Chapter 291 Proving the Riemann Hypothesis, Global Argumentation [Subscription Request]

Facts have proved that Xu Yuan's judgment on mathematics was not wrong. According to new ideas and mathematical branch methods, the subsequent proof of the Riemann hypothesis progressed very smoothly.

There was not even a bottleneck along the way.

All I can say is that choosing the right direction is equivalent to walking on a flat road.

Just go directly to the end point.

Otherwise, faced with rugged and muddy roads, and even traps, no matter how long it takes, you will only end up with bruises all over your body.

For this reason, Xu Yuan specifically handed over other work and concentrated on proving the Riemann hypothesis.

I want to complete the entire proof process as quickly as possible in one go.

that's it.

Half a year passed in the blink of an eye.

When it came to June, the panel progress bar successfully grew to more than 90%.

The speed is astonishing.

The assistance of Tian Zhen and others was also indispensable in this process.

Otherwise, if he had completed the entire process by himself, even if the result would not have changed, the timing would definitely not have been as early as it is now, and the proof would have been completed in less than a year.

2020 6 Month 15 Day.

on Tuesday.

It has been just one week since the college entrance examination ended. For high school students, now is the most comfortable and relaxing period.

Even colleges and universities have entered the graduation season.

It was at this time that the Academy of Mathematics and Systems Science, where the editorial board of the Journal of Mathematics was located, declared a formal curfew and prohibited any entry or exit.

It is no exaggeration to say that even Ma Zhiming, the editor-in-chief of the Journal of Mathematics, actively abides by it.

A temporary office was set up on the next floor.

As for why such a big move was suddenly made, it is naturally related to the Riemann hypothesis.

After half a year of intensive research by the research team, it can be said that Xu Yuan’s derivation of the entire process of proving the Riemann hypothesis has only a few steps left, except for the final key conclusion of the argument.

After discussion and decision, everyone agreed to directly launch an offensive.

The entire research team gathered in the room to conduct closed-door research until the entire proof process was completed.

Although it is normal to go without rest for two days after fully devoting yourself to it, it is obviously worth it compared to thoroughly proving the Riemann hypothesis.

Directly controlling the entire building where the research team is located can also prevent others from disturbing their thinking.

Simply because of the significance of the Riemann hypothesis, any concession is justified.

-

"I won't say much about the pre-war mobilization. Anyway, soon the whole world will cheer for what we did today."

"The problem that has troubled countless mathematicians for more than a hundred years will become a theorem in our hands today."

"Let's get started now."

In the spacious conference room, there are many writing boards and manuscripts piled on the desks.

Xu Yuan was dressed simply, facing Tian Zhen and other members of the research team, with a smile on his face and speaking confidently, as if he had already predicted the outcome of what they were doing.

If you continue to look further, you will find that there is water, instant noodles and other food piled up in the corner.

It seems that he will not leave in the next two days.

at the same time.

Tian Zhen and the other four people had excited expressions on their faces.

All I have to do is pick up a pen and write down these four words.

Can't wait.

I still remember when Xu Yuan just announced that he was going to study the Riemann hypothesis and formed a research team for the first time, they basically signed up to participate in order to study mathematics topics with Xu Yuan. They didn't think too much about whether they could prove the Riemann hypothesis.

After all, the Riemann hypothesis is so famous.

But they never expected that under Xu Yuan's leadership, they would actually reach this point.

In the past six months or so, they have all been involved in research on the proof of the Riemann hypothesis.

Although I mainly calculated the relevant formulas after decomposition, I was always amazed by the methods proposed by Xu Yuan.

I have a deep understanding of the gap between myself and Xu Yuan.

You know, as a mathematics professor, it is a rare thing for them to discover new things in the familiar field of mathematics. If they continue to maintain the same state as before, I am afraid that their own mathematics level will be difficult to improve.

Therefore, in addition to being grateful for being a member of the team, they also believed that Xu Yuan's method would definitely prove the Riemann hypothesis.

"It's Dean Xu."

Taking a deep breath, everyone shouted in unison, then immediately returned to their seats and started calculating.

Everyone has been assigned the work to be done.

simply put.

It is responsible for calculating some steps in the proof process, and then converging them to Xu Yuan to complete the final conclusion argumentation, so that Xu Yuan can focus on important nodes.

No need to spend extra time on these calculations.

Of course, the pressure on Tian Zhen and the other five people was much greater than that on Xu Yuan.

After all, if there are errors in numerical calculations, the conclusions may be biased.

All of them will need to be checked at that time.

But pressure can also be a motivation. Being a member of the team that proves the Riemann hypothesis is an honor that every mathematician wants most.

soon.

