Scholar's Advanced Technological System

837 Boundary Approach Method! After successfully killing time on the balcony, Lu Zhou left the waiter some cash for the drinks. He then immediately went to the parking lot and got into his black sedan.

“Back to Zhongshan International.”

“Okay.”

Wang Peng, who was in the driver’s seat, nodded and soon began driving.

He talked about the Riemann zeta function with the lady for a long time. Even though, for the most part, he was talking by himself, he was still somehow inspired by the conversation.

Lu Zhou, who was sitting in the back seat, suddenly spoke.

“I need a tool.”

Wang Peng paused for a second.

“… What tool?”

“… Nothing.”

“Do you want to go to the supermarket?”

Lu Zhou shook his head and smiled.

“If only they sold it at the supermarket.”

Wang Peng felt like if he kept on asking, he would be muddled by Lu Zhou’s response. Therefore, he shut his mouth and focused on driving.

Zhongshan International wasn’t far from the Purple Mountain Hotel, and after a ten-minute drive, Lu Zhou was back in his gated neighborhood.

The car stopped at his front door. Lu Zhou told Wang Peng not to come in tomorrow. After that, Lu Zhou walked home and up the stairs.

“It’s not realistic to solve the π(x) function using a general method. There have been thousands of people who have tried to solve this problem in the past. Even though this idea might work, the most obvious pathway must have been attempted before.”

“A novel approach requires a novel tool!”

“I need a new tool!”

The quad-rotor drone flew next to Lu Zhou, following him up the stairs.

Xiao Ai curiously asked Lu Zhou.

[Master?]

“Give me a cup of coffee, instant, send it to the study room.”

[But it’s so late… (°ー°〃)]

“It doesn’t matter, I don’t plan on sleeping tonight.”

[Okay, Master, but please stay healthy.]

Lu Zhou opened his study room door and replied, “Okay!”

Climbing the Riemann hypothesis mountain at once was unrealistic. This mountain had stood in the mathematics world for far too long. Countless people had attempted to challenge it, only to stay at the bottom. Even though there were now signs pointing toward the top of the mountain, there wasn’t a single tool they could use to climb the mountain.

No matter what kind of proof he was going to use, he had to lay a solid foundation.

This way, it would give himself some hope…

Lu Zhou sat down at his desk and threw the pile of used draft papers into the bin. He then took out a new stack of blank draft paper.

Lu Zhou looked at the draft paper on his desk and smirked. He shook his head and muttered to himself, “… This is probably the least expensive project I’ve done this year.”

When he tried to prove Yang-Mills Equations, he requested CERN to conduct several sets of expensive experiments.

For a pure mathematics problem like the Riemann hypothesis, the costs were draft paper and his brainpower…

…

Lu Zhou hadn’t devoted himself to one research project for a long time.

Ever since he became the chief designer of the Lunar Orbit Committee, he had played the role of an academic leader. Rarely did he participate in the forefront of scientific research.

However, Lu Zhou wasn’t out of practice.

When he devoted himself to a mathematics problem, the strings of numbers and Greek symbols flowed through his brain like music.

The rising vapor from his cup of coffee gradually disappeared. The street lights on the asphalt roads went out. The Purple Mountain was pitch black. After a while, Lu Zhou heard the birds chirping outside, and this made him stop writing.

“The new cohomology mathematical tool ‘Étale’ created by Grothendieck while researching Weil’s conjecture made a huge impact on the development of algebraic geometry and the entire mathematical field. That ultimately led to Deligne’s proof of Weil’s conjecture.

“If I want to find a way to climb the mountain, I have to climb the smaller mountain first… A weak Riemann hypothesis.”

When it came to the twin prime conjecture and the Polignac’s conjecture, the latter was contained within the former. Even though the former didn’t lead to a direct proof of the latter, it could inspire one to prove the latter.

That was how the mathematics world was explored.

From proving the weak form of a conjecture, to proving the conjecture, to then proving a stronger form of the conjecture; once all of these were completed, all of the clues became connected, and the tower of mathematics was built.

Lu Zhou wrote down a line of equations on a new piece of draft paper.

[Re(s) = 1-c/ln [ Im(s) +2] (u003e0) …]

Lu Zhou smirked, and his dignified look gradually disappeared.

“If I want to prove that all zeros are distributed on the zero limit line, I should start by excluding areas where zeros do not exist! Re(s)≤0 and Re(s)≥1, as long as I think of a way to enhance this proof to all areas outside the critical line, that is, Re(s)u003c1/2 and Re(s)u003e1/2, I can prove the Riemann hypothesis!

“I’ll start from the right limit!”

This proof method was called the critical zone method! Instead of proving what percent of zeros were on the zero limit line, the proof attempted to shrink the critical zone area containing all zeros, eventually reaching the critical line!

As long as he could prove the right boundary of the critical zone from Re(s) = 1 and the left to Re(s) = 1-ε(ε u003e 0), for all values of epsilon, he could prove the Riemann hypothesis!

He had an idea, and all that was left to do was execution!

His intuition told him that this piece of the puzzle was in the algebraic geometry field! Unfortunately, that was one of his main weaknesses…

“If only I had someone to talk to.”

Lu Zhou shook his head.

Especially Professor Deligne…

Unfortunately, some things couldn’t be explained through email. Video calling might work, but the atmosphere wasn’t the same as talking in person.

It seemed like he could only rely on himself.

“I won’t rely on others.”

Even then, Lu Zhou couldn’t hold back his curiosity. He opened his computer and went on Mathoverflow.

He was soon disappointed.

When he uploaded his thesis on arXiv, he hoped it would help lay the foundation for others. He wanted to see some interesting discussion on Mathoverflow, as that might inspire him.

But now, it seemed like his plan was clearly unsuccessful.

Even though this was supposed to be a professional mathematics discussion community, full of PhDs, most people were more interested in gossip.

Although there were some academically focused discussions, most of them were outdated.

“Looks like I have to retreat for a few days.”

Lu Zhou leaned back on his chair and picked up his phone. He told Wang Peng not to disturb him for a few days. He then yawned and went into his bathroom.

He was hoping to get inspired throughout the night, maybe even produce some in-progress results. However, the situation was much worse than he had thought.

Since he decided to go on a retreat, there was no reason for him to stay awake anymore.

Before he would officially start working, he planned on making up for last night’s sleep…