Chapter 176 Ge Guai Open Class, Wang Hao: Who can be faster than me?
Director's Office.
Wang Hao looked at Qiu Hui'an with eyes full of relief and appreciation. He listened patiently to Qiu Hui'an's explanation, and then asked, "Have you used this method to cover Chebyshev's theorem?"
The Bertrand-Chebyshev theorem is a weakening of Legendre's conjecture.
The content is that if the integer n is greater than 3, then there is at least one prime number p, which is consistent with p being greater than n and less than 2n2.
There is also a weaker statement that for all integers n greater than 1, there is at least one prime number p, which is consistent with p being greater than n and less than 2n.
This problem was first raised by Chebyshev, and later Chebyshev completed the proof himself.
Legendre's conjecture has not been proven yet.
Qiu Hui'an nodded and said, "I have used this method to cover Chebyshev's theorem."
"But if I want to cover Legendre's conjecture, I can't find a good entry point. The range of prime number intervals in Legendre's conjecture is even smaller."
"And operations involving squares are much more difficult than simple addition and multiplication."
Wang Haodao, "Your idea is very good, really very good. I think it is possible to prove Legendre's conjecture using this method, and it can even be used to study Zhou's theorem."
"Let's analyze it together now."
"Your method covers Chebyshev's theorem, so it should be like this..."
As Wang Hao spoke, he began to write on the paper. In just ten minutes, he wrote a complete proof.
Qiu Hui'an sat by and watched dumbfounded. He spent half a month studying to complete this proof, and the previous thinking time was more than a month.
In the end, Wang Hao just listened to the idea and wrote the proof.
"Teacher Wang, you are so awesome!" Qiu Hui'an said with a wry smile, "The idea is exactly the same as mine."
Wang Hao didn't care.
This time he did write the proof based on his own understanding, rather than relying on "The Gift of Teaching".
In related research, he has gone much deeper than Qiu Hui'an. The proof of Chebyshev's theorem is also very simple, and there are even many ways to demonstrate it.
He just thought of the method and completed the proof.
However, in the process of writing the proof, he found that the task inspiration value had increased by '1' point.
Suddenly.
His discussion with Qiu Hui'an became more enthusiastic.
This is discussion, not teaching.
Wang Hao has not studied Legendre's conjecture, but only briefly thought about it when instructing Qiu Hui'an.
He prefers that students can complete their own research, otherwise it will be equivalent to him doing the research instead of the students.
This is very important for students' growth.
At the same time, Qiu Hui'an is indeed very good.
When discussing issues, Qiu Hui'an always came up with ideas and incidentally gave Wang Hao some points of inspiration.
Wang Haodu felt a little incredible. At the same time, he felt that Qiu Hui'an was a genius. He had four times the inspiration boosting effect of "The Gift of Scientific Research", but he still had to be truly inspired, but Qiu Hui'an could have continuous inspiration.
"It seems that he is not far away from proving this conjecture." Wang Hao thought with a sigh.
He and Zheng Yaojun had discussed it before.
Zheng Yaojun felt that it would be extraordinary if Qiu Hui'an could complete the proof of Legendre's conjecture during his graduate studies.
If the proof is completed within one year, it can definitely be described as a genius.
Legendre's conjecture is indeed a small conjecture, but it is only compared to Zhou's theorem. It is a difficult problem in number theory. It is quite amazing that a graduate student can prove it, even if it is completed under the guidance of a tutor.
Wang Hao and Qiu Hui'an discussed for nearly an hour.
After Qiu Hui'an left, he quickly checked the mission.
【Task 2】
[R&D project name: Proof of Goldbach’s conjecture (difficulty: S).]
[Inspiration value: 47.]
"It's 47 o'clock!"
He didn't do serious research on the proof of Goldbach's conjecture. He just had a happy-go-lucky mentality. If his inspiration value could rise a little, it would go up a little. It didn't matter if it didn't.
In this kind of mentality, there is certainly not much inspiration.
My previous inspiration value was only about 20 points, and I had some research ideas, but I didn't really think about it in depth.
Now that he had found the direction of his research, Wang Hao went to the door and hung the "Do Not Disturb" sign. Then he stayed in the office and began to do research seriously.
The general solution he thought of was the ‘covering method’.
Simply put, Goldbach's conjecture proves that any even number can be expressed as the sum of two prime numbers.
The idea behind the 'covering method' is to prove that all prime numbers combined in pairs (including itself) can cover all even numbers. As long as complete coverage can be proven and no even numbers are missed, Goldbach's conjecture will naturally be covered directly.
If it is within a bounded range, the proof is naturally very easy, even for analyzing prime numbers.