In the spacious office, Xu Yuan and six other people became extremely focused.

The only sound left in the room was the rustling sound of the pen tip scratching across the draft paper.

As time passed, there were more and more steps to prove the Riemann hypothesis, and Xu Yuan felt completely relaxed because he suddenly noticed that the progress bar on the panel was rising and it was just one step away from reaching 100%.

……

When people are extremely focused on doing something, they don't notice how time is passing quickly.

The only thing on their minds was to complete the proof.

However, compared to the research team who were immersed in solving the calculations, Ma Zhiming outside was very nervous.

Especially when more than twenty hours passed and it was the morning of the next day.

Seeing that still no one came out of the building, it would be a lie to say that I wasn't worried at all.

"Why hasn't anyone come out yet? It's not good for your health if you don't rest for such a long time."

Downstairs in the headquarters building of the Journal of Mathematics, Ma Zhiming was looking at the entrance to the hall which was cordoned off, pacing back and forth in an anxious state.

There was no way to calm down.

Of course he knew the difficulty of proving the Riemann hypothesis, and he even believed that Xu Yuan could complete the proof, but he didn't need to stay up all night to do it. If Xu Yuan's health really had problems because of this, it would be a huge loss for the country.

Proving the Riemann hypothesis is certainly helpful to the development of mathematics, but its importance cannot be compared with Xu Yuan.

"Don't worry, editor."

"Academician Xu is very measured in his actions, so nothing will go wrong."

"Someone should be coming out soon."

"Why don't we go in and take a look to see what's going on?"

"That's absolutely not possible. If it disrupts the team members' train of thought, the loss will be huge."

……

The editorial board members around were also busy at this time and gave their opinions to Ma Zhiming one after another.

Some people think that they should trust Xu Yuan unconditionally, and as long as he doesn't come out, they should wait patiently and not disturb him.

Others were worried about Xu Yuan's health and suggested sending someone into the building to check on the situation. However, as soon as this suggestion was made, Ma Zhiming immediately shook his head and rejected it.

Ideas and inspiration are very important to mathematical research. Right now, all team members are immersed in solving difficult problems. If there is a sudden noise at this time, it is very likely to interrupt their original train of thought.

It will be difficult to pick it up again.

This will result in a disconnection and an inability to perfectly connect with the previous steps.

Besides, the reason they chose to close the entire building was to create a good environment for Xu Yuan and others to answer questions.

If we send someone in to check the situation at this time, wouldn't it be unnecessary to block the building?

After listening to what everyone around him said, Ma Zhiming finally decided to wait for a while.

"Then let's wait and see."

But even though he said that, his eyes kept looking towards the entrance of the hall.

And I made up my mind silently.

If Xu Yuan doesn't come out in the afternoon, he will go in and call him out even if it will interrupt the research team members' thinking.

This was also the request he specifically raised at the previous meeting.

After all, even if the Riemann hypothesis was proved a little later, it wouldn’t matter much.

Xu Yuan’s health is the most important thing.

The weather in June was already quite hot, but none of the editorial board members of the Journal of Mathematics chose to go back to the temporary office, and they all continued to sit downstairs and wait patiently.

I want to be the first to witness the proof of the world's most difficult mathematical problem.

Later, as the sun gradually rose higher, the people in the yard simply built a few simple awnings.

Xu Yuan didn't know that Ma Zhiming and others were waiting downstairs. At this moment, he and Tian Zhen and others had not rested for the whole day, but their spirits were still high.

Perhaps in the state of deep learning, efficiency has not decreased.

The black pen in his hand wrote mathematical symbols on the writing board, and the speed was getting faster and faster.

Finally, after writing the last symbol of the formula, he suddenly stopped writing.

At the same time, the corners of his mouth slightly raised, revealing a smile.

"Finally... it's done."

As he muttered softly to himself, his eyes fell on the progress bar on the virtual panel in front of him.

-

Task: Proof of the Riemann hypothesis

Subject: Mathematics

Progress: 100%
Result: Completed
Throughout the proof process, he used methods from multiple branches of mathematics and combined them to produce a new proof tool.

Even the content of quantum mechanics in physics is included.

Now the progress bar has reached 100% success, which means that his proof of the Riemann hypothesis was successful.

What had just been written on the writing board was the proof of the Riemann hypothesis.

And not afraid of anyone's arguments.

Just like the proof of the Goldbach conjecture and the Hodge conjecture in the past, no matter who wants to overturn his conclusion, in the end they will find that this is the most correct proof process and conclusion. At this time, Tian Zhen and other members of the research team also noticed Xu Yuan's pause.

Then, as if they had thought of something, they all stood up and looked towards Xu Yuan.

