Research starts with PhD students

Chapter 187 It is never weapons that destroy humanity!
On the west side of the ETH Zurich, there is a three-story building full of classical style.

The entrance is decorated with Baroque bas-reliefs and ancient Roman columns, making it look full of historical vicissitudes.

This is the teaching building for the mathematics major.

In a classroom on the first floor, Bill McIver was giving a lecture to students.

Bill McIver is already in his fifties. He is also a tenured professor at the university. He is personally very famous and has trained many outstanding doctoral and master's students.

There is never a shortage of students in his class, and many students from other majors come to attend his classes specifically.

This is even more true now.

In recent days, the international mathematics community has been talking about Bill McIlroy's name because the paper he published proved the existence of singularities in the NS equation, which also negated the smoothness of the solution set of the NS equation.

This was strongly opposed by a large number of mathematicians.

Even within the Swiss Federal Institute of Technology, many mathematics professors believed that Bill McIlroy's research was wrong.

“But my research is fine.”

Bill McIver was also talking about this issue. He was very confident and taught his students that "science is about daring to question and dare to break the rules."

"At the International Congress of Mathematicians in August, Zhang Shuo demonstrated the singularity of the turbulent position and proved that the Nastok equations do not have singularities at that position. After that, almost everyone believed that the Nastok equations were smooth."

"But this is uncertain. The absence of a singularity in one location does not mean that it does not exist in other locations."

"That's why the Clay Institute didn't consider awarding the $100 million. Proving the location of turbulence doesn't tell the whole story."

Bill McIver spoke confidently for a few sentences and then talked about the importance of partial differential equation theory. "In the research direction of complex equations, theoretical research is more important."

"Partial differential equations is a subject that requires a lot of accumulation. It is very funny that many young people know very few methods but hope to complete various major research projects."

"Because most of the difficult research cannot be solved by existing methods, if we only use basic knowledge to do difficult research, the future development prospects will be very limited."

He did not mention Zhang Shuo's name, but in fact, even the students who were listening to the lecture felt as if he was implying Zhang Shuo.

Zhang Shuo is one of the young people who has completed major research in the field of partial differential equations.

Bill McIver did not talk about Zhang Shuo directly because he knew it would cause controversy. Zhang Shuo had just won the Fields Award and had done a lot of important research in partial differential equations and computational mathematics.

At the same time, Zhang Shuo is also an idol in the academic field, and many young scholars admire him.

In the field of partial differential equations research, Bill McIver's views are not an exception. In fact, there are many scholars who have been engaged in the research of partial differential equations for a long time and feel surprised, incredible and incomprehensible that Zhang Shuo has frequently completed major research.

They don't like this kind of success either.

After conducting research for a long time, they believe that partial differential equations is an accumulative discipline and that various large-scale studies require small breakthroughs rather than completing the research directly.

Kiyoshi Ito, Gauss Prize winner, is such a master in the field of partial differential equations who has won international recognition.

He devoted his entire life to the study of partial differential equations, achieved many results over decades, and made outstanding contributions to the improvement of the theory of partial differential equations.

Many scholars in the field of deviation fractional equations consider Ito Kiyoshi to be a "standard figure".

Zhang Shuo, it’s hard to understand.

Zhang Shuo has completed several research projects, but they still insist that partial differential equations is a subject that requires accumulation rather than completing major research directly.

That doesn't really solve the big problems either.

For example, the NS equations, the Monge-Ampere equations, and if we expand the scope to include the Yang-Mills equations, the Einstein equations, etc., each is a partial differential equation.

Many scholars have studied these famous equations and have contributed a large number of papers.

But, is the problem solved?
Many so-called results are of little significance. Until now, no equation has been fully demonstrated.

Bill McIver made some digressions and also talked about the importance of partial equation theory, and then returned to the topic of the class.

At this moment, a boy suddenly raised his hand.

McIver looked over in confusion, "Jeff, what's wrong?"

The student named Jeff stood up and said, "Professor McIver, I think there is something I must tell you."

"Just now, the Institute for Advanced Study at Princeton released a message pointing out the problems in your paper."

