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Chapter 168 You said you didn’t deny his research!

 Buckmaster, professor at MIT, winner of the Ramanujan Award, and academician of the Amerikan National Academy of Sciences.

He is a very famous expert in the application field of partial differential equations and a recognized authority in the field of research and application of NS equations. He has been committed to the research of theoretical applications of NS equations.

As early as five years ago, Buckmaster began to question and challenge whether the main methods of studying NS equations could be successful, and published the results of his research with his colleagues.

The results at that time were not yet complete, but only demonstrated the inconsistency of the description of the physical world by NS equations under certain assumptions.

The current research results prove that the output of the NS equation is unreasonable, that is, the deviation value is too large and unstable, under the condition that the solution set of the NS equation is allowed to be rough.

To illustrate, for example, if a certain parameter is adjusted to 5, the output value is 10; if the parameter is adjusted to 6, the output value becomes 60; if the parameter is adjusted to 7, the output value becomes 11, and the output value

The numerical value does not change slowly with the parameters, but fluctuates greatly.

This means that the deviation value is too large and unstable.

In the case of 'allowing the solution set of NS equations to be rough', the numerical value output by the equation is not stable. To a certain extent, it can be inferred that the equation itself is also unstable, which refutes the solution set of NS equations to a certain extent.

Smoothness.

Buckmaster himself was also interviewed. He explained, "Smooth solution sets are used to express that the physical world is complete, but mathematically speaking, they do not always exist."

"Many times, we can only study equations using rough solution sets, which are weak solutions."

"It's like sketching a face. Each line is not necessarily drawn in a fixed position, but the overall trend is fixed."

"If the line on the face is drawn on the nose, we believe that it is not a successful sketch, but a low-level mistake."

"If this kind of error occurs on the weak solution set, then it can be considered that the smooth solution set is also incomplete (smooth) to a certain extent."

Buckmaster's explanation in the interview said whether the logic is reasonable or not depends on personal judgment, but the proof he made was logically rigorous.

Wang Hao downloaded the original version of the paper and read it carefully for more than two hours, but could not find any problems.

As for the derivation details, to be published in the top academic journals in mathematics, it has to go through two rounds of review, and it is almost impossible to make similar low-level errors.

"impossible!"

Wang Hao frowned and thought, "There can be no mistakes in the process, and there are no logical problems..."

"Does it prove to be correct?"

"This is impossible!"

If Buckmaster's argument is correct, it means his research is wrong.

How is this possible?

The human brain may make mistakes in thinking, but can the system's judgment of knowledge inspiration not be as rigorous as Buckmaster's logic?

Or did Buckmaster transcend the system?

"impossible!"

Wang Hao was determined to confront this paper. He reviewed it from beginning to end, but still couldn't find any problems, so he simply set up a task——

【Task 4】

[Research project name: Identify Buckmaster’s research problem (Difficulty: C).]

[Inspiration value: 0.]

"!!"

"Difficulty level C? He is indeed a recognized top expert in NS equations!"

Wang Hao was shocked when he saw the difficulty of the task. He was just looking for a question in a research paper, and the difficulty actually caught up with a study. No wonder he couldn't find anything after looking at it for three hours.

I asked Buckmaster to find this problem by himself. He probably couldn’t find it himself!



Buckmaster's research was indeed very influential.

Although it has not shaken the international mathematics community, scholars related to the study of partial differential equations and NS equations will read his papers, and even some scholars who use NS equations will also read his papers.

Including some scholars studying aerodynamics and fluid mechanics, as well as experts in application fields.

etc.

Buckmaster's research refuted the NS equation to a certain extent.

In fact, there are many studies that deny the NS equation every year, but this time it is Buckmaster, a recognized top expert in the field of NS equation research.

In addition, Buckmaster's paper was published in "Basic and Applied Mathematics", so the authoritative journal is naturally persuasive.

Then, his paper proved to be logically rigorous.

When no one finds the problem, they will be very surprised. Some people even proposed to find real-life examples of NS equations that are not smooth based on Buckmaster's research.

Of course, most people are still calm.

Many times, there are still differences between mathematical logic and physical reality, because in terms of application, as long as the tool used is effective, there is no need to prove that it will always be effective.

It is still only a theoretical research in the mathematical community, and the paper does not 100% deny the NS equation. It only demonstrates that the NS equation may be invalid through the study of rough solution sets.

For Wang Hao, this is not the case.

Buckmaster's research directly conflicts with his own research. He must find the other party's mistakes, otherwise it will be equivalent to denying his own research.

