After successfully killing time on the balcony and leaving two banknotes on the tray of the hotel waiter, Lu Zhou immediately went to the parking lot and sat on the black red flag that had been waiting.

"Back to Zhongshan International."

"Okay."

Wang Peng, who was sitting in the driver's seat, nodded, and quickly started the car and drove onto the road.

Although he had basically been talking to the lady with a long name about the Riemann zeta function before, he didn't even expect that this kind of discussion about the cow playing the piano would also give him some inspiration.

Sitting in the back seat of the car, Lu Zhou, who had been silent for a long time, suddenly burst out with a sentence.

"I'm missing a tool."

Wang Peng, who was holding the steering wheel, was slightly stunned.

“…… What tool? ”

"Nothing."

"Need a trip to the supermarket?"

Lu Zhou smiled and shook his head.

"It would be nice if the supermarket had one for sale."

Feeling that if he was allowed to continue, he was afraid that he would be in a state of confusion for the rest of the way, considering that he was still driving, so Wang Peng wisely closed his mouth and stopped talking, focusing on the road ahead.

The location of the Purple Mountain Hotel is not far from Zhongshan International, but after a dozen minutes' drive, Lu Zhou soon saw the familiar gate of the community.

The car stopped at the door of the house, and after explaining that he would not be used to find himself tomorrow, Lu Zhou went straight back to his home and walked quickly to the stairs.

"It's not realistic to solve the π(x) function in a general way, and there are 1,000 people who have challenged this problem in the past century and a half, if not 10,000, but even if this idea works, the traditional approach must have been considered."

"Disruptive outcomes often require disruptive approaches to solve."

"I need new tools!"

The quadcopter drone whined and floated beside it, and staggered up to the second floor with Lu Zhou.

Unable to recognize the command contained in Lu Zhou's self-talk, Xiao Ai, who was following behind, asked curiously.

"Master?" 【(•̀∀•́)】

"Make me a cup of coffee, if it is instant, just send it to the study."

"But it's so late......" [(°ー°〃)]

"It's okay, I don't have any plans to sleep tonight."

"Okay master, but please be sure to pay attention to your body." 【(=ﾟωﾟ)】

Stretching out his hand and pushing open the door of the study, Lu Zhou only threw down three words and walked in quickly.

"Got it!"

It is unrealistic to climb the Riemann conjecture at once, this Everest has stood at the top of the mathematical world for too long, and countless people have tried to challenge it, but most of the time it is at the foot of the mountain, so that latecomers can find a large number of road signs to the top of the mountain, but there is not even a staircase to draw on.

Regardless of which proof method is used, the original road must be repaired before it can lead to the top of the mountain.

At the very least, he had to see the hope of proof......

A fart. Gu sat down at the desk, crumpled all the scratch papers piled up in the corner of the table and threw them into the paper basket, Lu Zhou took out a new stack of scratch papers and piled them on the table.

Looking at the paper basket that had been stuffed, and the pile of scratch paper on the table that was about to be filled, the corners of Lu Zhou's mouth suddenly hooked up a smile, and he shook his head and said to himself.

“…… It's probably the most cost-effective project I've done in years. ”

Even when it came to proving the Young Mills equation, he wrote to borrow CERN's equipment to do several sets of experiments in theoretical physics, and spent a lot of money.

But for a purely mathematical problem like the Riemann conjecture, I am afraid that all that will be consumed is scratch paper and brain cells......

……

For Lu Zhou, it seems that it was a long time ago to devote himself to the study of a topic.

Since he became the chief designer of the Lunar Orbit Construction Committee, he has played more of an academic leader's role, and rarely charged at the forefront of scientific research like an ordinary scientific research dog.

However, even so, that familiar feeling was not unfamiliar to Lu Zhou.

Especially when he is fully engaged in the problems on paper, the strings of Arabic numerals and ancient Greek symbols that flow from the tip of his pen are like the notes of classical music, merging cheerful rhythms with serious rhythms to form a silent but soul-stirring symphony.

