Kakutani conjecture, also called Hailstone conjecture, Kratz problem, 3X 1 problem, the content of the conjecture is any natural number x. If it is an odd number, calculate 3x 1. If it is an even number, divide it by two.

If you keep calculating like this, you will eventually fall into the 4-2-1 cycle at the bottom.

The content of this conjecture is very simple. Because of this, it has become well-known. There has always been a strong interest in solving the Kakutani conjecture in the mathematical community.

Probably for this reason, the Kakutani conjecture has become very valuable, even more valuable than the seven major mathematical conjectures of the millennium.

The first person to offer a reward for the Kakutani conjecture was seventy years ago, a man named Paul Endos, who was willing to provide $500 to the prover of the Kakutani conjecture.

Later, many people in mathematics, business and even other fields launched bounties for Kakutani's conjecture. Although the amount was not large, it was enough to prove people's interest in Kakutani's conjecture.

The current highest prize for the Kakutani conjecture comes from a Japanese company called Baku Times. They announced that they will provide 120 million yen to the prover of the Kakutani conjecture.

According to the exchange rate at the time, it was equivalent to US$1.2 million.

In addition, some scientific institutions have also set bonuses for proving the Kakutani conjecture, ranging from twenty thousand, fifty thousand, one hundred thousand... too many to count.

At the same time, there are also related rewards in China.

Kakutani's conjecture was selected into the "10,000 Scientific Problems (Mathematics Volume)" jointly published by the Ministry of Education, the Ministry of Science and Technology, the Academy of Sciences, and the Natural Science Foundation of China. It was listed as the fourth difficult problem in the mathematics volume and set a

Millions of RMB for settlement.

The fact that so many individuals, scientific institutions, and companies have announced rewards for solving the Kakutani conjecture is enough to show the appeal of the Kakutani conjecture.

If someone can complete the proof of Kakutani conjecture, he can get all the above bonuses.

Even if it was just for a large bonus, Wang Hao was very motivated to complete this research. This was one of the reasons why he put the proof of the Kakutani conjecture before the summary of mathematical methods.

After confirming that he could complete the proof of Kakutani's conjecture, Wang Hao began to immerse himself in research.

at the same time.

Wang Hao's on-site demonstration of a square built into a curve also aroused heated discussion on the Internet. Many people who saw it could only praise, "Wang Hao, that's so cruel!"

"Students ask questions and answer them immediately. This is still a problem that has not been proven in mathematics."

"This is what you call a top mathematician. After reading those reports about how powerful a certain mathematical genius is, how powerful are you? Let's compare?"

Many professional scholars feel that Wang Hao's research is completely irrational and logical. He solved a problem that has not been solved in the mathematics community with just a little thought?

This is so buggy!

Only professional scholars will read all of them. They found that Wang Hao really spoke well and smoothly, and to a certain extent they doubted whether the proof was made on the spot.

"Perhaps it has been proven and is just an explanation?" Someone raised doubts.

When the news broke, many scholars were indeed skeptical. Mainly because they could not understand that someone could temporarily solve an unfinished proof in mathematics. Similar problems, even if they are carefully studied, will most likely have no results.

…

However, some authoritative mathematicians also stood up and said, "You can't doubt just because you can't do it. In the mathematical world, when you are also doing basic research, the gap is much larger than imagined."

This is the difference in talent.

Scholars from several domestic universities have discussed this issue.

Some old mathematics professors can understand why Wang Hao can easily complete proofs that have not yet been completed in the mathematics world, while others can't get the results after hard research.

This is the gap between people, and the gap in the mathematical world is even greater.

Those mathematicians who can achieve results in the field of basic mathematical research must be extremely top-notch and extremely smart people.

This kind of person cannot be understood by ordinary people.

For example, Terence Tao.

Terence Tao is not famous because he won Fields. It can even be said that most people don’t know what field of research he relied on to win Fields.

Terence Tao is most famous for his "child prodigy resume".

When he was only 8 years old, he had already entered secondary school and was studying mathematics and physics at Flinders University, not far from home.

He won the gold medal in the Olympic Mathematics Competition at the age of 13. This record has not been broken until now.

He entered the Department of Mathematics at Flinders University at the age of 14, and received an honorary science degree at the age of 16. A year later, he obtained a master's degree and was admitted to Princeton University in Amerika to study for a doctoral degree.

If you put this resume on display, even other Fields laureates would feel ashamed of themselves.

It sounds like going to college at the age of fourteen is not a big deal, but consider that he first won an International Olympic gold medal, setting a record for the youngest age to win an Olympic gold medal.

