Setting the Crowd Off Again
Shen Qi switched to the fourth page.
It's still all mathematical formulas.
∣logξ(1+it)∣≤logloglog∣t∣+A, logξ(σ+it)<<(log∣t∣)^2-2σ+ε
Shen Qi simultaneously explained the core points, "If the Riemann Hypothesis holds true, then except for s=1, logξ(s) is regular in the half-plane σ>1/2. Therefore, please see the next page."
Page 5, page 6, page 7... all the way to page 20, are all numerical formulas.
The entire room was silent. Some people understood, some didn't, and some only half understood.
Page 21 contains only one formula:
ζ(s)=e^A+Bs∏∞n=1(1-s/ρn)(1-s/1-ρn)e^(s/ρn+s/1-ρn)
"Do you all remember the core expression mentioned in Riemann's manuscript? Riemann once said that his conjecture must be true, and he also made a proof. However, because the expression obtained from the proof was not simplified to a form that could be published, the Riemann Hypothesis has always been the Riemann Hypothesis, not the Riemann Theorem."
Shen Qi paced back and forth on the stage, then suddenly stopped. He glanced back at the big screen and said, "My team and I have finally obtained the legendary expression, which is right here on the screen! So, in the setting of the twin matching method, the nth twin matching pair satisfies Re(ρn) = 1/2. What does this mean? It means that the Riemann Hypothesis is almost a correct proposition."
Wow!
The entire venue erupted in cheers.
The twin matching method and the legendary expression were confirmed, and new shocks kept coming, exciting mathematicians.
"Almost, why almost?" some mathematicians couldn't help but blurt out, asking loudly.
According to normal procedure, there is no Q&A session during the presentation. Otherwise, the constant chatter would affect the efficiency of the presentation, especially since there are other presenters later on.
Q&A sessions are typically held after public presentations, with leading experts in the relevant fields asking questions about the presenter's work, which the presenter then answers.
But Shen Qi's speaker segment was so explosive that the audience almost lost control.
"Please remain calm. My presentation is time-limited, and there are 17 other speakers waiting to present after me," Shen Qi said, gesturing to the room. "If anyone is interested, we can discuss this in detail at the roundtable."
Once order was restored, Shen Qi continued his explanation, "Yes, I used the word 'almost' here. Why not 'certainly'? Because we discovered and confirmed that the expression Riemann described as 'not simplified to the point of being publicly available' is not just one, but a set! I know this is a revolutionary and entirely new concept. Now, please look at the second expression."
"What? There's another expression!" The mathematicians were completely flustered; they had barely calmed down for a minute before they exploded again.
"Please look at the second expression." Shen Qi continued switching between PowerPoint slides.
The second ζ(s) core expression is displayed on the large screen:
0=e^A+Bss∏∞n=1(s-ρn)(s-1+ρn)e^(s/ρn+s/1-ρn)
Brush!
Gong Changwei stood up. He had seen Shen Qi's first expression before and had offered some opinions and suggestions.
The second representation of ζ(s) was something Gong Changwei had never seen before, and the second expression was different from what he had expected.
Although there are some differences, it's absolutely perfect!
Brush!
Maynard stood up, feeling similarly to Gong Changwei, only with a touch more shock and a sense of defeat.
Swish swish swish!
Everyone in the audience stood up, preparing for a momentous historical occasion.
Shen Qi's first expression gently knocked on the door of a new world; his second expression kicked the door open!
"Combining the first expression, we can see that the second expression proves that the result of s traversing to the nth pair of twin matches in the set {non-obvious zeros of the Zeta function } is true. Therefore, the Riemann Hypothesis is a correct proposition. My team and I have proven the Riemann Hypothesis from a qualitative perspective." After the passionate outburst, Shen Qi summarized his report in a calm tone.
Innovative, logically clear, rigorously deduced, with a reasonable framework and impeccable settings... Shen Qi and his team did it! They proved the Riemann Hypothesis!
At least that's how it appears!
Rumble!
A thunderous and sustained round of applause erupted throughout the venue. Mathematicians, the host, organizing committee staff, IMU representatives—everyone stood and applauded, cheering for Shen Qi.