Strong emotions kept welling up in my heart.

It seemed like it would explode in the next second.

After swallowing nervously, Tian Zhen was the first to unable to hold back and ask tentatively.

"Xu Yuan."

"We...are we successful?"

Hearing this, Xu Yuan turned around with a smile on his face, and finally nodded heavily in response to the expectations of several people.

"Yes."

"We have completed the entire proof of the Riemann hypothesis."

Almost at the moment Xu Yuan finished speaking, Tian Zhen and others stopped suppressing their emotions and immediately cheered excitedly, hugged and high-fived each other, making a deafening sound.

"Did you hear that? We succeeded."

"We have completed the entire proof of the Riemann hypothesis!"

"All the hard work during this period has not been in vain."

Xu Yuan watched everyone's performance in front of him. Although it was not the first time for him to prove a world mathematical problem, and it was difficult for him to have a big fluctuation in his mentality like them, he was still excited. After all, the time spent this time was really too little compared to the previous successful proof of the Hodge conjecture.

The cheers lasted for more than a minute until Tian Zhen and the others calmed down a little.

Only then did Xu Yuan begin to explain what happened next.

"Everyone must be very tired after not having a rest for such a long time. Let's go back and have a good sleep to replenish our energy."

"We will reverse the proof tomorrow."

Because of the existence of the panel progress bar, Xu Yuan was able to come up with the most correct proof process in one go.

But in actual situations, a lot of deductive reasoning is still needed in the proof process.

Make sure there are no loopholes or even errors in it.

Otherwise, if it is published directly, once it is found by other people, the conclusion of the entire paper will be overturned.

All previous efforts were wasted.

Moreover, because of these incidents, this paper proving the Riemann hypothesis, a world-wide mathematical problem, will surely attract worldwide attention. I wonder how many mathematicians will derive and prove it by then.

Therefore, we must ensure that there are no problems before we officially release it globally.

After hearing what Xu Yuan said, Tian Zhen did not answer immediately. Instead, he moved his lips and looked embarrassed.

After a slight hesitation, he spoke:

"Dean Xu, we want to conduct a demonstration first."

As the words fell, the other four people beside him nodded.

After hearing this, Xu Yuan didn't know what to say. However, judging from his current excitement, he might not be able to fall asleep smoothly even if he went back.

When it comes to proving the conclusion of the Riemann hypothesis, we can use computer-assisted verification.

In addition, the institute can also call upon the supercomputer of the Academy of Sciences, so it won’t take too long.

Unless you repeat the verification multiple times.

With this thought in mind, Xu Yuan no longer hesitated and finally agreed.

"That's fine."

"But I feel unwell and need to rest immediately."

"Don't worry, President Xu. We understand." When Tian Zhen heard that Xu Yuan had agreed to this, he immediately made the assurance with a smile on his face.

Although the others did not respond, their nodding like chicks pecking at rice made the problem clear.

But it is worth mentioning that although Xu Yuan agreed that they could verify it, he would not choose to stay.

After all, he hadn't slept for such a long time, so he did feel sleepy.

Besides, he was confident enough in his proof process and didn't need to wait for the verification results.

After explaining things to Tian Zhen and the others, he pretended to walk towards the door of the conference room and prepare to leave. However, as soon as he pushed open the door of the conference room, a lot of familiar figures suddenly appeared in his field of vision.

After noticing the familiar Ma Zhiming in front of the crowd, Xu Yuan subconsciously called out.

"Ma Yuan, what are you doing?"

"What happened to Xu Yuan just now? We suddenly heard a loud noise, so we hurried up to take a look." Ma Zhiming said a little embarrassedly: "Is it the proof of the Riemann hypothesis..."

They were originally sitting comfortably downstairs. Although the weather was hot, it was not unbearable.

Just as I was thinking about when to go in and ask Xu Yuan to stop, I suddenly heard a loud noise coming from upstairs.

This scared them and they thought there was an emergency.

So without thinking too much, he immediately went into the building and went straight to the meeting room where the research team was.

After hearing what Ma Zhiming said, Xu Yuan looked at everyone's expressions and basically guessed the cause and effect.

Therefore, he didn't keep the secret any longer and nodded immediately to tell everyone the good news.

"We have just completed the entire proof of the Riemann hypothesis."

Even though it was just a short sentence, and it was even spoken in a light tone, but in the hearts of Ma Zhiming and other editors, it was as exciting as a blockbuster bomb.

Everyone present came from the field of mathematics, and they were all very clear about the value of this news.

My heart was almost instantly filled with joy and excitement.

"Great."

"This is definitely the greatest miracle in the history of mathematics."

"It is unimaginable that the proof of the Riemann hypothesis can be completed so quickly."

