The Kakutani conjecture, also known as the hail conjecture, the Klatz problem, and the 3X+1 problem, is that the content of the conjecture is any natural number x, if it is an odd number, it is calculated as 3x+1, and if it is an even number, it is divided by two.

If you keep doing this, you will end up in a 4-2-1 cycle at the bottom.

The content of this conjecture is very simple, and because of this, it has become widely known, and there has always been a strong interest in solving the Kakutani conjecture in the mathematical community.

It is probably for this reason that the Kadoya conjecture has become very valuable, even more valuable than the seven mathematical conjectures of the millennium.

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

Later, many people in the fields of mathematics, business, and even other fields launched a reward for Kakutani's conjecture, although the amount was not large, but it was enough to prove that people were interested in Kakutani's conjecture.

At present, the top prize for the Kakutani conjecture comes from a Japanese company called Baku Times, and they announced that they will provide 120 million yen to the certifier of the Kakutani conjecture.

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

In addition, there are some scientific institutions that have also set bonuses for the proof of the Kakutani conjecture, which is 20,000, 50,000, and 100,000...... There are too many to count.

At the same time, there are also related bounties 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 Committee, and was listed as the fourth problem in the mathematics volume, and was set to solve it with 1 million yuan.

The fact that so many individuals, scientific institutions, and companies have announced bounties for the solution of the Kakutani conjecture is enough to see the appeal of the Kakutani conjecture.

If someone is able to complete the proof of Kakutani's conjecture, they will receive all of the above prizes.

Even if it was just for a large prize money, Wang Hao was very motivated to complete this research, which is one of the reasons why he put the proof of Kakutani's 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.

Meanwhile.

Wang Hao's on-site proof of completing the built-in square of the curve also caused heated public opinion on the Internet, and many people watched the video, and they could only praise it, "Wang Hao, it's too cruel!" ”

"The student asks a question and answers it immediately, or is it a question that has not been proven by the mathematical community."

"This is called a top mathematician, look at those reports that a certain mathematical genius is so powerful, how powerful, to compare?"

Many professional scholars feel that Wang Hao's completion of research is simply unreasonable logic, a problem that has not been solved in the mathematical world, and he solved it with a little thought?

That's buggy, isn't it?

Only professional scholars will watch all the videos, and they found that Wang Hao did speak very well and smoothly, and they also doubted to a certain extent whether it was a proof made on the spot.

"Maybe it's been proven, just to explain?" Doubts have been raised.

When the news broke, there were indeed many scholars who doubted, mainly because they couldn't understand that someone could temporarily solve the unfinished proof in the mathematical community, and similar problems, even if they were carefully studied, there was a high probability that there would be no results.

However, there are also authoritative mathematicians who stand up and say, "You can't doubt because you can't do it, and in the mathematical community, the gap between doing basic research is much bigger than imagined." ”

That's the talent gap.

Scholars from several universities in China have discussed this.

Some old professors of mathematics can understand why Wang Hao can easily complete the proof that has not been completed in the mathematics community, while others can't get results after hard work.

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

Those mathematicians who can make achievements in the field of basic research in mathematics must be extremely top-notch and extremely intelligent people.

This kind of person is incomprehensible to ordinary people.

For example, Tao Zhexuan.

Tao Zhexuan's fame is not because he obtained Fields, it can even be said that most people don't know what field of research he relied on to obtain Fields.

Tao Zhexuan is best known for his 'prodigy resume'.

At the age of eight, he was already in secondary school and studying mathematics and physics at Flinders University, not far from home.

At the age of 13, he won the gold medal in the Mathematics Olympiad, a record that has not been broken until now.

He entered Flinders University's Department of Mathematics at the age of 14 and received an Honorary Degree in Science at the age of 16, and a year later, he received a Master's degree and was accepted to Ameri Kempton University for a PhD.

Even other Fields Medalists would be ashamed of themselves when this resume was put on display.

It sounds like a big deal to go to college at the age of fourteen, but consider that he won an international Olympic gold medal first, setting a record for the lowest age for an Olympic gold medal.

In the two years before he won the gold medal, he won the silver and bronze medals, in other words, he participated in the Olympiad from the age of 11 and was able to win prizes, while children of the same age had not yet graduated from primary school.

Another example is Pete Schultz.

Schultz went to university much later, but it took him only one year to get a degree in mathematics from the prestigious University of Bonn.

It is not easy for every student to graduate, but Pete Schultz completed all the subjects in one year, and obtained excellent results in mathematics majors.

Apparently.

This is not something that ordinary people can understand.

Many old professors of mathematics are very clear that the basic research field of mathematics is not able to produce results through hard work, talent is more important than hard work, they work hard all their lives, and can only do some research work on the leftovers of mathematical theory, and some young people can win the Fields Medal for their contributions to a certain field before the age of 30.

How does this compare?

The gap is too big, it is not hard to catch up at all, such as Wang Hao, a mathematical genius, it is normal to not understand.

The heated public opinion on the Internet actually has no impact on Wang Hao, at most, more people are talking about it, and it is Ding Zhiqiang who is more affected.

