"Draw any closed curve, end-to-end and not through itself. On this curve, it is proved that four points can be found so that they can be connected into a square......"

"Shape a square inside a closed curve, I think you've heard of it?"

Wang Hao thought a little puzzled, he felt that he had seen this problem, but he couldn't remember it a little.

The main reason is that his original research direction was partial differential equations, and now he is also studying analytic number theory, and does not involve too many geometric problems.

He just felt as if he had seen it, and thought it was a classic question on a course.

"Is this ......?"

"This ......"

Wang Hao pondered carefully and found that he was stumped.

There are too many sub-disciplines of mathematics, and the knowledge involved in different disciplines has a certain degree of repetition on the basis, but there will definitely be differences in advanced content.

Geometry and function theory are more involved, and there is also a certain connection with differential equations, but such a pure geometry proof problem is relatively small.

Wang Hao thought carefully for a few minutes, and did not think of a breakthrough in the proof, he knew that he did not have a very in-depth study in the relevant field, and there may even be some problems with the lack of foundation, and it is almost impossible to solve this problem in a short time.

Case......

Wang Hao put down the booklet in his hand and asked, "Ding Zhiqiang, are you stuck in this step of the certificate, or is there any problem that can't be solved?" ”

He seems to be checking the progress of the students in solving the problems normally.

Ding Zhiqiang secretly shouted, 'Sure enough', he knew that Wang Hao would definitely ask this, and when he found that the problem could not be solved, he might suspect that the student was deliberately embarrassing himself.

That's why he worked all night to study the relevant content.

Now the use comes.

"Then I'll talk about it."

Ding Zhiqiang said with confidence on his face, "In response to this problem, I have studied the proof of the built-in rectangle and regular triangle of the closed curve. ”

"It's a hypothetical line segment method, I'll talk about a rectangle first, and first draw a rectangle......"

Ding Zhiqiang began to explain while making pictures.

However, he used one night to carefully study two proof papers, and the process of proof was not complicated, but involved some advanced knowledge.

He spent a lot of time looking at this knowledge and understanding it.

Now it is to explain the things that he understands in turn, and there is no difficulty at all, as for the formulas and theorems involved, he can just say them directly, and then do the transformation, and there is no need to talk too much about them.

This little trick doesn't work in front of Wang Hao.

The same goes for Luo Dayong.

When he found that Ding Zhiqiang began to explain to Wang Hao, Luo Dayong was curious to come over to see what the specific topic was, and then he found that it was a proof of making a square in a closed curve.

Luo Dayong knows this problem, and he also knows that no mathematician has been able to prove it so far.

Seeing Wang Hao's confident face, he didn't ask directly, but patiently listened to Ding Zhiqiang's explanation.

Then, Luo Dayong was a little surprised, "This student is amazing, he knows so much advanced knowledge before he goes to graduate school." ”

"Although I only said the formulas and theorems, I guess I didn't understand it very deeply. But it's also remarkable. ”

Wang Hao felt the same way.

He didn't know the question Ding Zhiqiang asked, and no mathematician solved it, but when he found that Ding Zhiqiang said a profound content, he suddenly felt that his vision was really good.

This Ding Zhiqiang may be a genius!

Ding Zhiqiang is only a junior in the Department of Physics, and he is only a student of Xihai University, of course, he does not look down on the students of Xihai University, but the admission score line of Xihai University is low, and the enrollment of other provinces is just above the key line, and the admission score can be 100 points worse than Shuimu University and First University, and the average difference in mathematics can also be 20 or 30 points.

And some students who are talented in mathematics, even if they just memorize a formula, usually do problems at will, do not study hard, do not brush up on problems, and there is basically no problem in mathematics close to full score.

Of course.

Just the college entrance examination cannot directly evaluate a student, some students do not study well in high school, and they can start working hard in college, and they can also stand out later.

Ding Zhiqiang seems to be such a student.

At this time, Ding Zhiqiang seemed to enter a state of excitement, the more he talked, the more state he became, and what made him feel excited was that he realized that he was giving Wang Hao a lecture.

Although nominally, Wang Hao is inspecting his progress in solving the problem, but no matter what, he is also giving Wang Hao a lecture!

Who can do this?

Who else in the world will I be!

Ding Zhiqiang felt a domineering spirit in his heart, but soon felt a little nervous, because many people came to listen to his explanation.

The news spread in the hallway.

The female teacher surnamed Deng in the next office is a gossip person who is even more gossip than Zhu Ping, she saw a student at the door of the office giving Wang Hao a lecture, and it seemed to be very exciting, so she kept standing at the door to watch and see, and beckoned others to watch it together.

