Wang Hao picked up the A4 paper and stared at the standard red lines of the complex graphics on it without moving his eyes.
He really didn't expect that what Ding Zhiqiang was talking about was actually the complex plane corresponding to the real red line, and it was really related to the Riemann Hypothesis.
The professional explanation for the problem discovered by Ding Zhiqiang is
After the high-order particle function is substituted into the minimum prime number pair node, the five-dimensional algebraic geometry corresponding to the function obtained (including the imaginary number solution), a complex surface of the central sandwich, is related to the Riemann Hypothesis....
Could this finding be a coincidence? No.
There must be some inevitability.
One of the important reasons is that the Riemann function is one of the foundations for shaping higher-order particle functions.
But the problem is that the shaping process of higher-order particle functions does not use algebraic geometry methods.
So what do the new findings mean?
Staring at the red line on the A4 paper, Wang Hao frowned and thought for a long time. He couldn't think of any method for a while. The only thing that was certain was that the new discovery must have great potential. What it specifically represents needs to be studied carefully to know.
Qiu Hui'an also came over.
He noticed that Wang Hao had been staring at the A4 paper, and smiled and said, Teacher Wang, don't listen to Ding Zhiqiang, what he says is unreliable. "
"Before you came back, I had discussed it with him several times. The complex plane corresponding to the red line has absolutely no relationship with the Riemann Hypothesis."
"oh?"
Wang Hao thought and looked at Qiu Hui'an.
Qiu Hui'an said, "I thought what he said was possible at first, but later I discovered that this complex plane cannot be represented by a function at all, but is the intersection of countless high-dimensional graphics."
"For example, there are many straight lines in different directions. They intersect in pairs, and then connect these points together in series."
"It is almost impossible to express the obtained graph as an equation, unless all related straight lines are passed through... But the problem is that there are infinitely many straight lines..."
Wang Hao nodded thoughtfully after hearing this.
From what Qiu Hui'an said, we know that the two of them have indeed studied it carefully, and they already have a basic understanding of the complex plane represented by the red line, and know that it cannot be expressed by a single function.
He said, "Xiao Qiu, don't you think that the intersection of countless high-dimensional graphics and forming a complex plane is a magical thing in itself?"
"this......"
Qiu Hui'an hesitated for a moment and said, "It is indeed very strange, but I also know about algebraic geometry. It is not surprising that multiple four-dimensional and five-dimensional complex figures intersect on a surface. This and the corresponding function It’s related to equations.”
"Yes, you have a point."
Wang Hao nodded in agreement and then said, "But Zhiqiang is studying higher-order particle equations, so I think it is necessary to study a brand new idea in depth."
"Even if it does have no special significance, we still have to prove it before we can draw a conclusion."
"Besides, Xiao Qiu..."
"As your teacher, I think it is necessary to say that inspiration is very important when studying this matter, even more important than ability. You are all still young, so don't be limited by some inherent ideas."
"You think an idea doesn't make sense, but what if it does? Wouldn't you just miss a great discovery?"
"Forehead....."
Qiu Hui'an never expected that when he expressed his thoughts, he would be lectured by Teacher Wang Hao.
this.
He raised his head again and saw that Teacher Wang Hao looked like Ding Zhiqiang with a pleasant look, "Zhiqiang, I think your idea is very good, and it may bring new research directions."
"So, I decided to study with you!" "This is probably a new discovery!"
Ding Zhiqiang didn't speak for a long time. He was very uneasy, mainly because he was worried that Wang Hao would not agree with his idea.
This is important.
If it were someone else, such as Qiu Hui'an, he wouldn't care if he approved or not. At most, he would just debate with the other party, and he would never be convinced no matter what. Wang Hao is different.
If Wang Hao didn't agree with his idea, Ding Zhiqiang felt that he would lose confidence and would probably just give up.
Now that he heard that Wang Hao not only recognized his idea, but was also prepared to study it with him, he immediately felt very excited, "Teacher Wang, do you really think so?"
"Of course!"
Wang Hao patted Ding Zhiqiang's shoulder intimately, "Zhiqiang, your idea is great. I looked at the position represented by the red line and thought it was very different. There must be some kind of pattern in it."
