Genius of the Rules-Style System

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

The article narrates such a story: In the mid-1970s, on the campuses of prestigious universities in the United States, people were going crazy, playing a mathematical game day and night and forgetting food and sleep. This game is very simple: write any natural number N (N≠0), 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 N/2.

Not only students, but also teachers, researchers, professors and academics have joined in.

Why does this game have such enduring appeal? Because people discovered that no matter what kind of non-zero natural number N is, it will eventually be unable to escape back to the bottom of 1. To be precise, there is no way to escape the 4-2-1 cycle that falls to the bottom, and you can 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 1 is obtained for the first time.

Can every positive integer be calculated according to this rule and get 1? This is the Sygurac conjecture, also known as the "Hail conjecture, Kakutani conjecture". Including the later Kratz problem, it is an interesting '3X+1' problem in mathematics.

Foreign countries like to call the '3X+1' problem the Sygurac Conjecture or the Hail Conjecture, while in China it is called the 'Kakutani Conjecture' because it was a man 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 devoted a lot of energy but failed to produce rigorous proofs.

So conjecture is still just conjecture.

…

When Li Yi came to Zhao Yi's process and used part of Kakutani's conjecture, people in the venue felt that there were theoretical loopholes in the 'valid and irrelevant carry method'.

Unless Kakutani's conjecture is proven one day, there will always be a 'possible' loophole in the 'valid and irrelevant carry method'.

Therefore, mathematical theory is the basis of all science.

What people in the venue did not expect was that Zhao Yi's reaction was to thank Professor Li Yilai excitedly and said, "I didn't even find out that the Kakutani conjecture was proved"?

This turn of events is truly astonishing.

A group of people around him had their mouths open, and they didn't know how to react.

After Zhao Yi thanked Professor Li Yilai, he returned to the stage with an excited expression. Facing a confused and curious look, he did not talk about the Kakutani conjecture anymore, but continued to talk about the 'valid and irrelevant carry method'.

It was almost over at this point.

The proof steps including the 'Kakutani Conjecture' are the most critical part of the 'valid and irrelevant carry method'. As long as the steps are passed, the rest will be easy to understand.

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

"This is my valid and irrelevant carry method!"

"The above is my proof!"

"thank you all!"

After Zhao Yi said the last words, he took two steps back and bowed politely, and then the venue burst into violent applause.

The speech was a success.

Although it is doubtful whether the 'Kakutani Conjecture' has been proven, even if the 'Kakutani Conjecture' has not been proven, because computer performance does not involve theoretically possible 'counterexample numbers', the 'valid and irrelevant carry method' can definitely be used.

This is most important in the computer industry.

Computer algorithms do not need to be 'perfectly accurate', just like any software will have loopholes. The purpose of computer algorithms is to actually use them, without requiring theoretical perfection.

No one can guarantee that a car that leaves the factory will be 100% problem-free; an artificial intelligence translator does not require perfect translation capabilities and can guarantee an accuracy rate of more than 90%, which is already quite successful.

Computer algorithms are the bottom layer, and the accuracy requirements are higher. However, there is only the possibility of "inaccuracy" in the theory, which is equivalent to a 100% accuracy rate.

Therefore, the 'valid and irrelevant carry method' is already a very perfect algorithm.

The speech is over.

No one left the venue. Everyone was still sitting in their seats. They all looked at Zhao Yi curiously as he walked off the stage. They all wanted to know the question just now, "Did he really prove the Kakutani conjecture?"

They want answers.

Of course Zhao Yi knew what everyone was thinking, but it was impossible for him to prove a mathematical conjecture in detail in his speech on 'Effective and Irrelevant Carry Methods'. The reason why he was so excited also meant that the proof of the mathematical conjecture was of great significance. of great importance.

The "valid and irrelevant carry method" is just a computer algorithm. No matter how sophisticated the process is and how broad its application scope is, most ordinary people will not care about it at all.

The mathematical conjecture is different.

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

Leave your name in history!

The graduate student building of Yanhua University where he is giving the lecture is obviously not a suitable venue for demonstrating mathematical conjectures. What's more, he has not written any relevant papers and has not made any direct submissions.

just in case……

Some shameless guy has seen the whole process and quickly compiled and submitted the article, but the copyright of the proof cannot be guaranteed.