When he found that there were several teachers watching behind him, Ding Zhiqiang felt very nervous, but fortunately he had reached the final stage.

After completing the last step of the explanation, Ding Zhiqiang stopped and looked at Wang Hao with a little temptation, he didn't know how Wang Hao would react, but it was certain that Wang Hao definitely didn't know the proof of shaping the square in the curve.

He had studied it carefully, and it was a problem that mathematicians had not yet solved.

Wang Hao was silent for a moment and asked, "In other words, you have already studied the proof methods of rectangles and regular triangles, and you want to use this to study how to prove squares yourself, right?" ”

This is Wang Hao's understanding.

He didn't know that the closed curve has a built-in square, which is a problem that mathematicians have not yet solved, but by listening to Ding Zhiqiang's explanation, he knows that Ding Zhiqiang understands according to the answer, rather than proving it himself.

So he thought about it carefully and thought that Ding Zhiqiang had seen the two proof methods, so he wanted to study the proof method of the square by himself.

It's a great way to learn.

Look at some of the same type of proofs, and then try to complete one yourself.

Wang Hao suddenly admired Ding Zhiqiang even more, but he still didn't know how to solve the problem of squares.

Squares, because of the peculiarities of the figures, are obviously more difficult to prove than rectangles and triangles.

Wang Hao felt that it didn't matter if he couldn't think of it for a while, and he was a little embarrassed, but Ding Zhiqiang asked himself a question for the first time, such a good student, he couldn't answer the question the first time, maybe it would disappoint the student, right?

Students can't be disappointed!

Wang Hao was very concerned about his image in the hearts of students, so he simply looked at the task system, and then established a task.

[Task 2]

[Research Project Name: Proof of Built-in Square of Closed Curve (Difficulty: D).] 】

[Inspiration value: 0.] 】

"D-level difficulty?" Wang Hao glanced at the difficulty level of the task and suddenly realized the problem.

He originally thought that it might be an F-level difficulty problem, but the lowest difficulty in R&D is F-level, which is the kind of difficult question in the textbook, which can be deduced if you think about it carefully.

If it is a D-level difficulty, it is equivalent to the R&D problem has been involved.

In other words, this question has not been proven before, and it is a pioneering question, even if it is not very difficult, it can reach a D grade.

Many small problems and conjectures in mathematics are at this level.

The reason why those mathematical problems and conjectures have not been proven is not because of how difficult it is, but because there are too many of them, and those who have the ability do not bother to study them, and those who do not have the ability naturally need to say more.

The problem of the built-in square of the closed curve is one of them.

Top mathematicians don't spend a lot of time on this small proof, because even if it is proved, it is not very meaningful, and it is not easy to prove it even worse.

Wang Hao didn't think that Ding Zhiqiang was deliberately embarrassed for himself, he felt that the other party might really be researching and wanted to rely on his own ability to solve a problem that no one else had solved.

This spirit is worthy of recognition.

Wang Hao asked, "The proof of a square is much more difficult than that of a triangle and a rectangle, and no one should have proved it before, right?" He said and looked at Luo Dayong.

Luo Dayong nodded.

Ding Zhiqiang showed a surprised expression, in fact, he was so panicked that he couldn't say a word, and he didn't know how to react.

Wang Hao said, "However, no one has proved it, it doesn't mean that we can't prove it, and the research is cutting-edge exploration." ”

"So, let's analyze it together."

"First of all, let's look at the proof of rectangle and triangle, which is very valuable for the proof of square."

"Let's review the ......"

After Wang Hao finished speaking, he began to repeat Ding Zhiqiang's explanation, because of his in-depth understanding of basic knowledge, his explanation was much more detailed, and even Luo Dayong listened to it together.

When he listened to it for the second time, he found that Wang Hao's explanation could make people understand more deeply.

Soon others came over as well.

Teacher Deng, who was standing at the door just now, had slowly approached, as if he wanted to know what they were talking about, and Zhang Zhiqiang simply walked over directly.

Zhang Zhiqiang did go to the computer lab, went to the computer to check carefully, and found that the built-in square of the closed curve was a problem that no one had proven.

I see!

No one could prove it before, and it was normal for him to not be able to solve it, but why did this student ask such a question?

Zhang Zhiqiang felt very strange, and he regained his spirits and came back.

This time he came back very confidently, because no one else had proved that he would not be very reasonable, and he was only a professor in the computer department.

When Wang Hao began to explain, there were several people standing next to him, and two teachers were standing behind, and it was difficult to squeeze in if he wanted to get close to listen.