"Let's study it together..."
Ding Zhiqiang immediately said, "Come and see the process of making rough drawings... This is what I think..."
The two discussed it seriously.
Qiu Hui'an returned to his seat with depression, and then looked up at Wang Hao and Ding Zhiqiang who were discussing enthusiastically, and couldn't help but feel a sense of sourness in his heart.
Also students.
Why do you feel like you are being treated differently?
The position marked by Ding Zhiqiang’s red line is indeed somewhat unusual. Just like what Qiu Hui’an said, the complex plane corresponding to the red line is the intersection of countless high-dimensional graphics. As long as the graphics are made normally, the position of the red line must be Mark it out.
During the discussion between Wang Hao and Ding Zhiqiang, they also came to understand the complex plane corresponding to the red line.
He also pondered the key.
Ding Zhiqiang said, "The complex plane corresponding to the red line is related to the Riemann Hypothesis." So what is the correlation?
Riemann Hypothesis, there is also a complex plane.
In the Riemann Hypothesis, the straight line with Re(s)=1/2 on the complex plane is called critical-line (critical line).
Using this terminology, the Riemann Hypothesis is expressed as—all nontrivial zeros of the Riemann zeta function are located on the critical-line.
That is, all non-trivial zero points of the Riemann zeta function are located on the straight line Re(s)=1/2 on the complex plane (Re(s) represents the real part of the complex number s).
Although it can be determined that the two complex planes have a certain correlation, just like the problem encountered by Ding Zhiqiang, he did not analyze the minimum pair of node functions (the binary function equation obtained by substituting the high-order particle function into 5 and 17) .
Without derivation and other analysis, it is impossible to make any verification.
If you just use thinking to make inferences, it is obviously impossible to come up with any results.
Wang Hao simply asked Qiu Hui'an to join in. The three masters and apprentices carefully analyzed the minimum pair node function. At the same time, he also established a task.
[Task 4. 】
[Research project name: Finding the correlation between the intersection complex plane of the minimum pair of nodal functions and the Riemann hypothesis (difficulty: S). 】
[Inspiration value: 0. ] "S level difficulty..." "Not bad."
When he saw the difficulty of the research project name, Wang Hao frowned slightly. He always felt that the newly found research direction was very important, and he thought it would be an 'S+' level of difficulty.
S level.....
"Perhaps it is not necessarily the difficulty that determines the outcome, but some kind of key has been found?" Wang Hao thought carefully.
This is how it feels.
Although major mathematical research in the past mainly relied on systematic feedback and inspiration, after solving so many major mathematical problems, Wang Hao's understanding of major directions such as number theory and function theory has definitely reached the top. degree.
Relying on his understanding of mathematics, he is also very confident in his own feelings.
In a new study, sometimes feelings matter. Like Ding Zhiqiang...
Wang Hao glanced at Ding Zhiqiang, who was immersed in thinking, and couldn't help but nodded with satisfaction. He immediately settled down and continued to devote himself to the analysis of the minimum pair node function.
Ding Zhiqiang's place
There is no analysis of the minimum docking point function, mainly because of the difficulty.
This function is really too complex.
As a function similar to a partial differential equation, it is understandably difficult to analyze and convert it. Most similar functions are impossible to analyze.
If it is to perform algebraic geometry analysis through splitting, it is also very difficult to connect them together. They studied together for two days without making any progress.
The whole process brought little inspiration value, only a pitiful 1 point.
Wang Hao thought that he should find an expert in algebraic geometry. He immediately thought of Kacher-Birkar and called him directly.
Today, Kacher-Birkar is no longer a pure scholar. Relying on his in-depth research on the semi-topological theory of superconducting, he was hired by the Superconducting Industrial Materials Company as a special consultant to the technology department.
This position brings a very high income. To be precise, the annual salary easily exceeds 10 million.
Birkar is almost fifty years old. With a high salary and a light job, he and his wife go on vacation when they have time.
At this time, Birkar was sunbathing on the beach, and his wife was helping to apply sunscreen. He found that the caller was Wang Hao, made a shushing gesture to his wife, sat up and said, "Wang Hao, long time no see, you Have you gone back to college?"
