Research starts with PhD students

Chapter 186 The gap is too big!
Bill McIver's paper is more than ten pages long, and the argumentation process is relatively complicated.

The most difficult thing to understand is the method used. The main method used is still "two-dimensional continuity versus three-dimensional", but other methods were used in the middle, and other research contents were involved.

When Zhang Shuo first browsed through it, he noticed a special change and found that he could not understand it.

Now, after taking a closer look, I discovered that it’s not just a method I’ve never encountered before, there are three things I don’t understand.

After checking the references, he found out that there were two studies involving Bill McIver himself, both of which were about the methodology of nonlinear partial differential equations. It can be understood that he derived a transformation formula for a type of partial differential equation and then used it directly in the current paper.

The paper also involves another method, which is also a very niche research.

Each of these three methods can be said to be a side door, and they are also very complicated and involve many logical problems.

Zhang Shuo also felt that Bill McQuay is indeed a theoretical expert in the field of partial differential equations. It is amazing to know about similar partial differential method research, and it is even more amazing to be able to apply it in research.

Partial differential equations is a large field, and there are so many related studies. Even if it is just theoretical research or methodological research, you can find a large number of papers and results.

Every paper result has its role. Some methodological research is very clever, but its application is very narrow, which leads to most people not knowing it at all.

Zhang Shuo didn’t know either.

The paper information provided by Luo Yongjun is very complete, and there are also three methodological papers mentioned in the references.

Zhang Shuo took it and looked at it carefully. He needed to understand the derivation process of the method used so that he could understand the proof process more deeply.

As understanding improves, the progress of new tasks is also constantly improving.

When the task progress reached '76%', Zhang Shuo was already working on the third method to be used, which was the research result of the late Japanese mathematician and Gauss Prize winner Kiyoshi Ito.

Then, progress got stuck.

It was only when Zhang Shuo finished reading the third method that he discovered that the task progress was stuck.

The task progress is stuck, which means there is no need to read the paper further, and the subsequent proof process is all wrong. The unknown occurrence of the error is the application of the third method.

Mathematical proofs work like this, if you make a mistake at one step, all of them will go wrong.

There was a problem at one point in the process, and all the subsequent content lost its meaning.

"It seems that this is the problem."

Zhang Shuo thought, "This is a very clever application of the conversion method. It may be that such a conversion cannot be done, or it may conflict with the previous method."

What exactly it is is not clear yet.

He looked at the time and found that he had been concentrating on his research for nearly two hours. He simply stood up, stretched, made himself a cup of coffee, and then lay down in a chair to rest.

Taking advantage of his free time, Zhang Shuo checked his email messages.

After winning the Fields Medal, my original mailbox received a large number of emails every day. Academic exchanges, conference invitations, and work issues were all normal. Some were even emails from advertisers asking about cooperation, some were emails from "fans" to say hello, or some other irrelevant people.

Therefore, you still need an assistant to help screen and transfer important email messages to the new email address.

What Zhang Shuo was checking was the contents of the new mailbox, which were emails that had already been filtered.

Li Liu Shuangyue is very efficient at work. Helping to clean up emails in the morning and afternoon has become her daily routine, but she still receives dozens of emails.

Among them, there are more than a dozen latest emails, all sent by mathematics professors from major universities, and several of them are messages from foreign scholars.

This information can be summarized in two questions:

"Have you read McIver's paper? What do you think of it?"

Zhang Shuo didn't know the specific problem yet, so he didn't give a professional response. He opened Weibo again and found that there were several private messages from people he followed on Weibo, and the content was the same as what he received in the email.

Following people’s private messages is a small matter. Even the original Weibo posts have added a lot of new comments.

He found that his account was also marked with various '@'s, asking him to comment on McQuay's paper or point out problems in the paper.

Many of those who sent the message were scholars in the field of mathematics, including even a mathematics academician.

Zhang Shuo suddenly developed a personal sense of mission, and felt that he had become a righteous hero who "maintained the smoothness of the solution set of the NS equation". He was called upon by the justice camp to stand up and help defeat the "evil" villain, Bill McIver, who dared to prove that the solution set of the NS equation was not smooth.

Zhang Shuo took a deep breath, thought about it, and simply posted a "justice" Weibo, "Bill McIver's proof process is wrong.

This is the problem, we can study it together. "

A picture was added to the Weibo post, which was a screenshot of the location of the problem in the paper.

Bill McQuay's paper had just been introduced to China and there were only a few reports in the media. It attracted little attention and only scholars in the mathematics community were concerned about it.

