After spending some time on the balcony, the banquet ended. Lu Zhou left two bills on the hotel waiter's tray and immediately went to the parking lot. He then sat in the black sedan that had been waiting for him.
"Back to Zhongshan International."
"Okay."
Wang Peng, who was sitting in the driver's seat, nodded. He quickly started the car and drove onto the road.
Even though he was talking to the lady with the long name about the Riemann zeta function, he didn't expect this kind of discussion to give him some inspiration.
Lu Zhou, who was sitting in the back seat of the car, suddenly spoke.
"I'm still missing a tool."
Wang Peng, who was holding the steering wheel, paused for a second.
"… What tool?"
"Nothing."
"Do you need to go to the supermarket?"
Lu Zhou smiled and shook his head.
"It would be great if the supermarket sells it."
Wang Peng had a hunch that if he continued to talk, he would be in a state of confusion for the rest of the journey. Considering that he was still driving, Wang Peng wisely shut his mouth and focused on the road in front of him.
The Purple Mountain Hotel wasn't far from Zhongshan International. It only took a ten-minute drive for Lu Zhou to see the familiar neighborhood gate.
The car stopped in front of his house. After Lu Zhou told Lu Zhou not to come find him tomorrow, he went straight home and quickly walked to the stairs.
"It's not realistic to solve the π (x) function using a normal method. Over the past century and a half, there have been thousands of people who have challenged this problem. Even if this idea is feasible, traditional methods must have been considered.
"Subversive results often require subversive methods to solve."
"I need a new tool!"
The quad-rotor drone floated next to him and followed Lu Zhou to the second floor.
Xiao Ai, who was following behind him, asked curiously because she couldn't understand the order contained in Lu Zhou's muttering.
"Master?" [(• ∀ • • ́)]
"Make me a cup of coffee, make it instant. Bring it to the study room."
"But it's already so late …" [(° ー ° 〃)]
"It's okay, I don't plan on sleeping tonight."
"Yes, Master, but please take care of your health." [(= ω ω ω)]
Lu Zhou reached out and pushed open the door of the study room. He then quickly walked in.
"Okay!"
It was unrealistic to climb the Riemann conjecture in one go. Mount Everest had been at the top of the mathematics world for a long time. Countless people had tried to climb it, but most of the time, they were stuck at the foot of the mountain. Although people could find a lot of road signs pointing to the top, they didn't even have a ladder.
Regardless of the proof idea, he had to fix the initial road before he could reach the top.
At the very least, he had to give himself a chance to prove it …
Lu Zhou sat in front of his desk and crushed all the draft papers in the corner of the desk. He then took out a new stack of draft papers and stacked them on the desk.
Lu Zhou looked at the already full wastepaper basket and the pile of draft papers on the table. He suddenly smirked and shook his head as he spoke to himself.
"… This is probably the most cost-effective project I've done in years."
Even when he was proving the Yang-Mills equations, he borrowed CERN's equipment to do several sets of theoretical physics experiments, which cost a lot of money.
However, pure mathematics problems like Riemann's conjecture only cost him draft papers and brain cells …
…
For Lu Zhou, it seemed like a long time ago that he had devoted himself to a research project.
Ever since he became the chief designer of the Lunar Orbit Committee, he had played the role of an academic leader. He rarely fought on the frontlines of scientific research like a normal scientist.
However, even so, the familiar feeling was not unfamiliar to Lu Zhou.
Especially when he was fully immersed in the problem on the paper, the strings of Arabic numerals and ancient Greek symbols that flowed from the tip of his pen were like the notes of classical music, combining the cheerful rhythm and serious rhythm into a silent but soul-stirring symphony.
The steam rising from the coffee cup gradually dissipated, and the street lights on the asphalt road gradually went out. The Purple Mountain was quiet at night. After a while, the light of dawn gradually appeared outside the window. Lu Zhou seemed to have been disturbed by the crisp chirping of the birds. He gently put down the pen in his hand and began to speak softly.
"In the research of Weil's conjecture, including the 'fake version' of Riemann's conjecture, Grothendieck created a new mathematical tool, the étale cohomology method, which had a huge impact on the development of algebraic geometry and even the entire mathematics field. In the end, it directly led to Deligné's proof of Weil's conjecture.
"If you want to find a way to the top of the mountain, you have to first conquer the nearest mountain … Weak conjecture of Riemann's conjecture."
Just like the relationship between the twin prime conjecture and Polignac's conjecture, the latter was related to the former. Even though proving the former did not directly lead to proving the latter, it could still play a role in proving the latter.
Exploration in the field of mathematics was like this.
From the weak form of a conjecture to the conjecture itself, and then to the strong conjecture itself. When all the problems were solved, when all the clues were connected, a mathematical edifice was also built.
Lu Zhou pushed aside the draft paper and wrote a line of calculations on the paper.
[Re (s) = 1-c/ln [| Im (s) | + 2] (> 0) …]
A smile gradually appeared on the corner of Lu Zhou's mouth, and the gloominess between his eyebrows also dissipated a lot.
"If I want to prove that the zero points are all distributed on the zero boundary, I can first start by eliminating the areas where zero points do not exist! Re (s) ≤ 0 and Re (s) ≥ 1 are known results. I just have to find a way to push this conclusion to all areas outside the critical line, which is Re (s) 1/2! Then I can prove Riemann's conjecture!
"I can start from the right boundary first!"
This proof idea was also known as the critical zone method! Unlike proving what percentage of the zero points were on the zero boundary, by constantly shrinking the critical zone that contained all the zero points, he would finally approach the critical line position. This was the core of the entire proof idea!
As long as he could translate the right boundary of the critical zone from Re (s) = 1 to Re (s) = 1-ε (ε > 0), thus eliminating the area where Re (s) ≥ 1-ε, no matter how small the value of ε was, it would play a huge role in the proof of Riemann's conjecture!
Now that he had the idea, all he had to do was solve this problem!
Although it was just an intuition, this intuition told him that this piece of the puzzle was likely in algebraic geometry! Unfortunately, this was also the field that he was not good at …
"If only I had someone to talk to."
However, the moment Lu Zhou thought about this, he immediately shook his head.
Especially Professor Deligné …
Unfortunately, some things couldn't be explained in an email. A video call might be one way, but it definitely couldn't compare to afternoon tea at Princeton.
So far, he could only rely on himself.
"I can't rely on others."
However, in the end, Lu Zhou couldn't help but be curious. He turned on his computer and logged into Mathoverflow to search for recent topics.
However, soon after, he showed an obvious look of disappointment on his face.
When he posted his thesis on arXiv, he hoped that it would be able to spark discussions on Mathoverflow. He wanted to see some interesting ideas.
However, it seemed like his hopes were obviously dashed.
Even in a relatively professional mathematics discussion community, the most popular ones were PhD students. People were more interested in gossip than solving specific problems.
Although some of the discussions were focused on the academic field, the content of these discussions was a bit "outdated".
"Looks like I have to go on a retreat for a few days."
Lu Zhou stretched his back and leaned back in his chair. He picked up his phone from the table and sent a text message to Wang Peng. After telling him not to look for him for a few days, he yawned, got up, and went to the bathroom.
At first, he was hoping that he could grasp something with that little bit of inspiration at night, or even complete an in-progress result. Unfortunately, the situation was much more serious than he imagined. At least, it was not something that could be done with a little bit of inspiration and a night's time.
Now that he had decided to go on a retreat, there was no need to waste time.
Before he started work, he planned on making up for the sleep he didn't get yesterday …
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