"Yes, Kachel, aren't you here?" "I'm in Acheng."
"That's really a good place." Wang Hao smiled and exchanged greetings with Birkar for a few words, and then got down to the topic, "I have a research project related to algebraic geometry. Are you interested?"
"Talk about it."
"You also know the idea of one of my students, Ding Zhiqiang. He believes that the intersection complex plane of the minimum pair of nodal functions has some correlation with the Riemann Hypothesis..."
Wang Hao gave a simple explanation.
While listening and thinking, Birkar asked, "I know Ding Zhiqiang, a very outstanding young man. Is this his idea? That the complex plane is related to the Riemann Hypothesis..."
"Yes." "Well..."
Birkar hesitated for a moment and said, "Let's do this. You study it first and then we'll talk about it when I get back."
"All right."
Wang Hao could tell from Bill Carr's tone that the other party didn't seem to be very interested.
This is also true.
If it was the research initiated by Wang Hao, Bill Carr would definitely be interested, but Ding Zhiqiang's thoughts... He never thought that Ding Zhiqiang was a super genius, at most he was just a talented young man.
That's all.
In the field of mathematics, there are too many outstanding young people. He himself is a super genius. In other words, mathematicians who can win the Fields Medal were all super geniuses when they were young.
No matter how talented Ding Zhiqiang is, he can't keep up with him when he was young.
When he heard what Wang Hao said, he really wasn't interested, and when he heard that it was Ding Zhiqiang's idea, he was even less interested.
Wang Hao failed to find Birkar, but he made up his mind to study it with Ding Zhiqiang and Qiu Hui'an.
Although he is not proficient in algebraic geometry, he definitely has the basics, but he has not conducted any special research. Ding Zhiqiang's level is definitely not bad, it can even be said to be quite high, and Qiu Hui'an can provide support in number theory. , it is enough to complete the research.
In addition, he also feels that scholars should be given opportunities.
If Bill Carr had participated in the research, he would have completely covered up Ding Zhiqiang. The idea itself belongs to Ding Zhiqiang. When it finally comes to fruition, even if Ding Zhiqiang’s contribution is great and Birkar’s name is listed, the academic community will definitely believe that it was Birkar who helped complete the research.
Famous scholars will have a great suppressive effect on young scholars. In the end, Wang Hao made the decision not to find other people to participate, but to study together with two students.
The three of them are completely devoted to research. It can be described as forgetting to eat and sleep. Even eating is mostly done in the office.
Chen Mengmeng is Wang Hao's assistant and is naturally responsible for taking care of the lives of the three of them.
She was also very curious about research and asked Ding Zhiqiang in a low voice, "Are you studying the Riemann Hypothesis?"
"No, it's to study a correlation with the Riemann Hypothesis... Are you interested?" Ding Zhiqiang asked.
"Not interested in."
Chen Mengmeng quickly shook his head, "I just asked." She was really not interested.
Now Chen Mengmeng's job is to be Wang Hao's assistant, and he can just do some general research while holding the position of associate professor.
In fact, she is not a very motivated character, otherwise she would not go back to Xihai to study for a comfortable life.
She felt that being able to complete the basic research on "Strong Annihilation Force" with Helen would be the pinnacle of her academic career.
If it's something related to theoretical physics, you might still be interested. But with the extremely high level of difficulty and interdisciplinary nature, you won't be interested at all. Even if you join the research, it won't be of much help.
Chen Mengmeng picked up a piece of A4 paper, looked at the dazzling mathematical symbols on it, quickly shook his head and put it back down, chuckled and patted Ding Zhiqiang's head with his hand, "Xiao Ding, come on!"
Ding Zhiqiang took a few mouthfuls of food and nodded slightly.
Watching Chen Mengmeng push open the door and walk out, he frowned and thought carefully, and suddenly felt something was wrong. Just now, the senior sister patted his head and called Xiao Ding'...
Why do you feel so insulted?
Ding Zhiqiang rarely works so hard.
To be precise, the previous efforts were forced and had to be done unwillingly, but now they are done from the heart.
When I discussed issues with Qiu Hui'an before, his ideas were never supported. However, Teacher Wang Hao stepped forward to express his support and decided to conduct research together. I felt that I had gained great trust.
