Chapter 122 The difference between geniuses and ordinary people and advanced geometric problems
The previous heated public discussion about the palindrome conjecture has not yet passed, and many people are still discussing it on the Internet.
Then they noticed that Wang Hao had posted a new blog.
"A small study proves the 6174 problem", the name of the new blog article still starts with "A small study", but the content of the research becomes the 6174 problem.
This is indeed a small proof.
Question 6174 can no longer be regarded as a mathematical conjecture, because its answer is certain, but the determination relies on four-digit coverage calculations rather than formal mathematical proofs.
No mathematician had ever used strict mathematical methods to solve this problem before.
Many netizens saw the new blog content and immediately commented, "It's another 'small' study. This study is really 'small'. It just proves a problem that others have not proved."
"I have gained more knowledge again, and I know a 6174 conjecture."
"The problem is that the content of the article is not popular science, but a real argument for the problem. Most likely, it is a strict argument."
"The disproof of palindrome numbers the day before has been confirmed by the Mathematical Science Center of Shuimu University and the Applied Mathematics of the Academy of Sciences. This article must be no problem."
"Although I can only understand the question, it doesn't stop me from thinking it's awesome. Who supports it? Who opposes it?"
Many people have paid attention to Wang Hao's latest publication, and they found that it can indeed be said to be a small study, but professional scholars are more concerned about the proof process itself.
When Qiu Chengwen heard the news, he took a look at the proof process and found that it was indeed an interesting argument. Compared with the refutation of the palindrome conjecture 196, he thought, "I still used the method of constructing equations and limit arguments. Two
The methods used in the research are somewhat similar? Is this a coincidence or..."
The methods used in the two studies are somewhat similar, but the methods used in the new study are relatively more complicated and have other differences.
Qiu Chengwen didn't know whether it was a coincidence or a real connection. He simply didn't dig into it and sighed to the professor next to him, "Wang Hao, you are really productive?"
"It's only been two days, right? Two studies, related to two little conjectures."
"No wonder last year, ten papers were published in one month. I used to think that all the papers I had accumulated were published together, but now I believe it."
"For him now, solving some small problems that no one has solved before may really be solving small problems."
The new research published by Wang Hao, which is the demonstration of problem 6174, can indeed be said to be a small achievement, but even if it is a small achievement, it has not been completed by others.
Many scholars found that he published his results on the blog again, and like other people in the complex office, they felt that it was a great waste. Similar results could definitely be published in an SCI, or even an excellent SCI.
Some people think it's normal if they think about it carefully.
In the field of scientific research on the basis of mathematics, without the qualifications to win the Fields Medal, it can be said that no matter how hard you work, you are just a jobber in the field of mathematical theory.
Many old professors have studied mathematics all their lives, but they have no top-level results.
Effort is useless...
This sentence is a little depressing to say, but in the field of basic mathematics research, it is a pure truth. Everyone who can achieve results in the field of mathematics and technology can be said to be the world's top genius.
For example, the famous Chinese mathematician Terence Terence Teru is considered to have an IQ higher than Einstein. This may be an exaggeration, but from this we also know how talented Terence Teru is.
The same goes for many other talented mathematicians. What they accomplished in a short period of time is something that most people would never be able to pursue in a lifetime.
The same is true for Wang Hao now.
He is undoubtedly a genius, and he is also the kind of genius who works hard and always achieves mathematical results.
In the eyes of others, mathematical results that are enough to be published in SCI are just a small research for him.
This is not Versailles, that is most likely what he thought.
People look at things differently.
Rich people will buy a bag worth tens of thousands or hundreds of thousands without even moving their eyes; poor people will feel expensive even if they spend 100 yuan on a meal.
In the field of basic mathematics research, Wang Hao belongs to the top level. Maybe he can produce small results in one or two days of research, while others need to work hard for similar small results for several months, a year or even several years.
Years may not be completed.
