Rule system

One day in 1976, the front page of the "Washington Post" reported a piece of mathematics news.

The article narrates a story: In the mid-1970s, on the campuses of famous American universities, people seemed to go crazy, day and night, playing a math game without eating and sleeping.This game is very simple: write a natural number N (N≠0) arbitrarily, and transform it according to the following rules:

If it is an odd number, the next step becomes 3N+1.

If it is an even number, the next step becomes N2.

Not only students, but even teachers, researchers, professors and scholars have joined.

Why is the charm of this game enduring?Because people have discovered that no matter what a non-zero natural number N is, it cannot escape back to the bottom 1.To be precise, it is impossible to escape the 4-2-1 cycle that falls to the bottom, and it will never escape this fate.

Everyone can start from any positive integer and perform the following operations continuously. If it is an odd number, multiply the number by 3 and add 1; if it is an even number, divide the number by 2.

This calculation continues until the first time you get 1 to be considered as the end.

Can every positive integer be calculated according to this rule to get 1?This is the Sugula conjecture, also called the "hail conjecture, Kakutani conjecture", including the later Kratz problem, which is an interesting '3X+1' problem in mathematics.

Foreign countries like to call the '3X+1' problem the Sugura Conjecture or Hail Conjecture, while in China it is called the Kakutani Conjecture, because it was a person named Kakutani who spread the problem to China.

This question sounds simple, but it is not easy to prove it.

For decades, many top mathematicians have invested a lot of energy and failed to produce rigorous proofs.

So guessing is still just guessing.

...

When Li Yi talked about Zhao Yi's process, he used a part of Kakutani's conjecture, which made the people in the conference feel that there is a theoretical loophole in the'effective and irrelevant carry method'.

Unless Kakutani's conjecture is proved one day, there will always be a loophole in the "effective and irrelevant carry method".

Therefore, mathematical theory is the foundation of all science.

What people in the venue didn't expect was that Zhao Yi's reaction turned out to be to thank Professor Li Yilai excitedly, and said, "I haven't found the proof of Kakutani's conjecture."

This turning point is really amazing.

A group of people around grew up with their mouths widened, and they didn't know what to do.

After Zhao Yi thanked Professor Li Yilai, he returned to the stage with excitement. Facing a doubtful and curious look, he did not talk about Kakutani's conjecture, but continued to talk about the "effective and irrelevant carry method".

This time is almost over.

The proof step that includes the "Kakutani Conjecture" is the most critical part of the "effective and irrelevant carry method". As long as the steps pass, the rest is easy to understand.

"...So we can be sure that this step is harmful to the overall progress, and we can choose to give up!"

"This is my effective and irrelevant carry method!"

"The above is my proof!"

"thank you all!"

After Zhao Yi finished speaking the last sentence, he took two steps back and bowed politely. Then there was fierce applause in the venue.

This speech was very successful.

Although it is doubtful whether the Kakutani Conjecture is proved, even if the Kakutani Conjecture is not proven, because the computer performance does not involve the theoretically possible “counter-example numbers”, the “effective and irrelevant carry method” can definitely be used.

This is the most important thing in the computer industry.

Computer algorithms do not need to be'perfect and accurate', just like any software will have loopholes, the purpose of computer algorithms is to really use them, not to be perfect in theory.

No one can guarantee that a car is 100% free from the factory; an artificial intelligence translator does not require perfect translation capabilities, and can guarantee a correct rate of over 90%, which is already quite successful.

Computer algorithms are the bottom layer, and the accuracy rate is more demanding, but only the possibility of'inaccuracy' in theory is equal to a 100% accuracy rate.

So the "effective and irrelevant carry method" is already a perfect algorithm.

The speech is over.

No one left in the venue. Everyone still sat in their seats, watching Zhao Yi stepping down with curiosity. They all wanted to know the question just now, "Did he really prove Kakutani's conjecture?"

They want answers.

Of course, Zhao Yi knows what everyone thinks, but it is impossible for him to prove a mathematical conjecture in detail in his speech on "effective and irrelevant carry method". The reason why he was very excited is also a proof of mathematical conjecture, which is of great significance. Of significant.

"Effective and irrelevant carry method" is just a computer algorithm, no matter how subtle the process and the wide range of applications, most ordinary people will not care at all.

Mathematical conjectures are different.

If a certain mathematical conjecture is proved, his name may appear in the mathematics textbooks of elementary and middle schools.

Keep your name in history!

The postgraduate building of Yanhua University, where he is currently speaking, is obviously not a suitable place for demonstrating mathematical conjectures. What's more, he has not yet written relevant papers and has not directly contributed.

just in case……

Some shameless guy, after watching the whole process, quickly sorted out and submitted the paper, the copyright of the certificate could not be guaranteed.

