From University Lecturer to Chief Academician

"Draw a closed curve arbitrarily, meeting end to end and not passing through itself. On this curve, prove that four points can be found so that they can be connected to form a square..."

"Creating a square inside a closed curve, seems to have heard of it?"

Wang Hao thought with some doubts, he felt that he had seen this question before, but he couldn't remember it.

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

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

"Is this a problem..."

"this……"

Wang Hao thought about it carefully and found himself stumped.

There are too many branches of mathematics. The knowledge involved in different subjects is basically repetitive to a certain extent, 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 for proof questions like this pure geometry, the connection is relatively small.

Wang Hao thought carefully for a few minutes, but he didn't think of a breakthrough in the proof. He knew that he didn't have deep research in related fields, and there might even be some problems with lack of foundation. If he wanted to solve this problem in a short time, it was almost impossible to rely on thinking alone impossible.

That being the case...

Wang Hao put down the booklet in his hand, and asked, "Ding Zhiqiang, are you stuck in any step of this proof, or are there any problems that cannot be solved?"

He seemed to be checking the students' problem-solving progress normally.

Ding Zhiqiang murmured inwardly, "As expected," he knew that Wang Hao would definitely ask such a question. 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 hard all night to study related content.

Now comes the use.

"Then I'll tell you."

Ding Zhiqiang said confidently, "Aiming at this problem, I have studied the proofs of built-in rectangles and regular triangles in closed curves."

"It's the method of using hypothetical line segments. Let me talk about rectangles first. First, I need to draw a rectangle..."

Ding Zhiqiang began to explain while making pictures.

He used one night to carefully study two proof papers. The proof process is not complicated, but involves some advanced knowledge.

It takes a lot of time for him to look up this knowledge and understand it.

Now it is necessary to explain the things he understands one by one, 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 explain them in too much detail.

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

The same goes for Luo Dayong.

When Ding Zhiqiang started to explain to Wang Hao, Luo Dayong came over curiously to see what the topic was, and then he found out that it was a proof of making a square inside a closed curve.

Luo Dayong knows this topic, and also knows that no mathematician can prove it so far.

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

Afterwards, Luo Dayong was a little surprised, "This student is amazing, he knows so much advanced knowledge before he is a graduate student."

"Although I only uttered formulas and theorems, I guess the understanding is not very deep. But it is also very remarkable."

Wang Hao felt the same way.

He still didn't know the question asked by Ding Zhiqiang, and no mathematician could solve it, but when he found out that Ding Zhiqiang said something profound, he suddenly felt that his vision was really good.

This Ding Zhiqiang may be a genius!

Ding Zhiqiang is only a junior student in the Department of Physics, and a student of Xihai University. Of course, he does not look down on Xihai University students, but Xihai University’s admission score is low, and other provinces have just passed the key line, and the admission score can be compared with Shuimu University. , For the first time, there is a difference of 100 points in the university, and on average, it can be 20 to 30 points in the first subject of mathematics.

And some students who are gifted in mathematics, even if they just memorize a formula, do the questions at will, don't study hard, don't study the questions very much, and basically have no problem getting close to the full score in mathematics.

Of course.

Just the college entrance examination cannot directly evaluate a student. Some students did not study hard in high school, but they start to work hard in college, and they can stand out later.

Ding Zhiqiang seems to be this kind of student.

At this moment, Ding Zhiqiang seemed to be in a state of excitement, and the more he talked, the more excited he became. What made him excited was that he realized that he was giving a lecture to Wang Hao.

Although nominally, Wang Hao was inspecting his progress in solving the problem, but no matter what, he was also lecturing on the problem to Wang Hao!

Who can do this?

Who else is in the world!

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

This matter spread in the corridor.

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

Ding Zhiqiang felt very nervous when he found several teachers watching behind him. Fortunately, he had reached the final stage of his speech.

After finishing the last step of the explanation, Ding Zhiqiang stopped and looked at Wang Hao tentatively. He didn't know how Wang Hao would react, but what was certain was that Wang Hao definitely didn't know the proof of forming a square inside the curve.

He has studied it carefully, and it is a problem that mathematicians have not yet solved.

Wang Hao was silent for a while, and asked, "That is to say, you have already studied the proof methods of rectangles and equilateral triangles, and you want to use this to study how to prove squares yourself, right?"

This is Wang Hao's understanding.

He still doesn't know that a closed curve has a built-in square, which is a problem that mathematicians haven't solved yet, but after listening to Ding Zhiqiang's explanation, he knows that Ding Zhiqiang understood it according to the answer, not proved it by himself.

So he thought about it carefully, and thought that Ding Zhiqiang wanted to study the proof method of the square after seeing the two proof methods.