"My thesis?" McIver was confused for a moment.

Jeff affirmed, "The singularity argument for the square channel in Cartesian coordinates."

McIver finally reacted.

He stood there for a long time with a frown on his face, then waved to the students, "This class ends here."

"Sorry, I need to go check it out."

After he said that, he hurried out of the classroom without even bothering to pack his things.

……

The level of the team temporarily formed by the Princeton Institute for Advanced Study is still very high.

After learning that Zhang Shuo pointed out the problem, they immediately conducted targeted research. Because everyone was very familiar with the argumentation process, after studying and discussing together, they found the problem in just one morning.

The logic is imperfect!
It's just as expected.

The transformation method studied by Ito Kiyoshi and the method used by McQuay were applied to the same equation transformation, which resulted in logical duplication and made the final proof logic incomplete.

This is not a direct error, but rather a demonstration that not all possibilities are covered.

Mathematical proofs require rigor and the logic must be 100% perfect.

In the message released by the Princeton Institute for Advanced Study, in addition to pointing out the problems in the paper, the work process was also introduced and Zhang Shuo's name was mentioned.

"We learned the proof position pointed out by Professor Zhang Shuo, and worked together to find the problem."

“Thank you, Professor Zhang Shuo!”

"The following is the list of members of this temporary team..."

The news released by the Institute for Advanced Study at Princeton quickly spread throughout the entire mathematics community.

Many scholars are paying attention to McQuay's research and are also discussing whether the solution set of the NS equation is smooth.

This is a problem with a very big impact.

If there is a singularity in the square channel in the Cartesian coordinate system, it is very likely that there are singularities in many other locations. Then the NS equation will no longer be reliable and will also affect many applications.

Related reports soon appeared in China, mainly because the issue involved Zhang Shuo.

Some media contacted Zhang Shuo's Weibo post and finally got the facts correct.

"Zhang Shuo found the problem early on, and he publicly posted on Weibo to point out the problem."

"The Institute for Advanced Study at Princeton learned about the news and did some research, so it was Zhang Shuo who discovered the problem..."

After the media sorted out the matter, they immediately reported it extensively, which also caused widespread discussion in the public opinion: "In the field of NS equations, Zhang Shuo is still more authoritative."

"Zhang Shuo is the real expert!" "A bunch of top mathematicians at the Institute for Advanced Study in Princeton are not as good as Zhang Shuo alone..."

Zhang Shuo also paid attention to public opinion in his spare time. He was impressed by the efficiency of the Princeton Institute for Advanced Study and could only smile bitterly at the misunderstanding of public opinion.

Now it can't be explained clearly.

In fact, he only knew the location of the problem but did not find out what the specific problem was because he felt that finding the problem was too troublesome and it would be better to continue with follow-up research.

If it can be proved that there are no singularities in the square channel under the Cartesian coordinate system, it will naturally show that McIver's conclusion is wrong.

Zhang Shuo continued to do his research patiently and stayed in the office the whole morning of the next day. By the afternoon, the task progress finally reached 100%.

One reason the research was completed so quickly was that McIver's paper contributed most of the progress.

In addition, research is also my own professional field. I have done singularity certification of turbulent positions, and then studied the flow directions in square channels under the Cartesian coordinate system. They are almost the same.

Of course, there are still some areas that require careful consideration, but with the added means of "氪币", there are no obstacles to the research process.

When submitting the task, the system also defaults to Bill McIver as the first contributor.

If it were someone else, Zhang Shuo would definitely share the results with the other person, after all, the other person contributed most of the research progress.

That's impossible now.

Even if he wanted to share his results with McQuay, the other party would not accept it.

That's simply humiliating!

After completing the research, Zhang Shuo thought about it and simply posted the subsequent proof on the Internet and sent a link on Weibo.

The subsequent proof does not contain much content, only more than six pages. With so much discussion in the public opinion and the attention of the international mathematics community, there is no need to submit it for publication.

Zhang Shuo simply posted the subsequent evidence on the Internet.

He didn't care at all.

Others do not see it this way. Proving the singularity problem of the NS equation at a certain position is definitely the most advanced achievement in the field of partial differential equations.