Ding Zhiqiang became famous.

Behind some videos, a little fat man who was favored by Wang Hao appeared, and Wang Hao also took out two books for the little fat man, and he was very enthusiastic about letting him learn to increase his basic knowledge.

So many people know that Wang Hao is optimistic about 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 the associated physics department, almost everyone knows Ding Zhiqiang, and they also know that he is a student who is favored by Wang Hao.

Ding Zhiqiang became a celebrity in the physics department.

When some teachers are in class, they will pay special attention to Ding Zhiqiang to see what is special about him.

In some courses, when the teachers ask students to answer questions by name, they will subconsciously think of Ding Zhiqiang, which makes it impossible for Ding Zhiqiang to skip class, and even has to listen carefully in class.

And that's not even the most painful.

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

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

"Read, read, Teacher Wang Hao is so optimistic about you, you can't let him down!"

The other two roommates also looked at it with approval, "Ding Zhiqiang, you can't be as discouraged as we are, read more books when you have time!" ”

"You're the hope of our dorm, and we expect you to be 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......"

"Hurry up and read books, don't play games."

“……”

Ding Zhiqiang put down his phone with a dark face.

A few minutes later, a roommate beckoned the others to open the black together, Ding Zhiqiang immediately picked up the mobile phone again, and actively entered the black room, "Add me one!" ”

He was immediately knocked out by T.

The roommate reminded Ding Zhiqiang again not to play games, and then said to the others, "Let's go, let's go to the next bedroom, we can't affect Ding Zhiqiang's study!" ”

"Yes, let's go!"

"Ding Zhiqiang, read well."

“……”

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

He wants to play games, he wants to be black, he doesn't want to read!

"Ah~~~"

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

……

On a weekend, Wang Hao spent most of his time in the department.

On weekends, the teaching and research department is still relatively quiet, a person is bored in it and patiently does research, and the progress of the results is relatively significant, and he has completed most of the proofs.

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

Even if he has the idea of the general direction, he knows that the overall process still takes a long time, and he feels that the whole proof process will take about 20 pages.

Twenty pages doesn't sound like a lot, but in fact, it's a lot of content compared to a proof of a problem, and each step of the proof needs to be carefully studied, so to speak, and each step is very difficult.

Wang Hao put 100% of his energy into doing research, and he would take a break when he felt tired halfway, and then he saw the mobile phone communication message sent by Cao Dongming.

"Professor Wang Hao, how is your research going?"

"Is there any progress?"

Cao Dongming sent several similar messages, and they were sent at different times.

Wang Hao remembered that there was another 'task one' study, and he glanced at it and found that the inspiration value had reached '130' points, and the research could be said to have been completed.

But he really didn't have the heart to do a summary of the content of material data mining, so he simply replied, "I've been very busy lately, and I will definitely summarize it when I have time." ”

He was just about to put down his phone when he saw a reply, "What are you busy with?" ”

Two seconds later, the message was withdrawn.

Another message came in, "Thanks, excuse me, you're busy." ”

“？？”

Wang Hao didn't understand it and didn't care too much.

In fact, Cao Dongming wanted to urge Wang Hao, but he was afraid of arousing Wang Hao's disgust, the project in his hand recently was progressing smoothly, just an adjustment of the smelting temperature, so that the two projects have made a lot of progress, and it is expected to be more than two months faster than the normal progress.

The pace of progress is astonishing.

The most important thing is that I feel that the goal is clear, and I can't do clueless experiments like the original, so I can only use continuous experiments and accumulate experience to improve the progress, not to mention the consumption of a lot of money, and it may not be able to achieve results.

Using the data analysis method researched by Wang Hao, the scientific analysis of the process can greatly reduce the cost consumption and quickly achieve the goal.

Cao Dongming has only experienced it once, and he has already fallen in love with this feeling.

Many people in the Institute of Aeronautical Materials learned the news, and they were also shocked, and they immediately paid more attention to Wang Hao's research, and many experts in material calculation and data mining began to carefully study Wang Hao's data analysis methods.

It's just that because the content of the method is too complex, it takes a lot of time to understand it all, and the understanding is not necessarily accurate in application.

The Institute of Aeronautical Materials still hopes that Wang Hao can explain again, especially how to apply his method.

Opposite side.

Cao Dongming looked at Wang Hao's reply and felt a little lost.

Qu Shigang suddenly asked, "How is it?" ”

Cao Dongming said a little depressed, "Professor Wang Hao said that he is very busy, and he will help tidy it up when he has time." ”

"That's an obvious reluctance to help!" Qu Shigang frowned vigorously, "It must have been the last time I made a report, and there were too few people to listen to it, and we couldn't entertain it well." ”

"Now he doesn't want to put any effort into it."

"Do you want to think of a way?" Qu Shigang thought about it and said, "So let's go to Xihai University and ask Wang Hao to talk about it?" It's okay to apologize, his method is too important for us! ”

A professor next to him pondered and asked, "This is a good solution, but in what name?" You can't say it's an apology, right? ”

Several people in the office fell into deep thought.