From the frequency with which Wang Hao publishes research results, we can know that he indeed spends very little time doing research. Because he uses less time and energy, it is normal for him not to care.
Zhang Zhiqiang can prove this.
Zhang Zhiqiang watched Wang Hao complete his research. He just listened to music to relax at noon, and then turned around and Wang Hao had already completed his research.
How long does the whole process take?
Zhang Zhiqiang felt that it would never take more than two hours.
However, Wang Hao had a different evaluation of the content. “This issue is very brain-consuming to research, and the proof process is more difficult than the previous content.”
"I also put a lot of energy into it..."
Zhang Zhiqiang didn't even wait for Wang Hao to finish, he looked at Luo Dayong, who had just walked over, and asked, "Luo Dayong, can we change tables? I think it's better to sit next to the window."
Luo Dayong sat back calmly, and then gently shook his head at Zhang Zhiqiang.
Zhang Zhiqiang was a little reluctant and immediately asked, "Why? How nice would it be for you two to be next to each other every day?"
Luo Dayong continued to shake his head and simply said, "The wind direction is not good in your place."
After he finished speaking, he turned his head and looked out the window.
"Is the wind direction bad?"
Zhang Zhiqiang thought about it carefully and was a little confused, "Could he be talking about Feng Shui? Impossible, he still believes this?"
"But……"
He couldn't figure it out at all, so he simply went to the window and opened the small crack in the window wider.
This chapter is not finished yet. Please click on the next page to continue reading the exciting content! Then he sat back and felt the air flow carefully. He found that in his position, he felt more cold wind, but he did not look up.
Luo Dayong, because Luo Dayong sat by the window, the conference held through the gap between the windows had a greater impact on him.
Zhang Zhiqiang felt it carefully again, then turned around and said, "I still don't understand, you mean that air flow will make people more energetic? So, working or doing research will be more efficient?"
Luo Dayong looked at Zhang Zhiqiang with confusion, and after a long time he said, "I just don't want to change."
Zhang Zhiqiang's expression froze.
He looked at Wang Hao to the right, and then at Luo Dayong to the left. He suddenly felt a crazy feeling in his heart, and he grabbed a handful of hair hard.
A handful, and it's gone again.
…
The second "Small Research" is to strictly use mathematical means to prove the problem of 6174 in four-digit numbers. Even ordinary people can see that the research is indeed "very small".
However, just because the study is small does not mean it is less difficult.
Wang Hao and Zhang Zhiqiang are telling the truth, and the research difficulty is higher than "proving that 196 is a counterexample to the palindrome conjecture".
The previous counter-example to the palindrome conjecture just used a conversion method from infinite to finite. It is not just 196, but other numbers can also be proved by this method, but the problem is just to calculate the number transformation, not strictly
The mathematical proof cannot help find other 'counterexamples'.
Problem 6174 seems to be very simple indeed, and the range is defined by four digits, but if it is a complete proof, the situation is completely different.
Wang Hao completed the research and gained some knowledge. At the same time, he also made a good discovery, "You can also quickly increase your inspiration value by patiently doing research on your own. You don't have to rely on teaching, or reading books or listening to lectures to gain knowledge."
Even if you do your own research, you still need to do highly relevant research.
The research on question 6174 brought about an increase of three points of inspiration value, and also increased the inspiration value of S-level research to '97' points in one breath, only three points away from reaching one hundred points.
Wang Hao couldn't wait.
He tried to prove Kakutani's conjecture again, but found that he still missed the "finishing kick". He couldn't continue halfway through. After reading it from beginning to end, he found that the overall direction was wrong, and a very critical issue was missed.
, it is simply impossible to prove it.
"The inspiration value is less than 100 points. I want to complete the proof of Kakutani's conjecture..."
"It's impossible!"
Wang Hao continued to 'refresh' the inspiration value.
He found two papers and read them carefully. He went to the library the next day and studied hard for a long time. Then he was very depressed to find that his inspiration value did not increase at all.