Wang Hao went to class.

Taking classes can greatly increase your inspiration value.

C-level research can often accumulate 100 inspiration points in one class. His course is "Modern Partial Differential Equations", which is closely related to the study of NS equations.

This is the last class at the end of the semester.

Wang Hao explained the content in great detail, and finally sorted out the entire course so that students could have a better understanding of the course as a whole.

This can help them have a deep understanding of the content, rather than just knowing the application of some basic mathematical methods.

One class, two classes.

[Inspiration value: 37.]

"Very few!"

This class brought surprisingly little inspiration.

Wang Hao was also very surprised. He originally thought that one class would be enough to complete the research, but he found that the increased inspiration value was only one-third.

This means that the key has not been found.

After returning to the Mason Number Laboratory, he was bored in the office and reviewed Buckmaster's research again. Later, Zheng Yaojun came over and simply studied with Zheng Yaojun.

Zheng Yaojun has also been engaged in research in the field of partial differential equations for a long time and has a certain personal understanding of NS equations.

He also knew about Buckmaster's research.

The two people reviewed and discussed the paper from beginning to end, hoping to find errors in the process or logic, but no progress was made.

"The process is probably correct, and if there is an error, it's probably in the logic."

"The final conclusion has been deduced, but there are still some points that need to be thought about carefully."

Zheng Yaojun frowned and said.

At this time, Helen knocked on the door and walked into the office. She also came to discuss Buckmaster's research issues, because she couldn't find any questions and wanted to ask Wang Hao's opinion.

"We are also studying this issue. I think the conclusion must be problematic." Wang Hao pursed his lips and said in thought.

Helen said, "I carefully sorted out the process and found no problems, but this conclusion..."

"It's hard to accept."

This general mathematician's reaction is like Zhou Qingyuan, who cannot accept the conclusion that the NS equation is not smooth, even if it is only an analysis of rough solution sets.

It's like seeing a perfect work of art with huge flaws, which makes people feel very depressed.

Zheng Yaojun suddenly became interested. He knew that Helen was Wang Hao's student, so he said from a position where he was somewhat unsure, "The process may not be all correct, it depends on this position."

He pointed to a location and said, "There may be a problem with the logic here. The deviation value analysis he mentioned may not be perfect."

Helen looked at Zheng Yaojun and said, "There are no uncertainties in mathematics, only right and wrong."

"...?"

The words that came up were "education", which made Zheng Yaojun unable to react for a moment.

Helen continued, "I also thought about the location you pointed out. The deviation value analysis they did is very complete. It does prove that there is a big difference?"

"But, how to define it?" Zheng Yaojun found out that he was being taught by the little girl and immediately asked back.

Helen said, "Just look at the curve separation. This data is enough to explain any problem. Study the deflection of the curve value. Judging from the direction, the deviation exceeds the limit value."

"Uh~~"

Zheng Yaojun thought about it and realized that it was indeed the case. However, when a female student pointed it out, he felt very humiliated. He immediately found another position, "What about here? He used an algebraic analysis method, but it was not sure to include all thresholds.

"

"Of course not all thresholds need to be included."

Helen said, "It only needs to be divided into part. One part cannot represent everything, but the content is only for explanation, not argument."

Zheng Yaojun immediately said, "You just said that there are only right and wrong in mathematics. Even if it is just an explanation, this explanation is not perfect."

"I think you don't understand the problem..."

"Ula Ula~~"

Helen and Zheng Yaojun argued over the content.

No matter what you say or what I say, no one can convince anyone.

Looking at this scene, Wang Hao touched his forehead helplessly. Helen was a bit inquiring and very unwilling to admit defeat.

Zheng Yaojun seems to have some.

What are a big professor and a little girl arguing about?

When the argument reached the end, Zheng Yaojun obviously began to stop talking about martial ethics and talked about some "completely beyond the outline" content, some of which even involved his own research.

Then, he won.

Because Helen was a little confused at the end. After all, she was a teenage girl. No matter how talented she was or how high her IQ was, she could not keep up with Zheng Yaojun in the field of knowledge.

In the end, Helen's cheeks turned red due to anxiety, and Wang Hao went over to comfort her, "Helen, don't compete with this guy. In two years, he won't be your opponent!"

Helen seemed to have heard it, like a child trying to get angry and saying harsh words, she pointed at Zheng Yaojun, gritted her teeth and said, "Just wait for me!"

"!!"

Helen is gone.

