At the beginning of the 20th century, Hilbert's speech on the Questions of the Century ushered in a new century-long journey for the Riemann conjecture.
Mathematics was like a small boat that was far away from the eyes of mortals. Because of this, it left behind a magnificent legend in the 20th century.
This century-long journey for the glory of the human mind finally came to an end.
With the attention of almost everyone in the world, this report on the Questions of the Century finally kicked off …
The venue of the report was packed with people.
Even the largest lecture hall in the Corinthia Hotel couldn't accommodate all of the attendees and those who had traveled thousands of miles to attend the conference.
Some people brought chairs from other places, some people sat on the floor, and some people even sat on their suitcases …
Reporters carrying cameras stood in the last row of the venue. There were only two or three cameras there.
In order not to interfere with the report, the ICM conference committee only gave a limited number of media access permits. Because of this, only BBC, CTV, and Columbia Television were present in this lecture hall.
The noise filled the entire venue, almost tearing the ceiling apart.
Almost everyone was talking about the upcoming report and the thesis that Lu Zhou published on arXiv yesterday.
Suddenly, the sound of a door opening came from not far away.
The door close to the podium opened, and a familiar figure walked into the lecture hall.
As if their mouths had been sealed, the entire venue quietened down in an instant.
Pairs of blazing gazes focused on that person at the same time.
Everyone was waiting for him to open his mouth and announce the start of the meeting …
Lu Zhou looked around at the audience and opened his mouth. However, just as he was about to start the sixty-minute report, he suddenly changed his mind when he saw the confused and expectant eyes in the audience. Instead, he spoke.
"I know you guys probably have a lot of questions, including the Riemann conjecture and our future. When I first walked in, I noticed that the guy sitting in the front row was already half out of his chair … I'm guessing he has a lot of questions for me, and he can't wait to ask me. "
There was a burst of laughter in the audience, and the atmosphere relaxed a little.
Lu Zhou looked at the young scholar who was blushing and sat back down. He paused for a second and spoke in a relaxed tone.
"Normally, I should end the nonsense and start the 60-minute report. However, due to the special circumstances, I plan on leaving five minutes before the report begins to answer some of the audience's questions. This way, the audience can focus on the report itself. If you have any questions you want to know before the report begins, you can raise your hand. "
Before he could even finish his sentence, many hands were raised up in the air.
Lu Zhou looked around the front row of the venue and picked a random person.
The Indian guy, who was chosen by Lu Zhou, quickly stood up.
This scholar in his thirties was wearing glasses and had curly hair. He came from the field of artificial intelligence, which was the bottom of the mathematician's disdain chain. He immediately asked a sharp question.
"Has the Riemann conjecture been proven?"
More than half of the audience perked up their ears.
For scholars who weren't in the field of analytic number theory, even though they were also concerned about how Lu Zhou proved the Riemann conjecture and how this set of mathematical methods could affect other disciplines, they were more concerned about whether the Riemann conjecture itself had been proven.
Even if it was just an affirmative statement.
Lu Zhou looked at the crowd and nodded.
"Yes, I can confidently say that from now on, it doesn't matter if you use it as a theorem."
Whispers began to spread in the audience.
Many people had surprised expressions on their faces.
Generally speaking, the more famous a scholar was, the more they cared about their reputation. Unless it was the kind of person who had completely let go of himself, very few people would use such an affirmative tone to claim that they had proven a major mathematical proposition.
After all, if it was a success, it would be fine. If it was a failure, it would not be easy to just say "sorry, I made a mistake".
The reason why Sir Atiyah, who once claimed that he had proven the Riemann conjecture, was frequently rejected in his later years was because he had done nothing "good" in the past ten years. He often claimed that he had proven something but could not explain it. When he claimed that he had proven the Riemann conjecture, even arXiv rejected his manuscript. Therefore, he had to find another way to publish his research results. (Note 1)
Many people were surprised by his courage and confidence. He didn't give himself any leeway at all.
After the Indian guy got the answer he wanted, he sat back down. A mathematics professor from Columbia University stood up.
"What happens after the Riemann conjecture is solved? Where does the field of analytic number theory go? What I mean is … Throughout the 20th century, countless breakthroughs in the field of number theory, including Fermat's last theorem, were more or less obtained from the exploration of the Riemann conjecture. Now that the hen that lays the golden eggs is gone, what should we do in the future? "
Compared to the previous question that could be answered with a yes or no answer, this question was undoubtedly a bit more sophisticated.
Lu Zhou thought for a few seconds and spoke.
"I can answer your question, but I want to put the answer at the end of the report."
Lu Zhou looked at the clock on the wall, cleared his throat, and spoke.
"It's about time. I'll have to trouble those who are still raising their hands to put them down."
"At the end of this report, I will leave enough time to answer all of your questions.
"Now, let's get to the main topic."
Lu Zhou turned around and walked to the whiteboard. He picked up the marker that was placed under the whiteboard.
Then, he wrote the first line of text on it.
[Proof: All non-trivial zeros of the Riemann zeta function are located on the line Re (s) = 1/2 in the complex plane …]
There was no special opening statement.
However, everyone's eyes were focused on the whiteboard.
The report on the proof of the Riemann conjecture …
It has already begun!
In the audience.
Tao Zhexuan, who was sitting next to Professor Fefferman, stared at the line of text on the whiteboard. He suddenly spoke with a hint of excitement.
"He changed the content of the report!"
"Isn't this inevitable?" Professor Fefferman looked at him with a strange expression. He said, "The entire mathematics world is concerned about this matter. Even if he wants to pretend that nothing happened, it's impossible."