This is a great way to learn.

I read some proofs of the same type, and then tried to complete a proof by myself.

Wang Hao immediately appreciated Ding Zhiqiang even more, but he still didn't know how to solve the square problem.

Square, because of the particularity of graphics, is obviously more difficult to prove than rectangle and regular triangle.

Wang Hao felt that it was okay to say that he couldn’t figure it out for a while, and it was a bit embarrassing, but it was the first time for Ding Zhiqiang to ask himself a question. For such a good student, if he couldn’t answer the question for the first time, it might disappoint the student. ?

Students cannot be disappointed!

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

【Task 2】

【Research project name: Proof of a closed curve built-in square (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, and the lowest difficulty level for research and development is F-level, which is the kind of difficult topic in textbooks, and he can deduce it after thinking about it carefully.

If it is a D-level difficulty, it means that research and development issues have been involved.

In other words, no one has been able to prove this question before, and it is a pioneering question. Even if the difficulty is not high, it can reach D level.

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

The reason why those mathematical problems and conjectures have not been proved is not because of how difficult they are, but because there are too many of them. Those who are capable don't bother to study them, and those who are not capable needless to say.

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

Top mathematicians will not 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 if it is worse.

Wang Hao didn't think that Ding Zhiqiang deliberately made things difficult for him. He felt that the other party might be really 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 a triangle and a rectangle. No one has proved it before, right?" He said and looked at Luo Dayong.

Luo Dayong followed and nodded.

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

Wang Haodao, "However, no one has proved it. It doesn't mean that we can't prove it. All research is cutting-edge exploration."

"Well, let's analyze it together."

"First of all, let's take a look at the proofs of rectangles and triangles, which are of great reference value for the proof of squares."

"Let's review together..."

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.

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

Soon others came.

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

Zhang Zhiqiang did go to the computer lab, checked it carefully on the computer, and found that the built-in square of the closed curve is a problem that no one has proved.

That's right!

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

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

This time I came back very confidently, because no one else has proved it, and it is very reasonable for him not to, and he is only a professor of the Department of Computer Science.

When Wang Hao started to explain, there were several people standing next to him, and two teachers stood 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."

After he finished speaking, he began to explain.

Wang Hao was explaining patiently, and the news spread quickly. Several people on the floor came over. They were attracted by "Wang Hao's lecture" because Wang Hao is a very high-level mathematics professor. There are not many opportunities to give lectures, even if you come to join in the fun, come and have a look.

Many people have a herd mentality.

When they found a group of people standing together, they would lean over and listen to a few words to understand what happened, and then they started to listen after they came over.

naturally...

Wang Hao found that knowledge and inspiration poured into his head continuously. The more he talked, 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. When encountering difficulties, he will repeat the explanation to let everyone understand better.

[Task 2, inspiration value +3. 】

[Task 2, inspiration value +7. 】

[Task 2, inspiration value +4...]

When Wang Hao talked about the built-in triangle proof of closed curves, the office was already overcrowded. If you look carefully, there are about 20 people, and many people are standing at the door listening, not sure whether they are listening or gossiping.

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

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

Wang Hao stopped talking and started the next step of explanation, "Those who just came here may not know that the reason why I'm talking about your knowledge is because of Ding Zhiqiang..."

He pulled Ding Zhiqiang to his side and gave a brief introduction to everyone, "Student Ding Zhiqiang asked me a question about a closed curve with a built-in square, so I want to analyze it with him and solve this problem."

"I just reviewed the proofs of rectangles and triangles."

"Then the next step, I think after I have the foundation, I can continue to prove the square."

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

Ding Zhiqiang was completely taken aback.

In the process of Wang Hao's explanation just now, he found that he had a deeper understanding of the proofs of triangles and rectangles, but the square in the next step has not been proved by mathematicians.

Now Wang Hao is directly talking about the next step of proof...

this……

The development of things seems to be different from what I expected?

Ding Zhiqiang stared blankly at Wang Hao, 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 everyone attending the class.

Others also realized what Wang Hao was about to say, and they quickly responded to the possible pioneering research.

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

Several teachers also realized the same, and several picked up their mobile phones and started filming.

Wang Hao didn't care, it was just a small research with D-level difficulty, so he said seriously, "I thought about it carefully, in fact, the method is the same, but the specificity of the square determines that the proof process will be more complicated Some."

"We need to shape two points..."

Wang Hao marked it in the picture, "The closed curve is uncertain, but because it is a closed curve, no matter how it expands outward, there must be a time to return."

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

"These two points are very important, please pay attention..."

