Buckmaster is a professor at the Massachusetts Institute of Technology, a Ramanujan Prize winner, and a member of the Ameriken National Academy of Sciences.

He is a well-known expert in the field of partial differential equations, and is also recognized as an authority in the field of NS equation research, and has been committed to the research of NS equation theory.

As early as five years ago, Buckmaster began to try to question and challenge the success of the main methods of NS equation research, and published the results of his own research with his colleagues.

At that time, the results were not perfect, and only demonstrated the inconsistency of the description of the physical world by the NS equation 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 of 'allowing the NS equation solution set to be rough'.

For example, if a parameter is adjusted to 5, the output value is 10; The parameter is adjusted to 6, and the output value becomes 60; When the parameter is adjusted to 7, the output value becomes 11 again, and the output value does not change with the slow change of the parameter, but fluctuates greatly.

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

In the case of 'allowing the NS equation solution set to be rough', the output value of the equation is not stable, and it can be inferred to a certain extent that the equation itself is also unstable, that is, the smoothness of the NS equation solution set is denied to a certain extent.

Buckmaster himself was interviewed and explained, "Smooth solution sets are complete to represent the physical world, but mathematically they don't always exist." ”

"A lot of times, we can only study equations with rough solution sets, that is, weak solutions."

"It's like sketching a face, each line doesn't necessarily fall in a fixed position, but the overall trend is fixed."

"If the line of the face is drawn on the nose, we think 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, to a certain extent, is also incomplete (smooth)."

Buckmaster explained in an interview that the logic is reasonable or not depends on personal judgment, but the proof he makes is logically rigorous.

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

As for the details of the derivation, it takes two rounds of review to get into a top academic journal in mathematics, and it is almost impossible to make similar low-level mistakes.

"Impossible!"

Wang Hao frowned and thought, "There can be no mistakes in the process, and there is no problem in logic......"

"Is it proven correct?"

"It can't be!"

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

How is this possible?

The human brain may be wrong in thinking, but the system's judgment of knowledge inspiration can't keep up with the logical rigor of Buckmaster?

Or rather, Buckmaster goes beyond the system?

"Impossible!"

Wang Hao was determined to get on the bar with this paper, and he reviewed it from beginning to end, but he still couldn't find any problems, so he simply established a task-

[Task 4]

[Research Project Title: Identifying the Problem of Buckmaster Research (Difficulty: C).] 】

[Inspiration value: 0.] 】

“！！”

"Difficulty C? He is recognized as a top expert in the NS equation! ”

Wang Hao was shocked when he looked at the difficulty of the task, he was just looking for a problem in a research paper, but the difficulty caught up with a study, no wonder he looked at it for three hours and couldn't find anything.

Let Buckmaster find this problem himself, I guess he can't find it himself!

……

The impact of Buckmaster's research is indeed significant.

Although it has not reached the level of shock in the international mathematical community, scholars related to the study of partial differential equations and NS equations will read his papers, and even some scholars who apply NS equations will also read his papers.

It includes some academics in the field of aerodynamics and fluid mechanics, as well as experts in the field of application.

Wait a minute.

Buckmaster's research has somewhat denied the NS equation.

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

In addition, Buckmaster's paper was published in Fundamental Mathematics and Applied Mathematics, and authoritative journals are naturally convincing.

Then, his thesis proved logically rigorous.

It is very surprising when everyone does not find a problem, and some people even propose to find a realistic example of the non-smoothness of the NS equation based on Buckmaster's research.

Of course, most people are still calm.

In many cases, there is a difference between mathematical logic and physical reality, because in terms of application, as long as the tool used is effective, it does not need to be proven to be valid forever.

At present, it is only a theoretical study in the field of mathematics, and the paper does not reject the NS equation 100%, but only proves that the NS equation may be invalid through the study of the rough solution set.

For Wang Hao, this is not the case.

Buckmaster's research is in direct conflict with his research, and he must find the mistakes of the other party, otherwise he will be denied his own research.

Wang Hao went to class.

Attending classes can greatly increase your inspiration points.

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

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

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

This will help them to have a solid understanding of the content, not just some basic mathematical applications.

One class, two class hours down.

[Inspiration: 37.] 】

"Very little!"

The inspiration from this lesson was surprisingly small.

Wang Hao was also very surprised, he originally thought that one class would be enough to complete the research, but it turned out that the increase in inspiration value was only one-third.

This means that the key has not been found.

After returning to the Mason Mathematics Lab, he was stuffy in his office and looked at Buckmaster's research again, and then Zheng Yaojun came to him, so he simply studied with Zheng Yaojun.

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

He was also aware of Buckmaster's research.

The two of them 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 presumably correct, and if there is an error, it may be logical."

"The final conclusion is also deduced, but there are some things that need to be carefully considered."

Zheng Yaojun said with a frown.

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

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

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

"It's hard to accept."

The reaction of the average mathematician, like Zhou Qingyuan, is that he cannot accept the conclusion that the NS equation is not smooth, even if it is only an analysis of the rough solution set.

It's like seeing a perfect work of art, but there are huge flaws, and it makes people feel very depressed.

Zheng Yaojun suddenly became interested, he knew that Helen was Wang Hao's student, so he said in his somewhat uncertain position, "The process may not be all correct, look at this position." ”

He pointed to a position and said, "There may be something wrong with the logic here, and the deviation value analysis he is talking about is not necessarily perfect." ”

Helen looked at Zheng Yaojun and said, "There is no necessary in mathematics, only right and wrong. ”

“……？”

came up with the words of 'education', which made Zheng Yaojun not react for a while.