Wang Hao simply stood up and walked to the small blackboard in the corner, "Since everyone wants to hear it, I'll talk about it here." ”

He finished and began to explain.

Wang Hao was patiently explaining, and the news spread quickly, and several people on the floor came over, they were attracted by the 'Wang Hao lecture', because Wang Hao is a very high-level mathematics professor, and there are not many opportunities to listen to Wang Hao's lectures.

Many people have a herd mentality.

When they noticed a group of people standing together, they would come over and listen to a few words to find out what was going on, and they would come over and start listening along.

Naturally......

Wang Hao found that the knowledge and inspiration in his brain continued to pour in, and the more he spoke, the more energetic he became, and he completely entered the state of teaching.

In fact, he just repeated what Ding Zhiqiang said just now, but his understanding of the content is more in-depth, and when there are difficulties, he will also explain them repeatedly to make everyone understand better.

[Task 2, inspiration +3.] 】

[Task 2, inspiration +7.] 】

[Quest 2, Inspiration +4......]

When Wang Hao talked about the built-in triangle proof of the closed curve, the office was already overcrowded, and there were about 20 of them if you looked closely, and there were many people standing at the door listening, and they didn't know whether they were listening or gossiping.

Because the proof process is not so complicated, Wang Hao finished it in half an hour.

The D-level difficulty research was too easy for him, and in the process of teaching and observing, the inspiration value quickly soared to more than 100 points.

Wang Hao stopped talking and began the next step of the explanation, "Those who have just come may not know that the reason why I am talking about you is because of Ding Zhiqiang's ......."

He pulled Ding Zhiqiang to his side and gave you a brief introduction, "Ding Zhiqiang, he asked me a problem about the built-in square of a closed curve, so I just wanted to analyze it with him and solve this problem." ”

"Just a look back at the proof of the rectangle and the triangle."

"So the next step, I think that once you have the foundation, you can continue to prove the square."

After Wang Hao finished speaking, he pushed Ding Zhiqiang back.

Ding Zhiqiang was completely blindsided.

In the process of Wang Hao's explanation just now, he found that he had a deeper understanding of the proof of triangles and rectangles, but the next square was not proved by a mathematician.

Now Wang Hao directly said that the proof of the next step will be carried out......

This one......

Things don't seem to be what you expected, huh?

Ding Zhiqiang looked at Wang Hao in a daze, but because of Wang Hao's introduction, he was pushed to the middle of the first row by the teachers behind him, as if he had become the leader of the audience.

Others were also aware of what Wang Hao was about to talk about, and there might be groundbreaking research, and they all reacted quickly.

Zhang Zhiqiang turned on his phone and started recording a video.

Several teachers were also aware of it, and several picked up their phones and started shooting.

Wang Hao didn't care, it was just a small study of D-level difficulty, so he said seriously, "I thought about it carefully, in fact, the methods are the same, but the particularity of the square determines that the proof process will be more complicated." ”

"We need to shape two points ...... when we come up"

Wang Hao made a note in the figure, "The closed curve is uncertain, but because it is a closed curve, no matter how much it is unfolded outward, there must be a time to return." ”

"We can assume that the farthest point is S1 and the farthest point on the right is S2."

"These two points are very important, everyone pay attention to ......"

"Wow, wow~~"

Wang Hao began to speak patiently, because there was enough inspiration to support it, and it was proved that the process was not so complicated that it could not be sorted out, so he patiently deduced step by step, and in the process of derivation, the inspiration value continued to increase.

This is the effect of a snowball, the more inspiration and ideas you have, the deeper your understanding will be, and the smoother you will be able to speak.

When Wang Hao explained for ten minutes, the matter spread outside the building, and even Zhou Qingyuan from the office of the School of Science knew about it, and he came over with a doctoral student under his command to take a look.

When he first entered the elevator, he found that the door of the office was full of people, and he went outside to take a look inside, and found that the inside was already occupied, and it was impossible to squeeze in again.

This......

"What is Wang Hao talking about? I've heard that it has something to do with closed curves and built-in squares? Zhou Qingyuan asked a teacher.

"Yes, Professor Zhou, this is a topic that no one has proven, Wang Hao is proving it on the spot!"

"I can't hear you well here, but it's nice to see."

"Hurry up and shoot, hurry up and shoot, I still have to send a short video."

Soon.

Wang Hao completed the last step of the explanation.

He was doing the proof and explaining at the same time, but the process sounded very smooth, because it did not involve too advanced ensemble content, and many teachers fully understood, including Luo Dayong and Zhang Zhiqiang.

