In the early twentieth century, Hilbert’s speech on Riemann’s hypothesis began a new century-long journey on Riemann’s hypothesis.
And the small boat that was mathematics, had now become a giant battleship.
At last, this century-long journey of exploring the limit of the human mind had finally come to an end.
Capturing the attention of everyone in the world, this report that answered the age-old proposition finally began.
The report venue was packed with people.
Even the largest lecture hall in the Corinthia hotel couldn’t accommodate all of the conference attendees, as well as people who traveled from thousands of miles away.
People brought in chairs, some sat on the floor, and others even sat on their suitcases…
The reporters were standing in the last row, and there were only a couple of cameras.
In order to prevent the report from being disturbed, the ICM conference organizing committee only granted limited press access. Therefore, only major media outlets such as BBC, CTV, and Columbia Television had their reporters inside the lecture hall.
The venue was chaotically noisy.
Almost everyone was talking about the report and the thesis Lu Zhou uploaded on arXiv yesterday.
Suddenly, there was a sound of a door opening.
The door near the stage opened, and everyone watched as a figure steadily walked into the lecture hall.
Everyone spontaneously became quiet.
Everyone was looking at the man.
They were all waiting for him to begin the report…
Lu Zhou was about to begin his sixty-minute report, but when he looked at the crowd, he changed his mind.
“I know you guys probably have a lot of questions about Riemann’s hypothesis. When I first walked in, I noticed someone sitting in the front row resisting the urge to stand up… I’m sure he has a lot of questions.”
The crowd chuckled, easing the tension in the air.
Lu Zhou looked at the blushing young man in the front row and spoke.
“I’m supposed to begin this report, but due to its special nature, I plan on using the first five minutes to answer some of the audience’s questions, to make it easier to understand the report. If you guys have any questions you want to ask before the report begins, you can raise your hand.”
Before he could finish speaking, numerous hands went up in the air.
Lu Zhou looked around and pointed at someone.
The Indian guy sitting in the front row stood up.
This scholar was in his thirties, and he wore a pair of glasses and had curly hair. He came from a field that mathematicians looked down upon—artificial intelligence. He immediately asked a question.
“Is Riemann’s hypothesis proven?”
Everyone in the audience began to listen intently.
Even though the scholars outside of the field of analytic number theory were also concerned with the method Lu Zhou used to prove Riemann’s hypothesis and how his tools could affect other mathematics branches, they were more concerned with whether or not the hypothesis was proven at all.
They wanted to hear it from Lu Zhou himself.
With everyone staring at him, Lu Zhou nodded.
“Yes, I am confident that from today onward, it has become a theorem.”
There was a commotion in the audience.
Most people looked surprised.
Generally speaking, the more famous the scholar was, the more they cared about their reputation. A famous scholar wouldn’t claim to have proven a famous mathematics proposition unless they were 100% certain.
After all, if they were wrong, their reputation could be ruined.
The late Sir Atiyah, who once claimed to have proven Riemann’s hypothesis, had his thesis frequently rejected in his later years. Mainly because he often claimed to have proven things without giving an explanation. Even arXiv refused his proof of Riemann’s hypothesis.
This meant that Lu Zhou had no way to back out of this, so people were surprised by his courage and confidence.
The Indian guy sat down. His question was followed by a mathematics professor from Columbia University.
“What happens now? What happens to the field of analytic number theory? I mean… Throughout the twentieth century, we’ve made countless breakthroughs in the field of number theory, including Fermat’s last theorem. Many of these tools stem from research on Riemann’s hypothesis. Now that Riemann’s hypothesis has been proven, what does this mean for the future of the number theory field?”
This question was much more complex than the previous question.
Lu Zhou pondered for about five seconds and spoke.
“I can answer your question, but I’ll do it at the end of the report.”
Lu Zhou looked at the clock on the wall and cleared his throat.
“It’s time to begin, leave your questions at the end.
“I promise to answer all of them.
“Let’s get straight to the point.”
Lu Zhou turned toward the whiteboard and picked up a marker.
Then, he wrote down a line of text—
[Proof: All non-trivial zeros of the Riemann zeta function are located on the line of Re(s) = 1/2 on the complex plane…]
He didn’t make any special opening remarks.