If we include the debate surrounding McQuay's study, the attention it has received is even greater.

Subsequently, a large number of media reported on this, and many scholars also came forward to explain the level and importance of the results.

At the very least, you can submit your paper to one of the four major mathematics journals!
The results of the four major mathematics journals were directly and carelessly posted on the Internet? It is indeed possible to publish them later, but the situation is different between publishing directly and posting them on the Internet.

The professors at the Institute for Advanced Study fell silent when they heard the news. They felt they were not qualified to say anything because the gap was too big.

Even if they work on a research project for several years, it is still difficult for them to publish a paper in one of the four major journals.

Zhang Shuo quickly completed the important research and nonchalantly posted the proof process on the Internet, showing an attitude of complete indifference.

In the office on the first floor, Wang Hui said with emotion, "We are in the same building, colleagues, and we are very familiar with each other."

“But it feels like we’re not in the same world at all!”

……

Zhang Shuo really didn't care about the research. It only took him more than a day to complete it, and it was just a singularity proof for a small location.

This can't even bring about a significant improvement in the progress of the "NS Equation Singularity Proof" task.

After posting the subsequent proof process on the Internet, he stopped paying attention to it and returned to the "theoretical research of strong splitting."

The task progress has exceeded 90%, and it will be completed with some more research.

This is the most important.

In the process of continuous research, time passed quickly. A week seemed to have passed quickly, and the task progress exceeded 99%, which was very close to completion.

At noon, Zhang Shuo did not go to have lunch, but continued to stay in the office.

At one o'clock, Li Liu Shuangyue came over with a lunch box and saw Zhang Shuo sitting at his desk with complicated eyes. She walked over and asked with concern, "What's wrong with you?"

Zhang Shuo glanced at Li Liu Shuangyue and forced a smile, "Nothing."

"You seem to be worried."

Li Liu Shuangyue continued to ask, "Did you encounter any problems?"

"No, it's already been done."

"Oh~~~"

Li Liu Shuangyue was still a little puzzled. She didn't ask too many questions, but opened the lunch box and put it on the table, then pulled Zhang Shuo over to eat. "No matter what, let's fill our stomachs first."

Zhang Shuo sat down on the sofa and exhaled softly, "Thank you."

Li Liu Shuangyue smiled with two dimples and sat next to Zhang Shuo, "Senior, I'm your assistant, why are you thanking me?"

Zhang Shuo took a few bites of food, then raised his head and asked a question, "Yueyue, have you seen science fiction movies? There are some high-tech weapons in them, for example, super-dimensional weapons, which can turn three-dimensional space-time into two-dimensional space, destroying everything in an instant..."

"Or maybe a water drop weapon. Anyway, something very powerful. What would you think if you developed such a weapon?"

"I?"

Li Liu Shuangyue stood up and pointed at herself, her mouth made a surprised sound. "Do you think so highly of me? Can I research such a weapon?"

"Forehead?"

"If I can do this, the first thing I want to do is thank you for your trust in me, Senior."

"Secondly, we have to thank the country. This kind of research definitely needs the support of a scientific research environment."

"Third... I haven't thought about it yet."

Zhang Shuo asked doubtfully, "Aren't you worried that such weapons will harm humans?"

"What's there to worry about?"

Li Liushuangyue smiled nonchalantly and said, "There are too many things that are harmful to humans, and environmental pollution is the most serious problem. Perhaps in the future, it is not weapons that will destroy humans, but the ecology of the earth."

"High-tech weapons can also be used for defense, right? For example, if a huge meteorite falls, we can destroy it, right?"

"For weapons, it's not about how much damage they can do, but how they are used. Nuclear weapons are already very powerful, so what does it matter?"

Zhang Shuo was silent for a moment, then a smile reappeared on his face, and he praised, "You are so cheerful."

"Is this a compliment?"

Li Liu Shuangyue's face was full of smiles. "My dad always says that I am simple and don't think about anything, but I think I am very smart. I am a doctor of mathematics."

She said this with a little pride.

Zhang Shuo also laughed, "Yes, you are much smarter than me."

(End of this chapter)