Zheng Yaojun was obviously a little proud, like a general who had won a battle.

Wang Hao gave him a break, "Old Zheng, Helen is only sixteen years old..."

Zheng Yaojun's smile disappeared immediately. He realized that it was his students who should be compared with Helen, not himself.

But his student, Hu Lidan?

and Helen...

"What a genius!" Zheng Yaojun finally sighed, "How come you have such a talented student? He is only 16 years old, but he is really better than me after two years."

Wang Hao shrugged, "Helen is indeed a genius, but I think another student, Qiu Hui'an, is the best."

"Why?"

"He's studying the Legendre Conjecture."

It's all explained in one sentence.

Zheng Yaojun pursed his lips hard, "Even if he can't prove it, he will definitely be very powerful in the future."

"yes."

"I envy you... there are so many gifted students. Next time you find such a gifted student, can you recommend it to me?" Zheng Yaojun said, "Although I am not a genius, I also want to have a gifted student."

A short, fat, small-eyed figure suddenly appeared in Wang Hao's mind.

no!

The young man is very talented, it would be a pity to follow Zheng Yaojun.

Zheng Yaojun didn't know what Wang Hao was thinking, but continued, "Wang Hao, do you think a genius like Helen is a normal person?"

"Um……"

This feels like a philosophical question.

Wang Hao thought carefully, are geniuses normal people?

Geniuses are the same as normal people. They have two arms and two legs, and their appearance is the same. The only difference is that their brain development is excellent?

But similarly, some people are born with great strength and outstanding physical development. However, the development of modern society has led to more emphasis on intellectual genius.

So geniuses are also within the range of deviations in 'normal people's' judgments...

yes!

Wang Hao's eyes lit up as he thought, he slammed the table excitedly, and suddenly shouted, "Bang!"

"I see!"

Zheng Yaojun was so frightened that he trembled all over.

Just listen to Wang Hao say, "Even a genius like Helen, when compared with you, is still within the normal range!"

Zheng Yaojun was stunned for a long time with his mouth slightly open, then he recovered and pointed at himself, "What do you mean..."

"I am a fool?"



After Wang Hao found the inspiration, he already discovered the problem. Buckmaster's paper was indeed correct, but being correct didn't mean anything.

They took their conclusions too seriously.

Perhaps even Buckmaster himself was the same. He found that when the solution set of NS equations was allowed to be rough, the numerical value output by the equation was not stable. He took it for granted that this refuted the smoothness of the solution set of NS equations to a certain extent.

There are problems with this logic itself, and to a certain extent, it does not mean ‘certain’.

As Helen said, there are only correct and incorrect mathematics, and there is no vague definition.

‘To a certain extent’, does it prove it or not?

After Wang Hao discovered the problem, he contacted his own research and immediately thought of the key and knew how to refute the research. He could prove that the output of the 'rough solution set' equation was bounded convergence. In other words, for the 'rough solution set'

'' research, the equation output confirms that there is instability, and it is within a certain range, rather than completely unstable.

The sketch example is really good.

For the conventional values ​​of the NS equation, it is impossible for a stroke to be drawn on the nose.

Therefore, Buckmaster's research cannot explain anything. It has nothing to do with whether the solution set of NS equations is smooth or not, and it cannot prove anything.

Wang Hao did not record any refutation of Buckmaster's research.

Because he had enough inspiration and the research was in the same direction, he could even prove on the spot "the bounded convergence problem of the equation output when rough solution sets are allowed."

He was recording inspiration from his own research.

【Task 1】

[Research project name: Research on Navier-Stokes equations (difficulty: S+).]

[Inspiration value: 60.]

Wang Hao couldn't help but smile when he looked at the inspiration value of the system tasks, and even said he was a little excited.

The last bit of inspiration was hard-won.

Zheng Yaojun looked at Wang Hao's continuous records and asked curiously, "Do you know the problems with that paper? Are you planning to deny his paper?"

"of course not."

Wang Hao shook his head and said, "What's the point of denying other people's papers? It can't be published as a result."

"Then you are..."

"My own research." Wang Haodao, "I already know how to prove the smoothness of the solution set of NS equations within a fixed range of values."

Zheng Yaojun was stunned for a moment and thought carefully, "Buckmaster proved that under the range of values, the NS equation is not smooth to a certain extent."

"Now we are proving the smoothness of the solution set of NS equations under the range of values."

"These two..."

His eyes suddenly widened and he reacted, "It's completely the opposite! You still said you weren't denying his research!"


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