However, everyone watched the whiteboard intently.
The report on Riemann’s hypothesis…
Had officially begun!
In the audience.
Tao Zhexuan, who was sitting next to Professor Fefferman, stared at the line of text on the whiteboard. He suddenly exclaimed, “He’s changing his report content!”
“Of course!” Professor Fefferman looked at him strangely and said, “The entire mathematics world is concerned about this matter, he can’t just pretend like nothing has happened.”
Tao Zhexuan said excitedly, “No, until a few minutes ago, I wasn’t sure if he’s going to talk about it.”
Professor Fefferman opened his mouth and spoke.
“… Your worries were superfluous. From what I know about him, he wouldn’t joke about this kind of thing.”
While the two were speaking, Lu Zhou continued to write; his pen danced on the whiteboard as he wrote down lines of equations.
[ζ(s)=2Γ(1-s)(2π)s-1sin(πs/2)ζ(1-s)…]
[…]
After he proved the first lemma, he began proving the next.
More and more calculations began to occupy the board. The concepts gradually became more and more complicated.
Academician Wang, Zhang Wei, Xu Chengyang, and Yang Yongan were all shocked.
Yang Yongan was amazed by the speed of Lu Zhou’s writing, and he couldn’t help but exclaim, “So fast!”
Zhang Wei, who was sitting next to him, said, “Looks like he really plans on finishing the entire paper within sixty minutes.”
In fact, everyone thought that this report would have to be extended.
After all, judging from the paper on arXiv, 60 minutes wasn’t enough time to explain the entire paper. There were too many complicated lemmas and corollaries.
But now it seemed otherwise.
If Lu Zhou continued to write at this kind of speed, it would take him around 40 minutes to finish explaining the entire thesis.
Xu Chengyang said, “Incredible… Does he not have to think at all?”
Lu Zhou didn’t even have a copy of the thesis in his hand.
What was incredible was that Lu Zhou even wrote down a brief explanation on certain steps, explaining why he wrote down this equation and how it was related to the problem.
It felt like…
Lu Zhou had memorized the entire proof.
Zhang Wei said, “Maybe he’s remembered all of the steps.”
Yang Yongan looked at him.
“That is… ridiculous.”
Qin Yue, who hadn’t spoken yet, suddenly said something, “It’s not ridiculous for him at all.”
Academician Wang, Yang Yongan, and Zhang Wei all looked at Qin Yue.
Qin Yue paused for a second and continued, “From what I know, he doesn’t have to remember the steps at all.”
Academician Wang Shicheng frowned and said, “So he’s proving it on the spot?”
“I’m afraid so.” Qin Yue nodded and said, “For him, solving a problem he already once solved is a piece of cake.”
Jesus Christ…
That means once he learns something, he’ll never forget it…
No wonder this guy is the best mathematician of our time.
The two other Fields Medalists sitting in the crowd were also shocked by Lu Zhou’s presentation.
“I can’t believe this…” Professor Akshay rubbed his nose and said, “By introducing a differentiable manifold into the complex plane… The method he used is completely beyond my understanding of differential geometry.”
Schultz, who was sitting next to him, said, “He’s doing a good job.”
Akshay said, “This is… surprising.”
Schultz: “Why?”
Akshay stared at the ceiling and said, “I don’t know how he thought of this. I don’t know if you feel this way, but it feels like a light is shining down from heaven, guiding the way for us.”
Schultz stared at the ceiling as well and chuckled.
“There’s nothing strange about this. We have no idea how long he’s been stuck in this maze. It seemed like he wasn’t going to be satisfied with sharing his in-progress results at this conference.
“So, I know what you mean. Because I feel the same way about those formulas, they are so obscure and difficult to understand. Just like how Grothendieck’s works have become the bible of algebraic geometry. But when we try to copy Grothendieck’s thought process, it’s like…”
Schultz paused for a second.
He was looking for an appropriate analogy.
Meanwhile, the first whiteboard on stage had already been fully written. A hotel staff member dragged another whiteboard on stage.
Lu Zhou picked up the marker and began writing again.
Schultz finally thought of it.
He spoke.
“It’s like they come from another universe…
“Like those equations don’t belong in this universe.”
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