However, when the range reaches infinity, it is very difficult to prove. We need to study the process of analysis coverage, and even analyze the problems that arise with prime numbers.
This kind of analysis is much more difficult than proving Legendre's conjecture.
…
Wang Hao was bored in the office for three consecutive days, and even asked students to deliver meals several times during the process.
He has been studying ideas.
Among them, the problem involving the analysis of prime numbers was the most difficult, and this problem remained stuck until the third day.
Of course, three days of research still paid off.
【Task 2】
[Inspiration value: 61.]
The inspiration value is 18 points higher than three days ago.
"This is the limit." Wang Hao thought. He followed Qiu Hui'an's idea to conduct research, but it is difficult for a research idea to directly solve a complex problem. There are many other difficulties in trying to prove it.
However, the inspiration value has exceeded 60.
Wang Hao hoped to complete the research in one go. He thought about it carefully and decided to open a related open class.
Once you have a general direction for research, it is relatively easy to accumulate inspiration points.
It is a good idea to open open classes.
When he walked to the elevator, Wang Hao met He Yi who was coming over.
He Yi held a report in his hand and immediately said when he saw Wang Hao, "Don't leave yet, just in time, I'm here to find you."
"Report?"
"Yes." He Yi pulled Wang Hao back to the office and said, "This is the project settlement report. Take a look at it carefully. If there are no problems, I will submit it."
In the past few days, He Yi and Xiao Xinyu have been doing project summaries and writing results reports. After the reports are completed, they must be given to the project leader for a look.
Wang Hao sat down again and looked through it.
I mainly looked at the introduction and summary of the results at the beginning and at the end. I browsed through it and found that there were no problems, so I handed it over to He Yi again, "Submit it directly."
"Don't you take a closer look?" He Yi said in surprise.
Wang Hao shook his head, "There's nothing interesting to see. Professor He, you said this is more professional than me. If there are no problems, just submit it directly. Submit it earlier, and you can apply for the next project earlier."
He Yi smiled and nodded, "Okay, then I'll submit it."
After handling this matter, Wang Hao went to the School of Science office of the Academic Affairs Office and mentioned that he wanted to open an open class.
"Open class?" The person in charge of the Academic Affairs Office was surprised, "Professor Wang, what public class do you want to teach?"
"Goldbach Conjecture."
"Goldbach's conjecture? Um..."
The content of this open class is really unexpected.
The Academic Affairs Office still recorded it, because it was Wang Hao who was offering an open class, so he was not worried that no one would come to listen. He was even worried that there would be too many people signing up to listen.
soon.
The information is disclosed on the school website.
Many people signed up immediately after hearing the news, especially graduate students who wanted to take more of Wang Hao's courses.
Wang Hao has two courses this semester, one is "Nonlinear Functional Analysis" and the other is "Complex Analysis", both are basic courses for graduate students in mathematics.
"Nonlinear Functional Analysis" is an old course.
"Complex Analysis" is a new course, which is the continuation and in-depth course of the undergraduate "Complex Variable Function" course.
Wang Hao decided to teach this course because an old professor had retired and it was difficult to find a new teacher for difficult mathematics courses.
He took over.
In addition, because "Complex Analysis" is a new course for him, teaching new courses will help increase his understanding of knowledge.
Because he may be very busy with two projects on hand, he is not offering elective courses.
There are only two classes a week, which is just right.
Now when I need inspiration points, it's still a bit troublesome that there are no relevant courses, so Wang Hao decided to open an open course.
This is the first time Wang Hao has offered an open class in school, and his courses are very popular.
There are some mathematical geniuses who are very good at doing research, but the opposite is true when it comes to teaching, probably because geniuses have high IQs and a deeper understanding of knowledge.
Questions that they think are so simple that they don’t need explanation are actually very difficult for ordinary students.
In other words, some courses for mathematical geniuses are difficult for ordinary students to follow.
Wang Hao is different.
He is recognized as a top mathematical genius. He has continuously completed top results in his twenties, and his lectures are also recognized as outstanding.
Anyone who has listened to Wang Hao's lectures feels that his courses are easier to understand. Even if he explains the same content, it is easier to understand when he lectures.
With a reputation as a genius mathematician and a reputation for teaching, Wang Hao's courses will naturally be very popular.
Because the course is so popular, the information about the open course has just been released and a large number of students have signed up.
Luan Haiping even came here specially.
Because this was Wang Hao's first time offering an open class, he was worried about what problems might arise during the lecture.
"Wang Hao, why did you suddenly think of talking about Goldbach's conjecture in public?" Luan Haiping asked curiously.
Wang Haodao said, "I just feel that there are few courses this semester. I thought I would tell you something when I have time, hoping to make more people fall in love with mathematics and understand mathematics research better."
