Not Impossible!

"Mary, I think we should calm down and have a proper talk. After all, we are a team, and unity is always better than conflict."

"I think so, Shen Qi. My attitude was a bit harsh before, I apologize."

Shen Qi and Mary adjusted their mindsets and chose to compromise in the face of academic challenges, resuming their collaboration on the problem of the Riemann zeta function ζ(2n+1).

One week later.

"Dr. Mary, your analysis of f(s) in the half-plane is incredibly disappointing! Even a typical Mathematics Department student in China wouldn't make such a ridiculous mistake!"

"Shen Qi, leave my office immediately, right now! And let me add, your proposal is absolutely terrible, worse than the first-year students in my tutoring class!"

"Mary, you've lost your mind!"

"Shen Qi, that's exactly what I wanted to say!"

This is the last time I'll be in your office! Goodbye!

Snap!

A loud slam of the door.

The argument continued, with the ambitious young Chinese math prodigy and the proud, stubborn German woman unable to reach an agreement on the details of the research project.

Ha!

Hey!

Ah!

Shen Qi bought a gym membership and started hitting the punching bag like crazy at a gym on campus.

Exhausted from the game, Shen Qi returned to his apartment and began writing his thesis.

As a revolutionary pioneer once said, don't put all your eggs in one basket; if you break one basket, you still have another.

Shen Qi was working on two projects simultaneously; one was abandoned, but the other remains.

The topic of "The Problem of the Riemann zeta function ζ(2n+1)" isn't entirely abandoned, but Shen Qi isn't in the mood to study it right now, so let's put it on hold for a while. German woman, if you're so capable, go ahead and do it on your own; we're on different paths and can't work together.

Shen Qi was free and unrestrained in his solo research on the topic of <using the Orbifold Fundamental Group to characterize Symplectic Orbifold Groupoid>.

"Clearly, ω1=s*ω0 is a symplectic structure on G1, such that s, t:(G1,ω1)→(G0,ω0) are symplectic mappings, and each symplectic group embryo is a Poisson group embryo..."

"Women are unreliable, only math is reliable."

Shen Qi's efficiency in working alone is astonishing; the Orbifold project progressed rapidly as he worked on it all by himself.

"Just to correct you, 'young married woman' is unreliable, 'young and beautiful girl' is reliable, hahaha, mission accomplished!"

Shen Qi and Mary argued for three weeks, but their progress on the <Riemann zeta function ζ(2n+1)> remained unchanged.

He worked alone for a week to complete the first draft of <using the Orbifold Fundamental Group to characterize the Symplectic Orbifold Groupoid>.

"Hey pretty girl, what are you doing?" Shen Qi was in a good mood today, chatting with Ou Ye online.

Ou Ye: "Preparing for the GRE."

Shen Qi: "Your number theory skills should be steadily improving, right? I'll send you a manuscript, take a look."

Ou Ye: "Okay."

After finishing the first draft of <Characterizing the Symplectic Orbifold Groupoid using the Fundamental Group>, Shen Qi had the time and energy to re-engage in the research on <The problem of the Riemann zeta function ζ(2n+1)>, working on it alone.

Based on the series derivation method, Shen Qi wrote a document containing his understanding of the recursive formula of the Riemann zeta function ζ(2n+1) and sent it to Ou Ye.

The most reliable partner is, of course, my girlfriend, and the most considerate little darling is, of course Little Yezi.

Ou Ye wasn't by Shen Qi's side, and the two couldn't always discuss academic issues, their hearts were connected.

Two days later, Ou Ye sent Shen Qi an email with an attachment.

The attachment states. "Qi, in order to obtain an efficient recursive formula for the Riemann zeta function ζ(2n+1), you adopted a series derivation method, which makes sense logically overall."

"However, there is a problem: this line of thinking cannot bypass Ramanujan Formula, and you are obviously using the Hadamard system as a basic framework. How to find a balance between the Hadamard system and the Hardy system is the biggest challenge."

"I haven't done anything else these past two days except calculate a formula, namely, in the Hadamard system, for any positive integer k (0 < t < 2π), there is a recursive formula:"

∫t^2k-1cos2ntdt=1/2(π/4)^2k-1sin..."

"Strangely, no matter how I try to reverse this recursive formula using mathematical induction, I cannot arrive at the conclusion of the initial assumption."

"Perhaps my computational derivation skills are limited, or perhaps... your series derivation method itself has flaws."

"Oh, okay, I must have miscalculated. You couldn't possibly be wrong."

"But I've been so busy lately. I can't afford to mess up the GRE; the pressure is immense. Zhou Yu'an got a very high score on his GRE."

"After you finish the GRE, I'll go all out and systematically calculate and verify your series derivation method for you."

I miss you.

"You must behave well in National First Prize."

Wishing you all the best.

After reading the email from Ou Ye, Shen Qi remained silent for a long time. Little Yezi was much more eloquent in the email than she was in real life.

Most importantly... Little Yezi actually said that my core idea has a flaw?

That shouldn't be possible; how could a young Chinese woman and a German woman have such similar views?

My girlfriend shouldn't be opposing my core ideas!

Ou Ye has never opposed me before; this is the first time.

Has Ou Ye's skill level improved, or has mine declined?

Was I wrong?

Was I really wrong?

Is there a flaw in my logical framework?

No, absolutely not!

I just reached level 10 in math, and all those 750,000 academic points were wasted?

"No, I can't be wrong, I can't possibly make a mistake! Ahhh!"

Shen Qi rushed into the gym and began punching and kicking the sandbag.

Hey!

I'll hit you!

I... I couldn't be wrong!

After finishing his punching, Shen Qi returned to his apartment and secluded himself for three days, revising his work on the problem of the Riemann zeta function ζ(2n+1). Based on the Hadamard system, Shen Qi improved his series derivation method.

"There are no loopholes, there won't be any loopholes. I've calculated it many times, and repeatedly made assumptions and derivations. If we want to ultimately prove the Riemann Hypothesis, this is the only way to set it up."

Shen Qi met with Professor Muller separately, bringing with him two papers.

"Shen Qi, your mental state is very poor. I think you need to rest for a while, and taking a vacation would be necessary," Muller said with some concern.

"I don't have time, I don't have any more time... This semester, I need to get my master's degree, and I need to publish another paper, preferably in Top Four Journals." Shen Qi's eyes were bloodshot, the price of several sleepless nights.

"You really don't need to be so hard on yourself." Muller began reviewing Shen Qi's two papers, "The Problem of the Riemann zeta function ζ(2n+1)" and "Characterizing Symplectic Orbifold Groupoid with the Fundamental Group Orbifold."

"So you went it alone after all, on the problem of the Riemann zeta function ζ(2n+1)." Muller shook his head and sighed. Shen Qi was too individualistic, and sometimes very stubborn.

"Professor Muller, please tell me, is it feasible to derive my recurrence relation for the Riemann zeta function ζ(2n+1) using a series method in the Hadamard system? Yes, I think so; there is no more perfect solution. I have decided to resubmit it to the * Annals of Mathematics *. Of course, this requires your opinion; you are my mentor."