Cao Dongming suddenly said, "Otherwise, we will join several departments to go to Xihai University in the name of inspecting the Navitas laboratory?" ”

"The Navitas laboratory at Seohai University is very distinctive in the research field of nanovitas materials, and there are many materials in aviation, which also need to use nanovitas technology. That's what we're going to ......."

"Great idea!"

Qu Shigang's eyes lit up when he heard it, "We are doing materials research, so we will go in the name of the investigation laboratory." When the time comes, even if you apologize in person! ”

"Face is small, research is big!"

"Yes, yes, yes......"

……

Complex building office.

Wang Hao's crazy mode is finally over, he has completed the main proof part, and the next job is to add some steps and carefully refine it from beginning to end.

If you want to submit a paper, you need to go through it again and list the main certification process.

It was Tuesday.

In the morning, the office was very deserted, only Zhang Zhiqiang and Wang Hao were there.

Zhang Zhiqiang noticed that Wang Hao had been busy, and he asked, "What are you busy with?" What kind of 'little research' is it? There was a bit of irony in those last words.

Wang Hao's so-called small research may become a big problem that cannot be solved for others.

Wang Hao nodded and said, "It's still a conjecture, but it's not a small study." ”

"What is it?"

"Kadotani conjecture."

"Oh~~"

Zhang Zhiqiang nodded calmly, reacted suddenly, and got up from the chair with a 'poof', "Really?" Kakutani conjecture? ”

"Right?"

"How's the research going?" Zhang Zhi asked compulsively.

"It's okay." Wang Hao hesitated and said, "It's not done yet." ”

"Oh~~"

Zhang Zhiqiang sat down again, and exhaled lightly, it is normal if it is not completed, Kakutani's conjecture is not a small problem, and it proves that it is definitely a big problem that shakes the world.

At this time, I heard Wang Hao add, "It is estimated that it will be tomorrow." ”

“——？”

Zhang Zhiqiang was stunned when he heard this, his eyes looked at Wang Hao without moving, his mouth was half-open, as if time had no effect on him, and it took a long time before he asked definitively, "You're not joking, are you?" ”

"Not ......"

"I'm X!" Zhang Zhiqiang squirted a mouthful of dirty words, and immediately reacted to cover his mouth hard, and he also glanced at the office door, and found that there was no one else at the door, so he quickly closed the door.

When he walked back again, he whispered, "Did you really prove it?" ”

"Not lying to me? Right? This is amazing, Kakutani guessed......"

"Is it still on your blog this time?"

His sneaky appearance made Wang Hao feel very strange.

How?

Lost sight?

Wang Hao didn't say anything more, but looked at Zhang Zhiqiang with a puzzled expression, as if he was looking at a fool.

Zhang Zhiqiang reacted, "Of course, it is impossible to post it on the Internet." How are you going to publish? Do you want to participate in an academic report or submit a paper? ”

"I haven't thought about it yet."

Wang Hao shook his head and said, he went to make a cup of coffee, and when he came back, he looked at his mobile phone, and found that there was a message from overseas, it was Bruce Pulitzer, the editor-in-chief of "New Advances in Mathematics".

Bruce Pulitzer sent a message to make an appointment with Wang Hao.

The four major journals of mathematics must not worry about manuscripts, but they must also have a good relationship with mathematicians in order to maintain high-quality submissions.

Bruce Pulitzer noticed that Wang Hao's content published on domestic blogs did not understand the explanation in Chinese, but that did not affect his understanding of the content, because some news had already reached abroad.

The proof of the counterexample of the palindromic number and the shaping of squares within curves are good little studies and very interesting.

The first proof completely disproves the palindromic number conjecture.

The second is a problem that most scientists have not been able to prove for a long time.

Both of these small studies can be published in New Advances in Mathematics, which does not occupy much space, but the content is classic, and there is certainly no problem in terms of quality.

Wang Hao noticed the message sent by Bruce Pulitzer and immediately asked, "Submit it now, can it be published in the next issue?" ”

He said that the next issue was in early March, and now it is the end of February.

After waiting for a short time, he received a reply from Bruce Pulitzer, "The next issue has been scheduled, and the submission is now, and it can only be published in April at the earliest." ”

Wang Hao quickly replied, "What if it's a proof of the hail conjecture?" ”

This time the wait was a little longer.

Bruce Pulitzer replied, "We will consider temporary reprinting of famous math problems, and we will publish them on our website." ”

Wang Hao replied with two letters, "OK." ”

Across the ocean.

Bruce Pulitzer was sitting in his office leisurely drinking coffee, and when he saw Wang Hao's question, he felt that the other party must be joking.

"Unexpectedly, Wang Hao is also very humorous......"

Bruce Pulitzer shook his head thinking about it, and then saw Wang Hao reply with two letters, and then continued to take a sip of coffee, reacted suddenly, and stared at the screen with wide eyes, "OK?" ”

"He's not going to come, is he?"

“！！”