Two years before he won the gold medal, he won silver and bronze medals respectively. In other words, he had been participating in Olympiads since he was 11 years old and was able to win awards, while children of the same age had not yet graduated from elementary school.

Another example is Peter Schultz.

Schulz went to college much later, but he obtained a mathematics degree from the prestigious University of Bonn in just one year.

Famous foreign schools are strict in admission and exit, and it is not easy for every student to graduate. Peter Schultz completed all the subjects in one year, and obtained extremely excellent results in all mathematics courses.

Obviously.

This is not something ordinary people can understand.

Many old mathematics professors know very well that in the field of basic mathematics research, results cannot be achieved through hard work. Talent is much more important than hard work. After working hard all their lives, they can only do some leftover research work on mathematical theory, while some young people

Before the age of thirty, a person can win the Fields Medal for his contribution to a certain field.

How does this compare?

The gap is really too big, and it is impossible to catch up with hard work. It is normal for a mathematical genius like Wang Hao to be unable to understand.

The hot public discussion on the Internet actually had no impact on Wang Hao. At most, it just caused more people to talk about it. The one who was more affected was Ding Zhiqiang.

Ding Zhiqiang became famous.

Behind some, a little fat man appeared who was favored by Wang Hao. Wang Hao also took out two books and gave them to the little fat man, enthusiastically wanting him to study and increase his basic knowledge.

…

So many people knew that Wang Hao was interested in a student named Ding Zhiqiang.

This is not talked about much on the Internet. After all, Ding Zhiqiang is just a student. A college teacher will have many students, and it is normal to be optimistic about a certain student.

But it is different at Xihai University, especially in the related physics department. Almost everyone knows about Ding Zhiqiang and knows that he is a student favored by Wang Hao.

Ding Zhiqiang became a celebrity in the physics department.

When some teachers are in class, they will look at Ding Zhiqiang in particular to see what is special about him.

In some courses, when teachers call students to answer questions, they will subconsciously think of Ding Zhiqiang, making it impossible for Ding Zhiqiang to skip class and even have to listen carefully in class.

This is not the most painful thing.

On the weekend, Ding Zhiqiang was finally able to take a break and picked up his mobile phone to play a game.

The roommate next to him saw it and immediately reminded him, "Ding Zhiqiang, what are you doing? How can you waste time playing games? Uninstall it immediately!"

"Read a book, read a book. Teacher Wang Hao thinks so highly of you, you can't let him down!"

The other two roommates also looked over with approval, "Ding Zhiqiang, you can't lose yourself in playing with things like us, read more books when you have time!"

"You are the hope of our dormitory, and we expect you to become a mathematician!"

"When you become a mathematician in the future, not to mention getting Fields, as long as you get a small prize, I can go out and brag..."

"Read a book quickly, don't play games."

"..."

Ding Zhiqiang put down his phone with a dark face.

A few minutes later, a roommate asked others to play blackmail together. Ding Zhiqiang immediately picked up his phone again and actively entered the room where he was playing blackmail, "Add me!"

He was taken off immediately.

The roommate reminded Ding Zhiqiang again not to play games, and then said to the others, "Let's go to the dormitory next door. We can't affect Ding Zhiqiang's study!"

"Yes, let's go!"

"Ding Zhiqiang, read carefully."

"..."

Watching his roommates walk out of the dormitory together, Ding Zhiqiang suddenly felt the urge to cry. Why is this happening?

He wants to play games and hack, but he doesn’t want to read books!

"Ah~~~"

Looking at the contents in the book, he felt like he was going crazy.

…

During one weekend, Wang Hao spent most of his time in the teaching and research office.

On the weekends, the teaching and research office was relatively quiet. He was alone in there doing research patiently, and the progress of the results was relatively remarkable. He had completed most of the proofs.

The Kakutani conjecture is not a trivial mathematical problem. The entire proof requires the use of the entire method studied, and it takes a long time to carefully consider, calculate, and derive.

Even if he had a general idea and knew the overall process, it would still take a long time. He felt that the entire proof process would take about twenty pages.

Twenty pages does not sound like too much. In fact, compared to the proof of a problem, the content is already very much. Each step of the proof needs to be studied carefully. It can be said that each step is carried out very efficiently.

Difficulty.

Wang Hao devoted 100% of his energy to research, and would take a break when he felt tired in the middle. Then he saw the mobile phone communication message sent by Cao Dongming.

…

"Professor Wang Hao, how is your research going?"
To be continued...