Tao Zhexuan said excitedly, "No, until a few minutes ago, I wasn't sure if he was serious, but now it seems that my doubts were unnecessary."
Professor Fefferman opened his mouth and spoke with a helpless expression.
"… If that's what you're thinking, then it's unnecessary. From what I know of him, he would never joke about this kind of thing. "
While the two were talking, Lu Zhou, who was standing on stage, didn't stop at all. The pen in his hand moved quickly, and in less than half a minute, he had written four or five lines.
[ζ (s) = 2Γ (1-s) (2π) s-1sin (πs/2) ζ (1-s) …]
[…]
After the first step, it was the second step.
More and more equations appeared on the whiteboard as he wrote them down. The difficulty gradually changed from being easy to understand to obscure and complicated.
Academician Wang, Zhang Wei, Xu Chengyang, and Yang Yongan were sitting in front of the stage as they looked up at the whiteboard. Their faces were filled with shock.
Yang Yongan was amazed by this series of exquisite and peerless maneuvers. He couldn't help but blurt out a word of praise.
"… So fast!"
Zhang Wei, who was sitting next to him, also had a complicated look on his face.
"Looks like he really wants to finish the entire thesis in 60 minutes."
In fact, before this report, he was prepared that this 60-minute report might be extended.
After all, judging from the content of the thesis on arXiv, it didn't look like it could be explained in 60 minutes. There were many complex logic in the thesis, and even the prover would have to spend a lot of time reviewing it.
But now, it seemed like he was overthinking.
If Lu Zhou kept talking at this speed, he would probably be able to finish the thesis in less than 60 minutes. Forty to fifty minutes was more than enough for this guy …
Xu Chenyang had a complicated look on his face as he said, "Unbelievable … This speed, does he not need to think at all?"
It would be fine if Lu Zhou was just writing the thesis, but he was only holding a pen in his hand.
What was even more incredible was that Lu Zhou would write a short explanation for some of the key steps, explaining why he wrote this step and what this step was for.
It was like …
It was as if the entire proof process had been engraved in his mind, and it was the kind that he understood completely.
Zhang Wei thought for a bit and said, "Maybe he already memorized all of the steps."
Yang Yongan looked at him with a moved expression.
"That … That's ridiculous."
At this moment, Qin Yue, who had been sitting quietly at the side, suddenly interjected.
"It's not ridiculous for the professor."
Whether it was Yang Yongan, Zhang Wei, Xu Chenyang, or Academician Wang, they all looked at Qin Yue.
Qin Yue noticed that they were looking at him, so he paused for a second and spoke.
"From what I know about the professor, he won't deliberately memorize these things."
Academician Wang Shicheng frowned and said, "Then is he really going to do it on the spot?"
"I'm afraid so." Qin Yue nodded and said, "For him, solving a problem that has already been solved is a form of entertainment."
Yeah …
Solving a problem that has already been solved is a form of entertainment …
No wonder Lu Zhou is this strong.
Academician Wang Shicheng and the others were shocked by Qin Yue's words. The two Fields Award winners sitting on the other side of the venue were also stunned by Lu Zhou's series of actions.
"Unbelievable …" Professor Akshay stretched his stiff neck and raised his index finger. He touched the glasses on the bridge of his nose and said, "Introducing differential manifolds to the complex plane … His method completely subverts my understanding of differential geometry and meromorphic functions."
Schulz was sitting next to him with his arms crossed. He smiled and said, "Looks like he's doing very well."
Akshay looked at him and said, "This is a bit … surprising."
Schulz: "What's surprising?"
Akshay stared at the whiteboard and thought for a bit. He then said, "I don't understand how he came up with this. I don't know if you can understand this feeling, it's like a ray of light coming from the sky, but when we look up, we can't see the source. "
Schultz looked at the whiteboard that had been buried. He suddenly smiled and spoke in a somewhat emotional tone.
"It's not surprising, we don't understand. It's just that we don't know how long he has been wandering in front of the maze. He doesn't seem to be willing to share his in-progress results with us before he makes a grand achievement.
"Therefore, I can understand your confusion, my friend. Because those equations are the same for me. They aren't so obscure that I can't understand them, but they still give me a surreal feeling. Just like Mr. Grothendieck's works, almost every scholar in this field has studied the classics that are regarded as the bible of algebraic geometry. But when we try to follow his train of thought, and trace it back to its origin, the conceit is most likely to fail. It's like … "
Schulz paused for a second.
It was like he was looking for an appropriate analogy. He thought for a long time.
At this moment, the full whiteboard on the stage had been dragged to the side by the staff and replaced with a brand new whiteboard.
Lu Zhou stood in front of the whiteboard for a few seconds. He then raised the pen in his hand and continued to write on the whiteboard.
Suddenly, Schulz thought of something.
Almost subconsciously, he blurted out the words that he hadn't finished speaking.
"It's like it came from the void.
"It's like those equations don't belong to this world."
(Note 1: Sir Atiyah publicly complained about this matter during the Q&A session at the Heidelberg report. In fact, it was rare for a scholar like him to be rejected, especially at arXiv, where even private mathematicians were treated with leniency.
A failed proof of a major mathematical proposition was an extremely serious blow to a scholar's academic reputation. The result of consecutive failures was the loss of everyone's trust. Even the Fields Prize and Atiyah's halo would be overshadowed by the impact of academic reputation damage. Thus, the academic world was an extremely realistic place.)
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