The rising fog from the coffee cup gradually dissipated, the street lights on the side of the asphalt path gradually went out, and the Purple Mountain under the night was quiet.

"In the study of the Wey conjecture, including the 'copycat' Riemann conjecture, the new mathematical tool Étale cohomology method created by Grothendieck has had a great impact on the development of algebraic geometry and the entire field of mathematics, and finally led directly to the proof of the Wey conjecture by Deligne."

"If you want to find your way to the top, you have to take the nearest mountain...... The weak conjecture of the Riemann conjecture. ”

Just like the relationship between the twin prime conjecture and the Polliniac conjecture, the latter is a relation implicit in the former, and although the proof of the former cannot directly lead to the proof of the latter, it can have an enlightening effect on the proof of the latter.

This is the case with exploration in the field of mathematics.

From a weak form of a conjecture to a conjecture itself, and a strong conjecture that is being generalized to the conjecture itself, when all the problems are solved, when all the clues are connected, a mathematical edifice is also built.

Thinking of this, Lu Zhou pushed aside the scratch paper that was full of writing and wrote a line of equations on the paper.

【Re(s)=1-c/ln[|Im(s)|+2](＞0)……】

The corners of his mouth gradually hooked up a smile, and the solemnity between Lu Zhou's eyebrows also dissipated a lot.

"To prove that all zeros are distributed over a zero boundary, you can start by excluding areas where there are no zeros! Re(s≤0 and Re(s)≥1 are known results, as long as we find a way to push this conclusion to all regions outside the critical line, i.e. Re(s)1/2! The Riemann conjecture can be proved! ”

"I can start with the right border first!"

This line of proof is also known as the critical zone method! Different from proving that the percentage of zeros is located on the zero boundary, by narrowing the area of the critical zone containing all the zero points, and finally approaching the position of the critical line, this is the core of the whole proof idea!

As long as he can translate the right boundary of the critical zone from Re(s)=1 to the left to Re(s)=1-ε(ε>0), so as to eliminate the region of Re(s)≥1-ε, no matter how small the value of this ε is, it can play a huge role in promoting the proof of the Riemann hypothesis!

The idea is already there, now it's all left to solve the problem!

Although it was only a subtle intuition, this intuition told him that this piece of the puzzle was most likely in algebraic geometry! Unfortunately, this is also one of the areas where he is least productive......

"If only there was someone to talk to."

However, as soon as this idea came to mind, Lu Zhou immediately shook his head.

Professor Deligne, in particular......

Unfortunately, some things can't be explained in an email, and video calls may be a way to do it, but neither the mood nor the feel is as good for academic communication as the teatime at Princeton.

At present, he can only rely on himself.

"You can't rely on others."

However, having said that, in the end, Lu Zhou still couldn't resist the curiosity in his heart, opened the computer and logged in to the Mathoverflow page, searching for recent topics.

Soon, however, there was a palpable disappointment on his face.

Having previously hung that paper on Arxiv, he was hoping to be able to spark some interesting ideas by sparking a discussion on Mathoverfolw.

But now it seems that his idea has clearly failed.

Even the more professional math discussion community is the most frequent haunt of PHDs, and people are naturally more interested in gossip than solving specific problems.

While there have been some discussions focused on the academic field, the content of these discussions is somewhat "outdated".

"Looks like we're going to have to go into retreat for a few days."

Stretching and leaning back on the chair, Lu Zhou picked up his mobile phone from the table, sent a text message to Wang Peng, and after telling him not to look for himself for a few days, he got up with a yawn and went downstairs to the bathroom.

At first, he was counting on the evening to be able to grasp something with that glimmer of inspiration, and even to get a phased result, but unfortunately, the situation was much more serious than he imagined, at least not with a little inspiration and a night of time.

Now that we have decided to retreat, there is no need to fight for that overnight effort.

Before starting his official work, he plans to make up for the sleep he didn't sleep yesterday......