I Wasn't Joking
Shen Qi returned to his apartment and began collaborating on the manuscript.
Based on the Riemann Hypothesis, the "Shen matching method" is used to derive the first expression of ζ(s): ζ(s) = e^A + Bs∏∞n=1(1-s/ρn)(1-s/1-ρn)e^(s/ρn+s/1-ρn).
To derive this expression, Shen Qi, Mary, and Jonas wrote a 27-page paper, with Shen Qi contributing 50% and Mary and Jonas contributing the remaining 50%.
After careful consideration, Shen Qi condensed the 27-page manuscript into 20 pages through more concise descriptions and arguments.
The second expression is: 0 = e^A + Bss∏∞n = 1(s - ρn)(s - 1 + ρn)e^(s/ρn + s/1 - ρn)
To derive the second expression, Shen Qi Faltings Faltings a 10-page paper, with each contributing half.
Shen Qi pondered repeatedly but could not simplify the second expression with a more concise description and argument.
Ten pages is already the most extreme condensation, and Shen Qi didn't change a single symbol. This shows Professor Faltings' skill; after all, he is Fields Medal winner and has been engaged in Mathematical Research for over forty years.
Shen Qi should thank Professor Faltings, Mary, and Jonas, who made significant contributions to this project; otherwise, Shen Qi would not have been able to obtain two core expressions in such a short time.
The significance of obtaining the two core expressions for ζ(s) is that Shen Qi can announce to the world, "My team and I have preliminarily proven the Riemann Hypothesis!"
The premise of both expressions is the "Shen matching method," a novel processing method created by Shen Qi.
Without this novel matching method that is so crucial, the following two expressions would not be possible.
From any perspective, Shen Qi is the soul of the team.
Of course, his team members and technical advisors were also very helpful. Working together, they completed the initial research results on the Riemann Hypothesis.
A math master of level 12 might not be able to solve the Riemann Hypothesis, but with the support of a math master of level 12, a Fields Medal winner, a Princeton University professor, math PhDs and doctoral students, and the entire Princeton University Mathematics Department, the team has achieved certain research results.
Shen Qi originally thought that a preliminary proof of the Riemann Hypothesis would require a lengthy argument, but he didn't expect it to be done in just 30 pages.
Therefore, the most important thing is the thought process, the most reliable thing is logic, and the most valuable thing is imagination. In addition, a little bit of inspiration and luck are also needed.
These 30 pages are very valuable. Shen Qi believes that once they are published, they will have a certain impact on the number theory community and the entire Mathematics Community.
The manuscript was completed by Shen Qi alone, so he was the only one who possessed the complete preliminary proof of the Riemann Hypothesis.
With three days to go before the Breakthrough Prize & New Horizons Prize award ceremony and academic conference, Shen Qi sent the abstract of his paper, "Proof of the Riemann Hypothesis Based on the 'Twin Matching Method'," to the Breakthrough Prize & New Horizons Prize organizing committee.
The abstract, consisting of only a few sentences, essentially states. "I, Shen Qi, and my team have made a preliminary proof of the Riemann Hypothesis using the twin-matching method."
"Shen matching method" is the internal name for "twin matching method". This new processing method has not yet been recognized by colleagues in the Mathematics Community, so it is more intuitive to call it "twin matching method".
The organizing committee was shocked. Their chief technical advisor called Shen Qi immediately, "Mr. Shen, are you kidding me!"
Shen Qi calmly said, "Mr. Jackson, I'm serious, I'm not joking."
"You, Shen Qi, have proven the Riemann Hypothesis?"
"Yes, I, Shen Qi, have proven Riemann Hypothesis, providing a preliminary proof. Due to confidentiality considerations, I can only submit an abstract of the paper to the organizing committee before giving a formal report."
"Do you still need to present 'The Muller -Shen Theorem and Supplementary Approximation Theorem in Banach space' at the conference?"
