How Could You See the Rainbow Without Weathering the Storm?

"It's very regrettable, Shen Qi. I believe that submitting this paper on the recursive formula of the Riemann zeta function ζ(2n+1) to the <Annals of Mathematics> will only result in another rejection," Professor Muller said with a solemn expression.

"Professor Muller, the mathematical techniques I used in this paper are superior to those in the one where I proved the Wash Conjecture."

"If you insist on submitting to the * Annals of Mathematics *, I have no objection. If the * Annals of Mathematics * accepts your paper, I will pay the publication fee for you. Good luck," Professor Muller said.

"Then what about the details, Professor Muller? What are the details? Where exactly did I go wrong?"

"Theoretically, ζ(2n+1) can be expressed as the sum of rational multiples of π^2n-1 and two fast-converging series. Yes, I agree with your series derivation, but I don't see what I'm looking for. Shen Qi, recalculate the uniform convergence; perhaps you'll find your real problem."

"Okay, I will calculate and verify again. Professor Muller, what about my paper on the orbifold topic?"

"I'll keep this orbifold paper with me for now. I need to study it carefully, so I can't give my evaluation at the moment."

Professor Muller rejected one of Shen Qi's papers, while the other requires further research.

Shen Qi spent a week proofreading the problem of the Riemann zeta function ζ(2n+1).

He felt like throwing up. Just seeing the name Riemann and the formulas and speculations related to it made Shen Qi want to vomit.

Vomit!

Wow!

Shen Qi couldn't help but vomit.

Pickled cucumbers, leafy greens, and other Yezi were mixed together, and it looked quite fresh.

"Damn Riemann."

Shen Qi muttered as he cleaned up the vomit on the floor.

Professor Muller has consistently disagreed with Shen Qi's paper on the Riemann zeta function ζ(2n+1), which uses series derivation to obtain the recurrence formula. On the same issue, Professor Muller has now sided with Mary.

There is also good news: Muller agrees with Shen Qi's arguments in his paper on Orbifold.

Shen Qi insisted that his understanding of the Riemann Hypothesis was correct.

"Riemann made me vomit, so I have to get an explanation from him."

While the world is drunk, I alone am sober. With his last bit of stubbornness, Shen Qi resubmitted his unilaterally revised paper, "The Problem of the Riemann zeta function ζ(2n+1)," to the "Annals of Mathematics."

Shen Qi was the only author, and he bore the entire burden alone.

Shen Qi submitted his paper, "Characterizing Symplectic Orbifold Groupoid with Orbifold Fundamental Group," to the Journal of Mathematics, a Swedish-sponsored journal and one of the Top Four Journals in China.

After arriving at Princeton, Shen Qi submitted papers to three of the Top Four Journals. Among them Proof of Diophantine Equation Wash Conjecture was published in the Journal of the American Mathematical Society. It was this paper that made Shen Qi stand out in the Chinese and American Mathematics Community.

The Annals of Mathematics has already rejected Shen Qi once.

Shen Qi has never had any dealings with the Journal of Mathematics.

Of the Top Four Journals, only the German-sponsored "Inventiones Mathematicae" remains Shen Qi doesn't have a good idea for writing another high-quality paper to submit to "Inventiones Mathematicae" yet.

During the period of waiting for the review of the "Annals of Mathematics" and "Journal of Mathematics", Shen Qi concentrated on studying the Riemann Hypothesis. He consulted a vast amount of literature, from Riemann himself to Haddamard, from Hardy to Ramanujan, and even the papers and academic monographs of living experts.

Hilbert once said, "If I were resurrected a hundred years from now, the first question I would ask myself upon opening my eyes would be, 'Has the Riemann Hypothesis been solved?'"

Hua Luogeng's teacher, the British mathematical master Hardy, devoted his life to proving the Riemann Hypothesis. Hardy was a man who dared to fight against God, but he still failed to defeat Riemann.

Hardy said on his deathbed that his biggest regret in life was not being able to prove the Riemann Hypothesis.

Hua Luogeng was also a master of Analytic Number Theory. He and Ramanujan were fellow students, both studying under Hardy at Cambridge University.

Hua Luogeng made outstanding contributions to the distribution of prime numbers and Goldbach Conjecture's conjecture, and Chen Jingrun was his prized student.

At the Millennium Conference in 1900, Hilbert made a famous prediction. "I am most concerned with three mathematical problems: the Riemann Hypothesis, Fermat's Last Theorem, and the α^β Conjecture. The Riemann Hypothesis is expected to be solved within fifty years, Fermat's Last Theorem within eighty years. But the α^β Conjecture is forever beyond the capabilities of mathematicians; it cannot be solved."

Contrary to Hilbert 'Alliance Leader predictions, the α^β conjecture was proved by T. Schneider in 1934, Fermat's Last Theorem was proved by Andrew Wiles in 1995, and the Riemann Hypothesis remains unproven.

What is the magic and value of the Riemann Hypothesis that has captivated so many mathematical masters for over a century?

The Mathematics Community generally believes that, starting from the Riemann Hypothesis, many interesting conclusions have been proven, which are not contradictory and are far superior to the proven unconditional results.

More importantly, some of the inferences were later unconditionally proven, thus the results obtained from the Riemann Hypothesis pointed the way for research on this problem. This is precisely the important value of the Riemann Hypothesis.

During the time he devoted himself to studying the Riemann Hypothesis, Shen Qi experienced nausea, loss of appetite, dizziness, and a disrupted biological clock from time to time.

"If RH holds true, then when 1/2 ≤ δ ≤ 2, we have... Ugh, wow!"

Shen Qi vomited again.

After cleaning the apartment floor, Shen Qi placed the trash can beside him and continued to study the problem of logζ(s) on the positive side of the half-plane δ>1/2, where s=1 is its logarithmic pivot.

"Wow!"

This time, Shen Qi didn't vomit on the floor; he vomited it all into the trash can.

"If I can't prove the Riemann Hypothesis, then I will... I will...!"

Shen Qi was blinded by rage, focusing on just one problem each day, yet he could never find the crucial breakthrough.

Anyone would be disgusted.

A month and a half after submitting his paper, "The Problem of the Riemann zeta function ζ(2n+1)," to the Annals of Mathematics again, Shen Qi suffered an even worse blow.

"Mr. Shen Qi, regarding the topic of <The Problem of the Riemann zeta function ζ(2n+1)>, we hope you have fully considered the essence of the problem before submitting your manuscript to us. This is the second time; we don't want to see a third. Thank you, and best of luck."

This is the email reply from the editor of the Annals of Mathematics; this time, even the reviewers' comments were not attached.

Wow!

Wow!

Shen Qi rushed into the bathroom and vomited violently into the toilet until there was no food left to vomit, only acidic fluid flowing out.

Shen Qi believed that his paper, "The Problem of Riemann zeta function ζ(2n+1)," could not be wrong. This paper was recognized by peer experts and played a very important role in laying the groundwork for his subsequent complete proof of the Riemann Hypothesis.

However, the reality was harsh. Even the experts didn't approve of Shen Qi's preparations, let alone a real confrontation with RH.

Shen Qi is ill and bedridden.

He had never been this sick before.

I recommend a book: <The Attacking Salty Fish Girl>