six conjectures.

It is conjectured that I, III, and IV are infinite products of ζ(s) and ξ(s).

Conjectures II and VI concern properties of non-obvious zeros.

The most far-reaching conjecture is the one about V, which is now known as the Riemann Hypothesis.

Jonas meant that there was no need for preparation, and that Riemann Hypothesis I, II, III, IV, and VI should be disregarded; the attack should proceed directly to the fifth hypothesis, RH.

Beneath this Swede's zen-like exterior lies a wild heart... Shen Qi thought to himself, "Jonas, if you keep playing like this, you might not graduate with your doctorate until you're 60."

On the same problem, Muller's four-person team held two different solutions.

The goal is the same: to ultimately prove RH.

Muller, Shen Qi, and Mary advocated for improvements and innovations based on the Hadamard system, using a conservative and prudent approach to gradually prove RH.

Jonas was clearly a fervent supporter of the Hardy system, and he adopted a radical approach in an attempt to achieve his goals in one step.

History tells us that neither Haddamad and his assistant Sherno, nor Hardy and his assistant Ramanujan, nor any of their top teams, could achieve a final breakthrough against RH.

However, Haddamad and Hardy. Both systems have their advantages and disadvantages, and how to make the most of their strengths and avoid their weaknesses depends on the users.

Jonas finally mustered the courage to work hard and achieve some results, only to discover that he was an outlier; the other three members of his team didn't follow his approach at all.

"I also respect Jonas's point of view. Meeting adjourned. Shen Qi, please stay," Professor Muller said.

Only Muller and Shen Qi remained in Muller's office. Muller said, "At least on the Riemann Hypothesis, we agree with each other."

"Yes, Professor Muller, Hardy and Ramanujan are both geniuses, but I prefer the Hadamard system. We must be cautious about the Riemann Hypothesis, even if it is only a preliminary result." Shen Qi is a pragmatist when it comes to the Riemann Hypothesis. It's best to be conservative until you reach the level of a master in mathematics.

"Now, let's talk about orbifolds, Shen Qi. I understand your question to be similar to the case of Symplectic Manifold ..." Muller shared his views on orbifolds.

"I see, I understand now." Shen Qi talked with Muller for an afternoon and an evening, and practically learned everything the old Muller had ever known.

"Young man, you need to learn to relax, relax!" Muller panted. "Shen Qi, you need girls, yes, young girls. Go, go to the Tiger Inn for a drink, there are all sorts of young girls there, and I'm just a wretched old man."

Shen Qi packed up his materials and said, "Professor Muller, I'm leaving now. I'll come back to ask you another question tomorrow."

"I'm very sorry, but I'm going to Yellowknife tomorrow to chase the aurora with my wife. We'll return to Princeton in a few days." Muller, afraid that Shen Qi wouldn't believe him, took out his plane ticket from the drawer to show Shen Qi. New York to Vancouver, then to Yellowknife—quite a hassle.

"Okay, have fun," Shen Qi said.

Girl, young girl.

When it comes to young women, Shen Qi naturally thinks of Ou Ye.

Ou Ye also missed Shen Qi.

When Shen Qi was around, Ou Ye's body couldn't take it.

Shen Qi is gone, Ou Ye's heart is still with him.

This longing was conveyed to the United States via the internet and international long-distance calls; it was filled with love.

"Little Yezi, you can't stop taking your medicine, remember?"

"Yes, it hasn't stopped."

"But I'm also worried that all medicines have side effects, and long-term medication is never a good thing."

"But... sigh, I didn't want it to be like this either."

"Good people are always blessed; the key is to have a positive attitude towards treatment."

"By the way, the red envelope Uncle Shen gave us was huge!"

"No, no, use the money from the red envelope to buy some good tonics, like snow frog, bird's nest, and shark fin. Don't stop eating them. Dietary therapy is a good method, better than drug treatment."

"Um... We have guests at home, and my dad called me downstairs. We'll talk again tomorrow. Happy New Year's Eve."

"Do you live in an apartment with two floors, a duplex, a villa, or a self-built house? Hey, hey..."

The call to Ou Ye was disconnected. It's the end of January now, and China is celebrating the Chinese New Year.

Shen Qi spent the New Year alone, and a sense of loneliness suddenly arose.

There were no family members, no girls, no couplets, and no firecrackers.

For Shen Qi, mathematics was all he had.

(Ten likes are important, but ten monthly tickets are equally important.)