"I have 45 minutes for my presentation. For the first 20 minutes, I will present 'The Muller -Shen Theorem and its Supplementary Approximation Theorem in Banach space,' and for the remaining 25 minutes, I will present 'A Proof of the Riemann Hypothesis Based on the Twin Matching Method.' Please approve."
"Mr. Shen, I can approve the first 20 minutes now. For the next 25 minutes, I need to confirm with Director Feierman at Princeton."
"No problem, I'll wait for your reply."
Shen Qi had already reported to Director Feierman beforehand that there were no problems within the Mathematics Department of Princeton University.
The organization's attitude is very clear: Shen Qi, go ahead and act all high and mighty; if anything goes wrong, the organization will cover for you.
Ten minutes later, Mr. Jackson from the organizing committee called again, "Mr. Shen, I look forward to your report in the next 25 minutes. See you in three days!"
Muller's office the day before his trip to Washington.
Shen Qi internally released his 30-page document, "Proof of the Riemann Hypothesis Based on the 'Twin Matching Method'," and gave a presentation, which was essentially a rehearsal.
Muller, Mary, and Jonas were seeing the full collaborative manuscript for the first time. They were excited, but also remained rational, with a deeper level of anticipation.
"Qi, with the technical support of Grader and Elon, you, Mary, Jonas have made a preliminary proof of the Riemann Hypothesis using the 'twin matching method' and two core expressions. I am very happy for you."
"But the core problem of the Riemann Hypothesis is that all non-obvious zeros lie on the line Re(s) = 1/2 in the complex plane. These two expressions can support it, but we still need support for support. Do you understand what I mean?" Professor Muller raised the most crucial question, namely, the problem of completely proving the Riemann Hypothesis.
"So we must get a third or even a fourth expression, which will take some time. In any case, we should publish the first two core expressions in a sufficiently simplified form. Yes, we did it. Thanks to Professor Muller, and to Mary and Jonas for their hard work." Shen Qi's idea was to reserve a spot first. His team was the first to use the "twin matching method" to obtain the initial proof of RH, and they owned the original academic copyright.
"I haven't made any substantial contribution, Qi. If you win the New Horizons Prize and receive an invitation to the International Congress of Mathematicians at IMU, you'll have to buy Mary and Jonas a good drink," Professor Muller said.
"Jonas, you've always been the one to treat me to drinks, but this time it's my turn. Whether I win an award or not, this bottle of good wine won't be shortchanged," Shen Qi said to Jonas.
"Oh, it's a deal." Jonas smiled.
"Mary, let's have a drink together, for the Riemann Hypothesis," Shen Qi said to Mary.
"On the condition that your report doesn't flop," Mary accepted the invitation.
The proof of the Riemann Hypothesis based on the 'twin matching method' is no longer just Shen Qi's work; the entire team has devoted all their energy to tackling this difficult problem.
Therefore, the performances in the next few days must succeed; failure is not an option.
The following day, Shen Qi, Jonas, Mary, and Professor Muller dressed in their most formal attire and went to NASA headquarters in Washington., the venue for the Breakthrough Prize meetings and awards ceremonies.
The Breakthrough Prize has a relatively short history, but the prize money is extremely generous.
The award's sponsors include globally renowned entrepreneurs such as Russian billionaire Yuri Milner, Alibaba Group's Jack Ma, Google founder Sergey Brin, Facebook founder Mark Zuckerberg, and Apple chairman Levinson.
The Breakthrough Prize is awarded in three categories: Life Breakthrough Prize, Fundamental Physics, and Breakthrough Prize in Mathematics, with each prize worth up to $3 million.
The $3 million Breakthrough Prize is usually awarded to established scientists. In addition to the $3 million grand prize, there are also the New Horizons Physics Prize and the New Horizons Award for Mathematics, each with a prize of $100,000, awarded to young physicists and mathematicians.
Shen Qi has been shortlisted for the New Horizons Award for Mathematics, and he is expected to win the award and the $100,000 prize.
Before that, Shen Qi needs to give a 45-minute academic presentation to try and win the New Horizons Award and worldwide recognition.