Whenever he thinks about Qiu Hui'an, who is not optimistic about him, Ding Zhiqiang also hopes that he can really research something.
As the research continued to deepen, Qiu Hui'an felt less good. He had always been a participant in the research, but later found it difficult to keep up.
The biggest problem is that the discussion is mainly focused on algebraic geometry and function analysis.
In this regard, he has no advantage.
So most of the time, Wang Hao was discussing with Ding Zhiqiang, and he could only listen to a few words.
Research made progress today.
Wang Hao and Ding Zhiqiang discussed 'the relationship between the red line corresponding to the complex plane and the Riemann Hypothesis' and talked about the relationship between inclusion and being included. Ding Zhiqiang believed that the relationship is likely to appear at the corresponding 'prime number point', while Wang Hao got A definite conclusion was drawn -
The complex plane corresponding to the red line contains all non-trivial zero points of the Riemann zeta function.
If the complex plane corresponding to the red line is regarded as a point set A, and all non-trivial zero points of the Riemann zeta function are set B, the relationship between the two is AnB = B (intersection), that is, A includes all B Inside.
This discovery seemed to illustrate the relationship between the two, but in fact, the inspiration value only increased to the '23' point, because the conclusion was obtained through system feedback and there was no complete proof process.
But with a definite conclusion, it is relatively easy to find a direction for the conclusion.
From the inspiration values, we can know that there is still a long way to complete the research. The main difficulty is that the function is difficult to analyze. In addition, the complex plane corresponding to the red line cannot be expressed by a functional equation at all.
Just like Qiu Hui'an's understanding, the complex plane is the intersection of countless high-dimensional graphics. If you want to express it, you must connect all high-dimensional graphics, but the number of graphics is infinite.
The next development came two days later.
This time it was Wang Hao who found the key. He found that connecting the Riemann function would make the research extremely complicated, so he simply eliminated the influence of the Riemann function, and finally came up with a new idea.
"Perhaps all the prime points of the minimum docking point function are on this plane?"
At first, Wang Hao just had an idea. After discussing it with Ding Zhiqiang for a while, he immediately came to a conclusion. Reflecting on the system tasks, his inspiration value quickly increased by 17 points.
Let's study now
The direction is very clear.
Bill Carr is finally back.
After he returned to Xihai University, he visited the Mason Mathematical Science Center and asked about Wang Hao's research with familiar people.
The research conducted by Wang Hao, Ding Zhiqiang, and Qiu Hui'an was not kept confidential, but because it was purely mathematical, other people did not participate and only had a vague understanding of the research content.
"It seems to be related to the Riemann Hypothesis." - Zhang Zhiqiang.
"Algebraic geometry and Riemann Hypothesis, seems to be analyzing the relationship between the two? I heard Chen Mengmeng say a few words." - Luo Dayong.
"According to what Luo Dayong said, it may be related to Hodge's conjecture? I don't know..." - Tian Hong.
Birkar looked confused.
Qiu Hui'an was walking in the corridor when he was immediately pulled over by several people and asked about Wang Hao's research questions.
"Nothing is kept secret."
Qiu Hui'an explained, "It is definitely not the Riemann Hypothesis. It is just a study of the correlation between a function and the Riemann Hypothesis."
"This is Ding Zhiqiang's idea."
"But I always thought... forget it." He finally shook his head and did not say anything. Bill Carr thinks he understands.
"It's just a small study." He judged. "Maybe it was Wang Hao who directed the students. Wang Hao always hoped that Ding Zhiqiang's doctoral thesis would be better."
"It makes sense!" "It seems so." "It should be."
Many people know that Wang Hao rejected Ding Zhiqiang's doctoral thesis and hope that he can complete better research.
Now that Ding Zhiqiang has an idea, it is indeed normal for Wang Hao to give him some advice.
Birkar couldn't help but sigh, "Wang Hao really values Ding Zhiqiang and spends so much time, energy and hands-on instruction."
Everyone else nodded in agreement.
Qiu Hui'an felt sour when he heard this. He was also a student of Wang Hao. He completed Legendre's conjecture during his graduate studies. Why didn't he receive such attention? Alas~~