"Wow wow ~~"

Wang Hao began to speak patiently, because there were enough inspirations to support him, and the proof process was not too complicated to sort out, so he patiently deduced it step by step, and during the derivation process, the inspiration value was still Constantly increasing.

This is a snowball effect. The more you talk, the more inspiration you get, the more ideas you have, the deeper your understanding, and the smoother you can speak.

When Wang Hao explained it for ten minutes, the matter spread outside the building. Even Zhou Qingyuan in the office of the Faculty of Science knew about it. He and one of his doctoral students came over to take a look.

When he got to the elevator, he found that the door of the office was full of people. He went outside and took a look inside, and found that the inside was already full of people, and it was impossible to squeeze in.

this……

"What exactly is Wang Hao talking about? I heard it has something to do with the built-in square of the closed curve?" Zhou Qingyuan asked a teacher.

"Yes, Professor Zhou, this is a topic that no one has proved, and Wang Hao is doing the proof on the spot!"

"I can't hear it clearly here, but it's good to see."

"Hurry up, hurry up, I'll post a short video."

soon.

Wang Hao completed the last step of explanation.

He was making proofs and explaining at the same time, but the process sounded very smooth, because it didn't involve too advanced set learning content, and many teachers fully understood it, including Luo Dayong and Zhang Zhiqiang.

Ding Zhiqiang understood a part of it, at least he understood the whole proof process, but he didn't understand much because some content that he hadn't been exposed to was involved in the middle.

After Wang Hao finished the explanation, he asked Luo Dayong again, "No one has proven this, 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 will post the proof process on my blog."

After he finished speaking, he looked at Ding Zhiqiang and said, "I have to thank classmate Ding Zhiqiang for this little certificate. You should understand everything, right? If not, you won't ask me any more."

"correct!"

Wang Hao suddenly thought of something. He went to his desk and found two textbooks, one was "Basics of Discrete Mathematics" and the other was "Ordinary Differential Equations". He handed them to Ding Zhiqiang and said, "Student Ding Zhiqiang, you There is great potential in mathematics and, most importantly, you are talented."

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

"It's best to fully understand these two books within three months. Then I'll look into them. If possible, 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 titles of the books, and realized what happened.

Teacher Wang Hao...

He actually completed the proof of the built-in square of the closed curve on the spot. In addition, he also left homework for himself. It is not an ordinary homework, but it is to understand two difficult mathematics professional books within three months?

Ding Zhiqiang suddenly had an urge to cry, and he found that he could not lose money by stealing chickens.

I came to the complex and took away two books.

three months?

In such a short period of time, if you want to thoroughly understand the contents of these two books, you probably don't even have a little leisure time, right?

He thought ahead of his own miserable life.

The understanding of the other teachers in the office was completely different, 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 numbers, which are well-known internationally. Can the students he is optimistic about be inferior?

Ding Zhiqiang left the office with envious eyes.

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

All the teachers seem to be very optimistic about his future prospects. This is the first time that he has received so much attention, and it is in a positive sense.

However, his purpose is not like this!

And he didn't want to spend three months trying to understand irrelevant complex mathematics...

...

The explanation is complete.

The people gathered in the office also slowly dispersed, but the matter was just beginning, and Wang Hao's performance was really amazing.

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

Because of a student's question, he made a proof on the spot.

It's just astonishing.

Some teachers even jokingly said, "Why don't I ask Professor Wang Hao how to prove the Riemann Hypothesis? Maybe he proved it on the spot."

Of course, this is just a joke.

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

There were some unproven small math problems on the Internet before, which were really small problems for Wang Hao, and everyone just laughed it off when they saw such words.

It now appears 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 proved.

The matter was soon spread on the Internet, and there was even a video of the whole process to prove the explanation. In the video, Wang Hao's face was blurred, but it was no different from not doing it, because everyone knew that he was Wang Hao.

There was a heated discussion on the Internet immediately.

During the hot discussion, Wang Hao published the third blog content --

"A small proof that a closed curve has a built-in square".

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."

Next comes the proof.

Discussions on the Internet aside, Wang Hao was very excited, because he found out that the inspiration value of the 'Prime Number Distribution Probability Research' had exceeded 100 points at some point.

At the same time, I also have a clear idea in my mind, knowing the specific content of the mathematical method researched, but because it is too complicated, it seems not easy to sum it up.

This will be a bit of a difficult job.

But never mind.

It is indeed difficult to summarize mathematical methods, but using mathematical methods to go to Kakutani's conjecture, there is already a clear idea.

"The summary of the mathematical method is temporarily put on hold, you can take your time, let's prove Kakutani's conjecture first."

"This conjecture is very valuable!"

Wang Hao happily started his research work.

(seeking a monthly ticket)