Shen Qi and his team, along with two Fields Medal winners, spent three whole months writing this 32-page report.
Even internationally renowned mathematicians who have never seen this report would find it difficult to fully digest and absorb these incredibly impactful new ideas in such a short period of time.
However, intuitive mathematicians have already deeply felt that Shen Qi's research report is very valuable. From a qualitative perspective, Shen Qi proved the Riemann Hypothesis.
"This is a major breakthrough in the History of Mathematics!"
"Well done, Shen!"
"A remarkable young man!"
The performance was met with rave reviews, and Shen Qi's perfect performance captivated mathematicians from all over the world.
It's a mess, everything's in complete chaos!
Shen Qi earnestly urged, "Everyone, please sit down and remain calm! I have three minutes left to give my report, and I'd like to say a few more words! Thank you for your cooperation!"
"You're not done yet?" The crowd suppressed their excitement and sat down, and order was temporarily restored to normal.
Shen Qi said, "I will later publish the full report, 'Proof of the Riemann Hypothesis Based on the 'Twin Matching Method', on arVix. Everyone is welcome to review it."
"The twin matching method and two core expressions have qualitatively proven the Riemann Hypothesis. Next, my team and I will try to explain the Riemann Hypothesis and the ultimate mystery of prime number distribution from a quantitative perspective and a completely new dimension. I will announce the third expression of ζ(s) at the next international conference, and perhaps a fourth one."
"If everything goes smoothly and our plan progresses as scheduled, it means that the ultimate mystery and laws of the qualitative and quantitative distribution of prime numbers will be solved in a short time— Goldbach Conjecture."
"If the Riemann Hypothesis and Goldbach Conjecture are solved, and the theoretical results are applied to real-world scenarios, then the security systems on Computer Science and the Internet may be redefined."
Shen Qi looked at his colleagues below the stage with a deep and firm gaze. "Theoretically, that's how it is. I'm not good at the specific applications. I studied basic mathematics. Let the applied scientists solve the application problems. I'll be responsible for providing the theoretical support."
"Ladies and gentlemen, I would like to say that the qualitative proof of the Riemann Hypothesis is only the beginning, and we will continue to move forward without stopping. Thank you, that concludes my report!"
Lê Conjecture, Goldbach Conjecture, the ultimate mystery of prime numbers!
Shen Qi still has a backup plan!
The atmosphere reached its highest point since the start of the conference.
Shen Qi became the most dazzling academic star at this year's Breakthrough Prize.
Chinese mathematician Shen Qi has proven the Riemann Hypothesis!
"The Millennium Prize Problem solved, Shen Qi achieves legendary status!"
Western and Eastern media outlets issued breaking news immediately, and Shen Qi's name spread throughout the world.
Meanwhile, the number theory experts hired by IMU were extremely busy.
Media outlets and individual mathematicians acknowledge that Shen Qi's proof of the Riemann Hypothesis is invalid, and the IMU is the final arbiter.
The IMU is verifying Shen Qi's report on the Riemann Hypothesis, and the number theorists, who are in a state of panic, have found it impossible for the IMU to give them a conclusion within a month.
Shen Qi's speech at the conference was relaxed and easygoing, but the report, "Proof of the Riemann Hypothesis Based on the 'Twin Matching Method'," contained a huge amount of information. If you calm down and study it carefully, it is estimated that it will take a month to verify just the first expression.
That evening, the IMU representative in Washington contacted Shen Qi and told him two pieces of news:
First, Shen Qi, your supplementary approximation theorem in Banach space will be officially named "Shen Proximity Theorem" by IMU.
Secondly, at the International Congress of Mathematicians in the second half of the year, Shen Qi, you will soon receive a formal invitation to give a presentation. We hope that your presentation will be about the ultimate mystery of the distribution of prime numbers. This is what you yourself declared this morning. IMU is giving you this opportunity to make a brilliant presentation at the highest-level mathematics congress held every four years.
"Okay, thank you." Shen Qi accepted the verbal invitation from the IMU representative.