"It seems that it won't be completed before the class starts next week." Wang Hao stopped his useless work with regret.
When it comes to the most critical time for S-level difficulty research, looking for some relevant information will not increase your inspiration value.
Inspiration, direction, and ideas are much more important than knowledge base.
Now he feels that something is wrong with his mentality. He is too anxious to increase his inspiration value to 100 points. He works hard but has no increase at all.
"You still have to relax and take things as they come..."
Wang Hao thought, "Anyway, there are classes next week. No matter how difficult it is, how many classes will there be?"
On the contrary, he was not in a hurry.
When he returned to the office, he simply studied with Zhang Zhiqiang, listened to music to relax his mind, and then read the news and followed the public opinion and gossip. It felt good to relax.
…
Dormitory Building 17, third floor.
Ding Zhiqiang, a junior in the Department of Physics, doesn't feel very good.
He was sitting next to the computer, reading the public opinions about the content of Wang Hao's blog with many complex emotions such as envy, amusement, anger, and depression.
At the same time, he also posted two words, "My teacher last semester was Professor Wang Hao. His level is very high and his lectures are also very good. Listening to Professor Wang Hao's lectures is simply a kind of enjoyment. I am bathed in knowledge."
enjoy……"
Next article, "Teacher Wang Hao's level is really high, but he is not very good as a person. His mind is smaller than a needle and he has a strong desire for revenge!"
Ding Zhiqiang's complicated mood can be seen from two comments.
When selecting courses a few days ago, Ding Zhiqiang clearly remembered that he did not choose Wang Hao's course, and he had learned the rules for selecting courses.
At that time, I breathed a sigh of relief, because I didn’t have to worry about whether to take Wang Hao’s class. Students from the Department of Mathematics would definitely take full classes.
As a result, I chose Wang Hao's class out of nowhere, and was considered by my roommate to be 'cheating again'.
That night……
Several roommates used their hands and feet to scold and yell at each other. There was no serious violence, but in retrospect it still didn't feel good.
Fortunately, everyone believed him in the end, because people in other dormitories also failed to choose to take classes, and people in the next dormitory stood up to confirm his statement.
The next day he went to ask specifically and found out that his name had been added to the list by Wang Hao. Naturally, he was envied by many classmates.
Why use the word ‘suffer’?
Several roommates still remember what happened last semester. They feel that they are not "preferred" by Wang Hao because they did not choose to take classes. They cannot say "100%", but it is also a very important reason.
They were directly excluded.
Ding Zhiqiang, who deceived them, was favored by Wang Hao.
What you don’t get is always in turmoil... This is not just a lyric, it is also very practical.
However, Ding Zhiqiang did not feel that he was being favored. After thinking about it, he still felt that Wang Hao was retaliating against him. The reason was naturally that at the beginning, he went to the Academic Affairs Office to make a report.
This is the reason why I feel so complicated.
Ding Zhiqiang thought Wang Hao was 'retaliating', but he had to admit that a junior student in the Department of Physics taking Wang Hao's class was enough to make many people envious, because others didn't even have the chance.
This chapter is not over yet, please click on the next page to continue reading! When others talked about it, Ding Zhiqiang felt a little proud and there was no way he would drop out of the class.
What to do now?
Should we just wait for classes to start and start classes as normal?
Ding Zhiqiang was unwilling to give up no matter what he thought, mainly because he felt that Wang Hao was seeking revenge and that he seemed to be 'dominated'.
"We must think of a way to say this!" Ding Zhiqiang started thinking about it, and he really came up with a way.
Ask a question!
Didn't everyone on the Internet say that Wang Hao is already a top mathematician, or is he the kind of genius who produces results efficiently?
If you ask a question and Wang Hao can't answer it, it can be regarded as a sigh of relief, right?
When the time comes, I will post a small post to expose it.
hey-hey.
Ding Zhiqiang was thinking, a light flashed in his eyes, and he began to look for problems. Asking questions must not be seen.