He continued, "I have been studying Goldbach's conjecture recently. Many people know this conjecture, and I think many students will be interested in it."
"That's true." Luan Haiping nodded and asked with interest, "How is your research going? Do you have any ideas?"
"Let's have some ideas." Wang Hao said thoughtfully.
"Really?" Luan Haiping was surprised when he heard this. Wang Hao had completed a lot of mathematical research, the most influential of which was the proof of Kakutani's conjecture.
The proof of Kakutani's conjecture was based on a mathematical method he studied himself, for which he won the Chen Shengshen Mathematics Award and the first prize of the National Natural Science Award.
However, Goldbach's conjecture is different from Kakutani's conjecture, and their influence is not at the same level.
Because the domestic publicity of Goldbach's conjecture has a greater influence than the international publicity.
Luan Haiping immediately asked, "Do you think the proof can be completed? How long will it take? One year, two years? Five years will do!"
Wang Hao hesitated and said, "It's hard to say. I just think about it when I have an idea. It proves that I still need inspiration."
Luan Haiping nodded as he listened and made a judgment in his mind. He felt that the time he spoke was too short. Wang Hao just had an idea and it would take a long time to prove it.
Even if it takes ten years, it is still quite amazing!
By then, Wang Hao was only in his thirties, and he had already completed the proof of Goldbach's conjecture, which is very amazing when you think about it.
That is truly a name that will last forever!
In recent decades, many top results have appeared in the world, but only two people have truly solved major mathematical problems, one is Grigory Perelman and the other is Andrew Wiles.
They proved Poincaré's conjecture and Fermat's conjecture respectively.
If Wang Hao can complete the proof of Goldbach's conjecture, he will be recognized as one of the top mathematicians in the world.
Ranking, at least top five!
How awesome is this?
Luan Haiping couldn't even imagine it.
…
at the same time.
In an office of the Department of Mathematical and Physical Sciences, Academician Wu Hui is inspecting the Key Laboratory of Superconductivity and submitting reports to Qian Sheng's research team.
He shouted in surprise, "The strength of the AC gravity field has reached 4.1 percent?"
"It's 4.1?" Fan Qingxue on the opposite side was also very surprised. The latest news they learned was that the basic science experiment in the capital had increased the intensity of the AC gravity field to 3.6%.
That is already a very high figure.
They are responsible for related research projects and can know some gossip. Xiang Qiansheng's research team is the focus of attention. Three weeks ago, the data was only 3.5%.
Now it has directly reached 4.1%?
Wu Hui was very surprised. After reading the introduction to the results, he began to read the content carefully.
Soon, he found the key point, "They have improved the superconducting material layout and adjusted the width of the nodes and conductors. The overall appearance has not changed, but the design seems more reasonable."
"The report said that changes in the layout of superconducting materials brought about a 0.4 percentage point increase."
"Very powerful ah!"
After Wu Hui finished speaking, he commented, "It seems that the other two institutions have no chance, and neither does the physics laboratory."
Fan Qingxue sounded a little less optimistic about the physics laboratory.
He participated in the first experiment in the physics laboratory and was very shocked by the results. However, the improvement in the first experiment does not mean that there will be a big improvement in the subsequent experiments.
The 4.1% data is really astonishing.
Of course, it also depends on other research. The increase in AC gravity field strength indicates one factor.
If the difference in improvement intensity is not large, it is necessary to compare the research content in other aspects.
Of course, speed is also critical.
Qian Sheng's team was the first to submit a report, which shows that their research speed is also very fast.
This is a bonus point.
While the two were talking, Wu Hui turned his head again and found that a new report had come over. He clicked on it and suddenly felt confused, "Report from the Physics Laboratory of Xihai University?"
"Isn't it possible? So fast?"
Wu Hui asked Fan Qingxue doubtfully, "Have the funds from the foundation just been allocated?"
Fan Qingxue said, "It should have just arrived, right? I even asked about it in the morning, and it seems that the payment was made today."
"Then why did they submit the report?"
Of course Fan Qingxue didn't know.
Wu Hui simply clicked on the report to check, and was shocked when he saw the summary of the results, "The intensity of the AC gravity field is 6.5 percentage points?"
After he finished speaking, he rubbed his eyes vigorously, as if he was worried that he had seen it wrong, "It really says 6.5 above."
Fan Qingxue immediately came over to take a look.
The two of them took a deep breath in unison, and they naturally knew what this data represented.
Even if other factors are put aside, this data alone can play a decisive role. 6.5% compared to 4.1% can be said to be a leapfrog improvement.
If the data is real, Xiang Qiansheng's team has no chance at all. Of course, Capital University's Basic Science Center also has no chance. The difference in results is so big that there is no need to compare in other aspects.