They learned the news not through public opinion, but through communication with foreign scholars, or by noticing the content of the new issue of "Applied Mathematical Theory".

Although there was no heat in the media, the issue still attracted attention immediately after Zhang Shuo posted the message on Weibo.

Many netizens were confused when they saw Zhang Shuo's Weibo post, and some commented, "What is this? Who is McQuay?"

"I was full of confidence when I finished reading the text, but after looking at the pictures, I discovered a despairing reality. Even if there was a gun pointed at my head, I still couldn't understand what was on it."

"When people are pushed into a corner, they can do anything, except mathematics..."

"This is the legendary heavenly book!"

“Even though the content is right in front of me, I still can’t understand it!”

Some of them were from the mathematics circle and knew what Zhang Shuo was talking about. Some of them were surprised and asked, "Master Zhang Shuo has found the problem?"

"Is there really a problem?"

"My advisor said that McIver's research couldn't be true. I can finally believe him for once!"

"So that's the problem. Ahem... I still don't quite understand."

"That's amazing! You found the problem so quickly, even though I don't understand it..."

It’s normal that you don’t understand.

In public opinion, only a few people could understand it, but it did not prevent netizens from spreading the news, especially those with higher education and access to mathematics circles. Soon many people knew the news.

Tan Youming, who was in the office opposite Zhang Shuo, was having a video chat with Qiu Chengwen, and they were also discussing McQuay's research issues.

Qiu Chengwen said, "I took a general look at the proof process, which involves several uncommon methods, but they are all well-established methods that have been published."

"I talked to several foreign scholars, and they didn't find any problems either."

"What did Zhang Shuo say?"

In the field of partial differential equations, especially the singularity proof of the NS equations, Zhang Shuo is the scholar with the most say in the world.

Tan Youming said, "I just told Zhang Shuo that he is watching it now. I hope he can find the problem."

"Then we have to wait two days?"

Qiu Chengwen nodded and said, "If there is any problem, Zhang Shuo should be able to see it, but the demonstration process is also very complicated, and it is too difficult to find the problem in a short time."

"I also estimate that it will take two or three days." Just as Tan Youming finished speaking, he heard an exclamation from the other side of the video.

"Director Qiu! Director Qiu!"

"Big news!"

"Zhang Shuo posted on Weibo that he had found the problem and also posted a picture."

Professor Zhou Hailiang rushed to Qiu Chengwen's office and told him the news.

Qiu Chengwen was completely confused.

Of course he understood, and that was why he felt confused.

He looked back at the video camera and asked, "Didn't you say Zhang Shuo just found out? How come he has already found out the problem?"

"Uh~~~"

Tan Youming also understood, and for a moment he felt a little confused and couldn't speak for a long time.

Later, he simply left a sentence, "I'll go and take a look!"

After he finished speaking, he left his seat and walked towards the office opposite.

……

In today's world of highly developed information technology, the speed of information transmission is unimaginable.

Zhang Shuo posted a message on Weibo, and just twenty minutes later, the Institute for Advanced Study at Princeton knew about it.

The Institute for Advanced Study at Princeton attached great importance to McIver's research. They formed a temporary partial differential equation research group to study McIver's paper. If the proof process is correct, then it is determined that the NS equation has a singularity in the square channel in the Cartesian coordinate system.

Otherwise, the research can be denied.

The members of the temporary group were very resistant to McIlvay's conclusion, or in other words, more than 90% of scholars engaged in pure mathematical research on partial differential equations believed that the solution set of the NS equations was smooth.

After Zhang Shuo completed the proof of the singularity of the turbulence transition position, this ratio jumped to 99% or even more.

The reason is very direct. If there are no singularities at the turbulence transition positions of the NS equation, how can there be singularities at other positions with low probability?

McIver's conclusion is correct, it feels like a beautiful painting has been splashed with dirty water.

This is totally unacceptable!
The temporary team started working yesterday and gathered together early today. It includes several professors from the Institute for Advanced Study at Princeton and Anton Kapustin, who came especially from the California Institute of Technology.

They gathered together and discussed McIver's proof.

"I didn't find the problem yesterday, and the previous part seems to be correct."

"It makes sense logically. I initially thought the problem was with his method. Both of the conversions were his own research."

"It involves several unconventional methods, which makes the proof process much more complicated. We still have to prove its logical problems step by step."

"That will take a long time, maybe a week? Or even longer."

Edward Hoffman then asked Anton Kapustin, "Have you contacted Zhang Shuo? Have you asked him?"