"Then should we announce this news to the academic community as soon as possible?"

“In this academic competition, overseas countries are destined to lose.”

They talked to each other excitedly, and although they had not proved it themselves, they were equally proud of it.

It was Ma Zhiming who calmed down first. He temporarily suppressed the excitement and joy in his heart, looked at Xu Yuan again and asked something.

"What do you think about announcing this to the academic community?"

"Now Oda and his team are verifying it. Let's wait until the verification results come out. Then we will hold a press conference on the Riemann hypothesis in the name of the Journal of Mathematics and the Mathematical Council."

Xu Yuan thought for a moment and replied, "At the press conference, the entire proof process will be published to the academic community."

So many things happened around the Riemann hypothesis, and it was finally proved in such a short time, so we certainly can't just publish it in the Journal of Mathematics and be done with it.

If you are not high-profile at this time, when will you be high-profile?

He just wanted to let everyone know that the world's top mathematical problem, which had been unresolved for more than a hundred years, had been completely proven and solved by them.

At the same time, he was telling all mathematicians that his proof process was not afraid of verification at all.

Even if all mathematicians in the world were to verify this paper that proves the Riemann hypothesis, it would be impossible to find logical loopholes to disprove it.

Ma Zhi naturally would not question Xu Yuan's decision, and gave an affirmative answer immediately after listening.

"no problem."

"Then do as you say, and we'll start preparing."

He said this without hiding the smile on his face.

From the time when Xu Yuan proved the Hodge conjecture and became a world-class mathematics master, to today when the domestic mathematics community finally had another major event.

Let the whole world know the huge potential of the domestic mathematics community.

Another thing worth being happy about is Tian Zhen and others who participated in proving the Riemann hypothesis.

I believe that after the proof paper is officially published, their names will soon spread in the academic community, allowing the country to have more top mathematicians.

After briefly discussing these things with Ma Zhiming, Xu Yuan decided not to waste any more time.

He immediately said goodbye to the others and left.

Although my energy was not affected by maintaining a deep learning state for a long time, I still feel very tired now that I have come out of the deep learning state.

He needs to go back and get some sleep.

Ma Zhiming was eager for Xu Yuan to go to rest quickly, and even urged him a few more times.

Soon when Xu Yuan's figure disappeared from sight, everyone couldn't wait to walk into the conference room to appreciate Xu Yuan's proof of the Riemann hypothesis.

What countless mathematicians have dreamed of seeing for more than a hundred years is now presented before them.

This feeling cannot be described in words.

I just felt my breathing quicken, as if my entire soul was immersed in those formulas.

……

the following few days.

After having a good rest and replenishing his energy, Xu Yuan still comes to the School of Mathematics and Systems Science on time every day.

Although there was no need to study the Riemann hypothesis anymore, the verification of the paper was not yet complete, so he took time out to work with Tian Zhen and others.

After all, if the verification is completed earlier, the press conference on the Riemann hypothesis can be held earlier.

It is worth mentioning that if it is just a one-time verification, it does not take much time at all.

However, in order to ensure that there are no errors or loopholes in the entire proof process, we can only use various verification methods to continuously prove it, so that other mathematicians will not find any doubts.

Finally, it was late June.

Although the outside world was still calm and there was no big news, the domestic mathematics community was surrounded by great joy.

"This is the result of our verification in recent times. With the help of supercomputers, after massive verification, it is proven that the conclusion of the Riemann hypothesis is valid."

"I think we can now publicly announce that the Riemann hypothesis has been formally and completely proved."

That morning, at the meeting of the School of Mathematics and Systems Science, Tian Zhen, as a representative, reported to those present the verification results of the proof process of the Riemann hypothesis during this period.

Although everyone knew the news, it was still exciting to hear it in this kind of occasion.

Suddenly there was warm applause in the conference room.

After the noise gradually died down, Ma Zhiming motioned for Tian Zhen to sit down, then turned to Xu Yuan and said:
"The journal and the board of directors have been ready in the past few days. Now that we have the verification results of the paper, should we hold a press conference?"

"You guys can make the arrangements, Dean Ma." Xu Yuan responded with a smile.

"You are the protagonist of this press conference. Since you have no objection, let's schedule it for three days later."

Ma Zhiming also smiled and finished talking to Xu Yuan. Then he confirmed the specific time for the press conference on the Riemann hypothesis.

And on the same day, the Journal of Mathematics and the Domestic Mathematics Council announced this matter at the same time.

As soon as this news came out, people both at home and abroad started discussing it.

It is hard to guess why the Journal of Mathematics suddenly held a press conference at this time and dropped such a bombshell on the academic community.

……

(End of this chapter)