The probability of this happening is not small, after all, the proof of mathematical conjecture is of great significance.

Zhao Yi looked at the eyes of the audience. He thought carefully, then returned to the stage and said, "Now I will show you the proof of Kakutani conjecture!"

Suddenly.

Everyone was refreshed.

Some people think that Zhao Yi is talking big words, but he is not talking big words. Only by listening can you be sure.

The venue was silent.

"A mathematical problem may have many ways to prove it. My way of proving it is to use the binary thinking of computers."

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

11011.

This is the number 27 in binary.

In Kakutani's conjecture, 27 is a very 'powerful' number. It looks a bit unspectacular, but according to the calculation method of Kakutani's conjecture, it takes 77 steps to reach the peak of 9232, and then 32 steps to reach the bottom. Value 1, the entire transformation 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 by calculating '3X+1'. The difference was that every number he wrote was expressed in binary. He wrote more than a hundred binary numbers in succession and arranged the blackboard fully.

Everyone in the audience had a headache when they saw it. The blackboard was filled with either 1 or 0, as if they were drawing.

During the entire calculation process, the only thing everyone in the room was sure of was that Zhao Yizhen was a super genius in binary. Even if it was a four-digit number over a thousand, he could even write out the converted binary number in one breath.

After Zhao Yi finished the calculation, he smiled at the audience and said, "My idea of ​​proving the Kakutani conjecture is to calculate the proof in the form of binary numbers. Due to time constraints, I will not disturb everyone."

“That’s it for today’s speech!”

"thank you all!"

…

Everyone in the venue was a little confused.

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

Is this...a eunuch?

Many people have the urge to vomit blood!

Only then did someone remember that Zhao Yi was talking about the 'proof idea', not the entire proof process.

If Zhao Yi really proves Kakutani, it would be quite good to come up with a proof idea in this insignificant venue. If it were someone else, he wouldn’t even be able to say a word about when the paper was confirmed to be published. It was cited by World Mathematics Only when the association approves will they give speeches everywhere and choose a larger stage.

Zhao Yi came off the stage and was warmly welcomed.

"Professor Zhao!"

"Professor Li!"

"Professor Wang……"

There were "professor seats" in several rows, and Qian Zhijin helped make introductions one by one, as if he had become "Zhao Yi's own person."

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

And...jealousy.

Every scholar wants to recruit a few good students. What achievements can the students produce? The teacher also has a good face. Zhao Yi is less than twenty years old and can create a new computer algorithm. At least in the computer field, he must be a leader. Super genius.

Anyone would want to take this kind of genius as a student.

Qian 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 were far from familiar. If you just looked at the old man's age and couldn't bear to refuse directly...

What is the significance of students and teachers?

This is no longer ancient times!

Qian Zhijin didn't care at all whether Zhao Yi became a disciple of Professor He. 'He's disciple' sounds very powerful, but it's actually just a title.

Professor He is really old, and his words in the academic world have a certain weight. However, the old professor has always disliked being too worldly, and he doesn’t care if students bring them out. Most of his students don’t know each other. In other words, they seem to be from the same school. One, there is a slight relationship, but actually it’s really hard to tell.

Qian Zhijin is more concerned about whether Zhao Yi chooses Yanhua University.

Professor He's process of accepting students is somewhat unreliable.

There are so many professors and experts at the scene. If someone in the past woos Zhao Yi, maybe Zhao Yi will choose another university. Before, Qian Zhijin only hoped that Zhao Yi would choose Yanhua University, but now he hopes that Zhao Yi will choose Yanhua University. Became a 'must'.

Zhao Yi must choose Yanhua University!

A monster like this, who was able to create a new computer algorithm on his own before going to college, and 'maybe' proved Kakutani's conjecture, has missed it for decades and can't wait to see it again.

You must seize this opportunity!

Qian Zhijin took advantage of the gap and went out to find Xu Chao and Qian Hong, and hurriedly explained, "You must be careful later and don't let Zhao Yi be pulled away by others!"

"You just keep following Zhao Yi, help him block his words, and take him away when you get a chance to visit our laboratory!"

"If he is taken away, it will be difficult for him to come back!"

"Do you understand?"

"!!"