The experiments done with this data, even without analysis, we know that they are definitely going in the right direction.
Wu Hui smiled bitterly, rubbed his forehead, and said, "Wang Hao is always able to surprise people. Xiang Qiansheng wants to steal his project, but it seems that the investment will be wasted."
"We are sending an expert team over again this time."
"this time……"
"I'll go there by myself!"
…
Xihai University, large classroom on the west side of the teaching building.
This conference room is the largest classroom in the school and can accommodate up to about 400 people.
In fact, the school initially planned to hold open classes in the large exhibition hall, because there were so many people signing up for Wang Hao's open classes that they were almost ready for a large-scale lecture.
Such activities are all held in large conference rooms or even open-air playgrounds.
After hearing this, Wang Hao immediately shook his head and refused, because speeches, performances and mathematical explanations were completely different.
You don't need to follow some speeches to listen carefully. You can understand them just by listening in the middle.
Mathematics is different.
When explaining a certain knowledge, if you fail to follow a certain point in the middle, it will be difficult to understand it later.
If he talks on stage and the people below him basically don’t understand it, it will be impossible to bring inspiration value, and it will be meaningless.
In addition, the content he explained was also difficult.
Ordinary students cannot understand it at all. They need at least a junior or senior year in mathematics to be able to understand a little bit. If they want to understand everything, they need at least a PhD in mathematics or an excellent graduate student.
For undergraduate-level students, it doesn’t make much sense to attend classes.
So in the end I chose the big classroom.
All the seats in the classroom were occupied, and the aisles and back rows were crowded with people. Some simply took a stool and sat down to listen.
Most of the people who come to attend the lectures are graduate students and PhD students from the Department of Mathematics, some are students from the Department of Physics and Chemistry, and the rest are professors and lecturers in the school.
Wang Hao stood on the podium, looking at the large number of people in the audience, and nodded expectantly. He tried the microphone, and then said, "The theme of my class is Goldbach's conjecture."
"Of course, everyone knows that Goldbach's conjecture has not been proven, so I will start by explaining the existing research related to Goldbach's conjecture."
"The following will explain some ideas and ideas that may solve the problem of Goldbach's conjecture."
This sentence is somewhat unexpected.
When Wang Hao said that he was explaining ideas that might solve Goldbach's conjecture, was he talking about other people's solution ideas, or was he talking about his own solution ideas?
Some people frowned slightly.
For example, Zhou Qingyuan was a little worried that Wang Hao would make his research public.
Before the research is confirmed and published, even just ideas and ideas may be plagiarized by others.
Wang Hao hadn't started speaking yet, and he didn't know exactly what he was going to say, so he just listened patiently.
"Let's start with Mr. Chen Jingrun's proof of 1+2."
Wang Hao started to speak, "I think Mr. Chen Jingrun has reached the pinnacle of application of the screening method. Why do you say that?"
"Because he used the sieve method to prove 1+2, which is the ultimate."
"Then let's talk about the screening method first..."
Wang Hao quickly threw himself into the teaching mode. He started with Chen Jingrun's 1+2 proof. After briefly explaining the idea, he talked about some other research results on Goldbach's conjecture.
These results do not use the screening method, but they are still of great reference significance.
After explaining the existing results, about an hour passed, and everyone had a fifteen-minute break.
Wang Hao also communicated with several professors.
Zhou Qingyuan asked, "What are you going to talk about next? What are your ideas and ideas for solving the problem?"
Wang Haodao, "The next step is to explain my research and analyze it from the perspective of group theory to cover Goldbach's conjecture, but my research is only half done."
He shook his head with regret.
Zhou Qingyuan immediately frowned, "It's not good for you to directly talk about your thoughts and ideas like this, right? If some villains know about it, take your thoughts and ideas and continue to study..."
Nothing was said next.
Several professors nearby also thought the same way. Your own thoughts and ideas are the most important. How can you say them in public?
Even imperfect ideas are the most valuable wealth of scholars. Maybe the ideas and ideas are correct, and the proof of Goldbach's conjecture can be completed.
Wang Hao smiled when he heard this. He glanced at the mission inspiration value and found that the inspiration value had risen to 83 points.
A hundred points high, only 17 points left!
If you can openly talk about your thoughts and ideas, others will understand and think along the way, which will definitely bring a lot of inspiration.
At that time, the proof of Goldbach's conjecture can be completed in one go.
Who else can be faster than him?
Even if he records his thoughts and ideas and then does research and analysis, or even directly writes related papers, it shouldn't be as fast as him, right?
Moreover, he only explained part of the ideas, just the beginning, and he would definitely not talk about new ideas.
Those contents added together will not exceed one-fifth of the proof!