Ding Zhiqiang understood part of it, at least the whole proof process was understood, but it involved some content that he had not been exposed to halfway, so he didn't know too much.

After Wang Hao finished explaining, he asked Luo Dayong again, "This has been proven by no one, right?" ”

Before Luo Dayong could speak, Zhang Zhiqiang hurriedly said, "Yes, I checked carefully, and no one has proved it." ”

Wang Hao said, "Then I'll post the proof process on the blog." ”

After he finished speaking, he looked at Ding Zhiqiang and said, "I also want to thank Ding Zhiqiang for this little proof, you should understand, right?" If there is no place to ask me again. ”

"That's right!"

Wang Hao suddenly thought of something, he went to the desk and found two teaching textbooks, one was "Fundamentals of Discrete Mathematics" and the other was "Ordinary Differential Equations", he handed it to Ding Zhiqiang, and said, "Ding Zhiqiang, you have great potential in mathematics, and most importantly, you are very talented. ”

"If you don't know how to study, I recommend you to understand these two books completely, just this semester."

"It's best to understand all these two books thoroughly within three months, and then I'll investigate them, and if I can, I'll recommend other books to you, your knowledge base is still lacking......"

Ding Zhiqiang took the two books in a daze, looked down at the names of the books, and realized what was happening.

Teacher Wang Hao......

He actually completed the proof of the built-in square of the closed curve on the spot, and in addition, he also left himself homework, which was not an ordinary homework, but to understand two difficult mathematics books in three months?

Ding Zhiqiang suddenly had the urge to cry, and he found that stealing chickens and rice was not successful.

I took a trip to the complex and took away two books.

Trimester?

In such a short period of time, if you want to eat the content of these two books thoroughly, I guess you don't even have a little leisure time, right?

He thought about his miserable life in advance.

The other teachers in the office had a completely different understanding, and they looked at Ding Zhiqiang with surprised eyes.

This little fat man is definitely not simple!

Wang Hao has completed the demonstration of Artin's constant and the results of Mersenne prime, and has a certain reputation in the world.

Ding Zhiqiang left the office with envious eyes.

He didn't know whether he should be happy or disappointed, and when he left, several teachers asked him his name, asked him about his major, and said words of encouragement to him.

All the teachers seemed to be optimistic about his future prospects, and it was the first time he had received so much attention, and it was in a positive sense.

But that's not his purpose!

And he didn't want to spend three months trying to figure out complicated math that didn't matter......

……

Explanation complete.

The people gathered in the office also slowly dispersed, but things had only just begun, and Wang Hao's performance was amazing.

He made a proof that the square is built into a closed curve, which is not a big deal, and it is nothing compared to other results, but the thing itself is very interesting.

Because of a student's question, he gave a testimony on the spot.

It's amazing.

Some teachers even joked, "Why don't I ask Professor Wang Hao, how does the Riemann conjecture prove it?" Maybe he proved it on the spot. ”

Of course, this is just a joke.

Others were also shocked by Wang Hao's level of genius.

There were some small math problems on the Internet that had not been proven before, but they were really small problems for Wang Hao, and everyone just laughed when they saw this kind of thing.

Now it seems to be true.

Wang Hao demonstrated this level of ability on the spot, and it seemed that there was no difficulty for him to make a proof that no one else had proven.

Soon the matter was spread to the Internet, and there was even a video of the whole process of proving the explanation, in which Wang Hao's face was blurred, but there was no difference from not doing it, because everyone knew that he was Wang Hao.

There was a heated discussion on the Internet.

In the process of heated discussion, Wang Hao released the third blog content--

"A Little Proof, Closed Curves Built-in Squares".

The content of this blog is a little different, the first sentence is to introduce the source of the proof, "This is a question from a student named Ding Zhiqiang, he is researching this problem, and his research has given me a lot of inspiration." ”

The next step is the proof.

Putting aside the discussion on the Internet for the time being, Wang Hao was very excited, because he found that at some point, the inspiration value of 'prime number distribution probability research' had exceeded 100 points.

At the same time, I also have a clear idea in my head, and I know the specific content of the mathematical method researched, but because it is too complicated, it seems that it is not easy to summarize.

It's going to be a bit harder.

But it doesn't matter.

It is indeed difficult to summarize the mathematical method, but there is a clear idea of using the mathematical method to solve the Kakutani conjecture.

"The summary of the mathematical method has been put on hold for the time being, so you can take your time, and let's prove the Kakutani conjecture first."

"This conjecture is very valuable!"

Wang Hao happily began his research work.

(Ask for a commuter pass)