If the question is too difficult, such as a famous mathematical conjecture, it is simply looking for trouble and deliberately making things difficult for others.
If the question is too simple, with Wang Hao's level of genius, he will definitely be able to answer it easily.
Ding Zhiqiang kept searching and searching. It took him more than two hours to find a problem that he thought was suitable, and then he began to research patiently.
Research is also necessary.
Before you ask a question, you must first do your own research. Only after you have done your research, and then ask questions if you can't do it, will you really be believed by others.
Ding Zhiqiang is the kind of person who is very perseverant after he has a goal. He even spent a whole night looking at the proof methods for similar problems, and he was still looking at it until eight o'clock the next morning.
By constantly looking up information and learning some basic knowledge on his own, he finally understood most of it.
"Almost, that's enough!" Ding Zhiqiang assessed himself. He looked at the time and saw that it was ten o'clock in the morning. With two dark circles under his eyes, he went to the complex office in high spirits.
He really didn't want to wait a moment longer.
…
This day is Friday.
Wang Hao was sitting in the office leisurely drinking coffee, playing music in his headphones, and occasionally glanced at the book in his hand to read some basic content in other fields.
"Is Teacher Wang Hao here?" a voice called from the door.
Wang Hao looked up and took a closer look and found that it was Ding Zhiqiang who was deeply impressed. He immediately said, "It's Ding Zhiqiang, come in!"
Ding Zhiqiang came over as soon as he entered the office, stood beside the desk and said, "Teacher Wang, I have a problem that I haven't been able to solve. I want to ask you."
"What topic?"
"A geometric proof problem." Ding Zhiqiang opened the prepared booklet. The several draft pages on it were full of mathematical content, as if they were all calculations he had studied carefully.
He flipped through the pages and said, "That's the question. Take a look."
"What question?"
Zhang Zhiqiang was sitting next to him. He experienced continuous blows from genius and felt a kind of frustration in his life. When he saw a student coming to Wang Hao to ask questions, he immediately cheered up and came over and said, "Let me take a look."
He noticed that Ding Zhiqiang seemed to be an undergraduate.
Even if he is an undergraduate in the Department of Mathematics, how difficult can the questions asked be? He has a PhD in computer science and his mathematics level is also very high.
Now is the time to prove your level!
Zhang Zhiqiang went over to take the booklet and read the title, "Draw a closed curve arbitrarily, connecting end to end and not crossing itself. On this curve, it is proved that four points can be found so that they can be connected to form a square..."
"Geometry problem? I know a little bit about it too!"
Zhang Zhiqiang had never heard of this problem, so he returned to his desk full of fighting spirit and asked Ding Zhiqiang to come with him.
The proof begins!
Ding Zhiqiang looked at Zhang Zhiqiang's high-spirited attitude, as if he could solve the problem immediately, and he couldn't help but feel confused, "No way? When I checked, it clearly said that it has not been solved so far, so why does it seem to be so simple?"
Then, he watched Zhang Zhiqiang think about the question seriously.
Think and think...
One minute passed, two minutes passed.
At the third minute, Zhang Zhiqiang finally put pen to paper and drew a closed curve in the shape of a flower.
Then, he looked at Ding Zhiqiang and said expressionlessly, "This question involves profound geometry at first glance, and it cannot be figured out in one or two minutes."
"This classmate, I still have something to do in the laboratory. You should ask Wang Hao. If it doesn't work, I will help you think about it."
Zhang Zhiqiang finished speaking seriously, quickly picked up the coat on the back of the chair, and rushed out of the office in a hurry.
Ding Zhiqiang was stunned when he took the booklet.
"Pfft!"
Next to him, Luo Dayong laughed, while Zhu Ping gave a sarcastic thumbs up towards the door.
Wang Hao tugged at the corner of his mouth, he was a little curious.
Even if it is some advanced geometry, you should know something about it, right?