Kapustin said, "I sent him an email yesterday, but it's still unread. Maybe China just got the news? They are a little later than us. Applied Mathematical Theory is not a journal with a big impact."

What Kapustin meant was that it was unlikely that Zhang Shuo was the first to see the contents of "Applied Mathematical Theory" and it was most likely that he had just learned the news.

Edward Hoffman also nodded and said, "Even if Zhang Shuo knew the news, it would be difficult for him to find the problem immediately. It still depends on our team."

After he finished speaking, he looked at the others and said seriously, "In the field of partial differential equations, I dare say we are the best team in the world."

"McIver's argument is a little complicated, but it's nothing to us."

"One week, get it done!"

"it is good!"

"no problem!"

"Hurry up and get to work!"

Several people were talking, and suddenly someone spoke up in a different voice, "Professor Hoffman, there is something I must say."

"I just received an email from an old friend saying that Zhang Shuo posted a message online confirming that he had found the problem in McQuay's paper."

"right here……"

"The third conversion method, the application location of Ito Kiyoshi's research."

The rest of the group was a little confused.

Edward Hoffman was also stunned. He loudly confirmed, "Are you sure? Zhang Shuo has found the problem and pointed out the location?"

"impossible?"

"There are so many of us, and we studied all day yesterday..."

"And the Chinese side is behind us. Zhang Shuo should have just learned the news."

The others were also a little confused.

Even if Zhang Shuo knew the news earlier, wasn't he discovering the problem too quickly?
With so many of them, can't they catch up with one Zhang Shuo?

……

in the office.

After Zhang Shuo posted the message on Weibo, he didn’t expect it to have such a big impact.

After resting for a while, he continued his research and found that the problem involved logical arguments of several methods.

Simply understand -

a proves b, b proves c, then can a prove c?

This simple logical deduction is certainly feasible, but because the methods involved are very complex, it requires careful consideration whether the logic is smooth.

After thinking for more than ten minutes, Zhang Shuo chose to give up temporarily, because he found that it was better to complete the proof directly than to think about the problem.

He simply spent a coin and continued to study the "argument for singularity in a square channel under Cartesian coordinate system".

The progress had reached '76%' before. After the '氪币' made the direction of the proof clear, I wrote a lot of argumentation content smoothly.

When he encountered the problem again, he chose "氪币" again, and the follow-up became very smooth again. He quickly wrote three pages of arguments.

At this time, Zhang Shuo suddenly began to reflect on himself.

He found that after completing high-difficulty tasks continuously, he did not hesitate to spend money on low-level tasks, as if he was used to high consumption. He did not even think about relatively small expenses and just spent the money directly.

"That's too extravagant!"

"I must be careful to think for myself in the future. I only have one research coin guaranteed every day. I can't do this anymore..."

"Increasing revenue is important, but reducing expenditure is also important..."

When Zhang Shuo was reflecting on himself, the office door was suddenly pushed open.

"Zhang Shuo, Zhang Shuo!"

Tan Youming asked doubtfully, "Have you found the problem?"

"Uh~~~"

Zhang Shuo was stunned for a moment before he reacted, "Did you see the Weibo post I posted?"

Before he could finish his words, several more people came into the office.

Qi Zhixiang, Wang Hui, Su Bingkang, Luo Yongjun, Sun Xingli…

A group of people looked over.

Zhang Shuo pursed his lips tightly and said with a wry smile, "It's already past the end of the workday. Are you all working overtime today?"

"What overtime? I saw your Weibo on the way and came back directly!"

"You found the problem, is it that location?"

"What's the specific problem? Is it the wrong way to use it, or is it a logical problem?"

"Tell me about it!"

Zhang Shuo shook his head and said, "I think there is a problem there, but I'm not sure what the problem is yet."

He said it calmly, but others didn't believe him.

Tan Youming noticed the manuscript paper on the table, picked it up and glanced at it, and asked in surprise, "Are you doing the follow-up argument?"

Wang Hui suddenly reacted and made a summary speech, "So, not only do you know where the problem is, you also continue to make subsequent arguments..."

"It's to prove that there are no singularities in the square channel in the Cartesian coordinate system, right?"

“This… is right…”

Zhang Shuo felt that he couldn't explain it clearly.

"Cattle!"

Wang Hui gave a thumbs up vigorously.

The others followed suit, and their expressions became much more complicated.

McIver's proof was complicated, and it was not easy for them to understand it as a whole.

It took Zhang Shuo more than two hours to not only find the problem in McQuay's research, but also to plan to do follow-up argumentation starting from the location of the problem, and he has already written a lot of content.

This gap is too big!

(End of this chapter)