Helen continued, "The position you pointed out, I thought about it a little bit, and the deviation analysis they did was very well done, and it did prove that there was a big difference? ”

"But how do you define that?" Zheng Yaojun found out that he was being educated by the little girl, and immediately asked back.

Helen said, "Just look at the separation of the curve, this data is enough to explain any problem, study the deflection of the curve value, judging from the direction, the deviation exceeds the defined value." ”

"Uh~~"

Zheng Yaojun thought about it, it was true, but when he was broken by a female student, he felt very faceless, and he immediately found another position, "What about here?" He used an algebraic analysis technique, but he was not sure that all thresholds were included. ”

"Of course, you don't need to include all the thresholds."

Helen said, "It only needs to be divided into parts, and one part does not represent all, but the content is only an explanation, not an argument." ”

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

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

"Ula Ula ~~"

Helen and Zheng Yaojun argue about the content.

One word, one word, no one can convince anyone.

Looking at this scene, Wang Hao touched his forehead helplessly, Helen has a bit of an inquiring personality, and she is very unwilling to admit defeat.

Zheng Yaojun seems to be a little bit too.

What is a big professor arguing with a little girl?

When the argument came to the end, Zheng Yaojun obviously began not to talk about martial virtues, and talked about some 'completely supernatural' content, some of which even involved his own research.

Then, he won.

Because Helen is a little incomprehensible in the back, she is a teenage girl after all, no matter how talented she is, no matter how high her IQ is, the knowledge involved cannot catch up with Zheng Yaojun.

In the end, Helen's cheeks flushed, and Wang Hao went over to comfort him, "Helen, don't worry about this guy, in two years, he will not be your opponent!" ”

Helen seemed to have listened, like a child who was angry and cruel, pointed at Zheng Yaojun, gritted her teeth and said, "You wait for me!" ”

“！！”

Helen is gone.

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

Wang Hao broke a cold water for him, "Lao Zheng, Helen is only sixteen years old......

Zheng Yaojun's smiling face immediately disappeared, and he realized that it should be his students who should be compared to Helen, not himself.

But his student, Hu Lidan?

and Helen......

"What a genius!" Zheng Yaojun finally sighed and said, "How can you have such a genius student?" I'm only 16 years old, and I'm really better than me two years later. ”

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

"Why?"

"He's working on the Legendre conjecture."

In a word, it is clear.

Zheng Yaojun pursed his lips vigorously, "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, the next time you find this kind of gifted student, can you recommend it to me? Zheng Yaojun said, "Although I am not a genius, I also want to have a genius student." ”

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

No way!

The young man has a very good talent, it's a pity to follow Zheng Yaojun.

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

"Hmmm......"

It feels like a philosophical question.

Wang Hao thought about it carefully, is a genius a normal person?

Geniuses are the same as normal people, they have two arms and two legs, and they are the same on the outside, the difference is only that the brain development is excellent?

But in the same way, some people are born with great strength and excellent physical development, but the development of modern society has led to the genius of the mind being more valued.

Therefore, genius is also within the range of 'normal people' judgment deviations......

That's right!

Wang Hao's eyes lit up when he thought about it, he slapped the table excitedly, and suddenly shouted, "Bang! ”

"I see!"

Zheng Yaojun trembled with fright.

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

Zheng Yaojun opened his mouth slightly and was stunned for a long time, then turned back and pointed at himself, "What do you mean......"

"Am I stupid?"

……

After Wang Hao found inspiration, he had already discovered the problem, and Buckmaster's thesis was indeed correct, but correctness did not mean anything.

They are taking the conclusion too seriously.

Perhaps even Buckmaster himself found that the output value of the equation was not stable when the solution set of the NS equation was allowed to be rough, and it was taken for granted that the smoothness of the solution set of the NS equation was denied to a certain extent.

This logic itself is problematic and, to a certain extent, does not mean 'affirmation'.

As Helen said, there are only correct and incorrect mathematics, and there is no vaguely defined statement.

'To a certain extent', is it proven, or is it not proven?

After Wang Hao discovered the problem, he immediately thought of the key and knew how to refute the research, he could prove that the output of the 'rough solution set' equation is bounded convergence, in other words, for the study of the 'rough solution set', the equation output is determined to be unstable, and it is also within a certain range, rather than completely unstable.

The example of a sketch is really good.

For the conventional values of the NS equation, it is impossible to have a stroke on the nose.

Therefore, Bakmaster's research does not explain any problems, and has nothing to do with whether the solution set of NS equations is smooth or not, and nothing can be proved.

Wang Hao did not document the research that refuted Buckmaster.

With enough inspiration, and the fact that the research is in the same direction, he can even prove on the spot that 'the bounded convergence problem of the equation output is allowed for rough solution sets'.

He's doing his own research on the inspired record.

[Task 1]

[Research Project Title: Navier-Stokes Equation Study (Difficulty: S+).] 】

[Inspiration: 60.] 】

Wang Hao looked at the inspiration value of the system task, and couldn't help but smile on his face, and even said that he was a little excited.

That last bit of inspiration didn't come easily.

Zheng Yaojun looked at Wang Hao's continuous records and asked curiously, "Do you know the problem with that paper?" Is it preparing to negate his thesis? ”

"Of course not."

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

"Then you are ......"

"My own research." Wang Hao said, "I already know how to prove the smoothness of the solution set of the NS equation within the condition of taking the value of the fixed range. ”

Zheng Yaojun was stunned for a moment when he heard this, and pondered carefully, "Buckmaster is proof that under the range value, the NS equation is not smooth to a certain extent. ”

"Now it is to prove the smoothness of the solution set of the NS equation under the value of the range."

"These two ......"

His eyes widened suddenly, and he reacted, "It's the opposite! You still say that you are not denying his research! ”

(End of chapter)