The probability of this happening is not small, after all, mathematical conjectures prove too significant.

Zhao Yi looked at the gaze of the audience, he thought about it carefully, then returned to the stage and said, "Let me show you the idea of ​​proof of Kakutani's conjecture!"

Suddenly.

Everyone is energetic.

Some people think that Zhao Yi is talking big, but he is not talking big, only after hearing it can he be sure.

The venue was silent.

"A mathematical problem may have many ways of proof. My proof method is to use the binary thinking of a computer."

Zhao Yi went to the blackboard and wrote a number--

11011.

This is the binary number 27.

In Kakutani's conjecture, 27 is a very'tough' number. It looks a bit unsurprising, but according to the calculation method of Kakutani's conjecture, it takes 77 steps to reach the peak of 9232, and then after 32 minutes to reach the bottom. The value is 1, the entire conversion process requires 111 steps, and its peak value is 9232, which is more than 342 times the original number 27.

Next, Zhao Yi began to calculate 27 in the way of "3X+1". The difference is that every number he writes is expressed in binary. He wrote more than one hundred binary numbers in a row and arranged the blackboard. fully.

Everyone in the audience had a headache. The blackboard was full of 1 or 0, as if they were drawing.

During the whole process of calculation, the only thing everyone in the field was sure of was that Zhao Yi was really a'binary' super genius, even if it was over a thousand four-digit numbers, he could even write the converted binary numbers in one go.

After Zhao Yi finished his calculations, he smiled towards the audience and said, "My Kakutani conjecture is to use binary numbers to calculate the proof. Because of time, I won't bother you."

"That's all for today's speech!"

"thank you all!"

...

The people in the venue were a little confused.

They thought that Zhao Yi was going to prove Kakutani's conjecture on the spot, but didn't expect it to end just after the beginning?

This is... the eunuch?

Many people have the urge to vomit blood!

It was only then that someone remembered that Zhao Yi was talking about'proof ideas', not the entire proof process.

If Zhao Yi really proved Kakutani, it would be quite good to give a proof idea to this innocent venue. If it is someone else, he would not even say a word. When will the paper be published and be recognized by World Mathematics Only when the association recognizes it will give speeches everywhere and choose a bigger stage.

Zhao Yi stepped down and received a warm welcome.

"Professor Zhao!"

"Professor Li!"

"Professor Wang……"

Several rows were filled with'professor seats', and Qian Zhijin helped to introduce them in turn, as if they had become'Zhao Yi's own person'.

Professor He was also very happy. The old man stood up trembled and said publicly that Zhao Yi was his disciple, and naturally he received a lot of congratulations.

And... envy.

Every scholar wants to accept a few good students. What results can the students make? The teacher also has a lot of face. Zhao Yi is less than 20 years old and can create a new computer algorithm. At least in the computer field, it must be a Super genius.

This kind of genius wants to be accepted as a student.

Luo Zhijin also stood aside and laughed. In fact, he was more sophisticated than Professor He.

The process of Zhao Yi’s apprenticeship yesterday was a bit of a joke. He and Professor He Yuan are not familiar with each other. In case one is looking at the old man’s age and cannot bear to refuse directly...

What is the meaning of students and teachers?

This is not ancient!

Luo Zhijin doesn't care if Zhao Yi approves of his teacher, Professor He.'Hemen disciple' sounds very powerful, but it's actually just a title.

Professor He is really old. There is a certain amount of weight in the academic world, but the old professor has always disliked being too secular, and the students don’t care about bringing them out. Most of his students don’t know each other. For one, it's really hard to say that there is such a relationship.

Luo Zhijin cares more about whether Zhao Yi chooses Yanhua University.

Professor He’s process of accepting students was a bit unreliable.

There are so many professors and experts on the scene. If someone wins over Zhao Yi in the past, maybe Zhao Yi will choose another university. Before Luo Zhijin only hoped that Zhao Yi would choose Yanhua University, now he is turning "hope" into A'must'.

Zhao Yi must choose Yanhua University!

Such a monster that has not yet gone to college, can create a brand-new computer algorithm alone, but also'may' prove to Kakutani's conjecture, missed it for decades and can't wait.

This opportunity must be seized!

Luo Zhijin took advantage of the gap to find Xu Chao and Qian Hong, and hurriedly explained, "Be careful later, and don't let Zhao Yi be taken away by others!"

"You have been following Zhao Yi, helping him block some words, and taking him away if you take the opportunity to visit our laboratory!"

"If he is pulled away, it will be difficult to come back!"

"Do you understand?"

"!!!"