I really just want to be a scholar

Chapter 506 Hail Conjecture, Cotangent Sequence, and Academician Wang’s Entrustment
In the VIP room of the waiting hall of the airport, Qin Ke was sitting on the sofa writing calculations, Qin Xiaoke dragged Ning Qingjun around the VIP room curiously, and his assistant Fang Yongtang communicated with the flight staff next to him With luggage checked.

This time, the four of them were going to Jizhou to visit the old academician Wang Heng. They bought a lot of gifts, and they had to take a high-speed train after getting off the plane. Assistant Fang was responsible for following up these travel matters.

Fang Yongtang has served Qin Ke and Ning Qingyun for more than a year.As assistants to these two small bosses, you don't have to be angry or worry about unspoken rules in the workplace, and Qin Ke treats people around you very well, and the salary is first-class. I don't know how many former classmates, colleagues and friends have heard about Fang Yongtang's work. Later, he expressed his real name envy.

Recently, the blind dates introduced to her by her family have also changed from the former urban white-collar workers to high-quality men with high social status such as company executives and university faculty members.

Fang Yongtang's eyes also became critical. Although she was almost thirty, she was considered an "old leftover girl" by everyone, and she was not considered pretty, but so what?Now she can learn to recharge after work, and her social status is also high. Every time she represents two small bosses to communicate with each other, who doesn't give her some face?
Moreover, she was used to the "super god" and true temperament of the two small bosses, so she looked down on those well-dressed so-called "elites".
In general, Assistant Fang is very satisfied with her job. If possible, she would be happy to spend the rest of her life with two small bosses. Therefore, she is very dedicated to her work, and she helps her in both life and company matters. Qin Ke and Ning Qingyun greatly lightened the burden.

Of course, working for these two small bosses also has a trouble, that is, because the work is so comfortable, it makes her face round.

Unlike Assistant Fang, who is mature and temperamental, and interacts with people with a smile, Qin Xiaoke, who is only 15 years old this year, is obviously much more cheerful and lively.

For Qin Xiaoke, going to Jizhou this time is a long trip, so she is very excited.

Moreover, this was the first time she was able to sit in first class on a plane, and she was full of expectations.

Before she and Qin Ke traveled from Yuanzhou to the capital, they only took the business class. This time, because the business class tickets were gone, Qin Ke was reluctant to let the two girls squeeze the economy class. Anyway, he is not short of money now. With a big wave of his hand, he asked his assistant Fang Yongtang to buy four first-class air tickets.

Qin Ke ignored the twittering of the little girl in the VIP waiting room. He had nothing to do, and resumed his research on the hail conjecture that had been interrupted for nearly ten days.

After all, it is impossible for him to handle matters related to the EDA project in public and expose himself as Mr. Q.

The hail conjecture is indeed a very interesting topic. Take any natural number, if it is an odd number, multiply it by 3 and add 1; No matter how big it is, it will eventually fall unstoppably and quickly like a hailstone, and become the three numbers of 2-4-2, which will continue to circulate, and finally become 1.

Qin Ke is now studying the special value of 27.

The special feature of 27 is that its rise and fall far exceed the other values ​​within 100. Qin Ke has seen it in a document before, saying that 27 needs to go through 77 steps of transformation before it can reach the value in the hail range. The peak value is 9232, and after 34 steps, it finally falls to the bottom value of 1.

That's a whole 111 steps!
As for the odd number 27, which is close to 23, only 16 steps are required for the entire hail range, which shows how special 27 is.

Because of the special nature of 27, many mathematicians have tried to use 27 as a breakthrough to solve the hail conjecture, and have basically reached a conclusion—this is the key point of a branch of a certain hail tree.

Therefore, the key point of the branch refers to the part of the natural numbers diverted from here, which has an independent and powerful "hail effect".

For example, with 27 as the branch key point, 54, 108... will have a relatively long hail distance, and the "hail effect" will exceed the nearby numbers.

After Qin Ke completed the entire rising and falling process of 27 with mental calculations in his mind, he has been calculating how many key points of branches similar to 27, hoping to find common laws from them. What useful rules can be found.

It is indeed one of the top 3 mathematical problems in the world. No wonder some people call it "the next Fermat's conjecture". It cannot be proved by any current mathematical method within 1 years."

Although Professor Tao said such discourse similar to giving up, in fact, among the world-renowned mathematicians, he is the one who gave the probability proof of the Hail conjecture—"Assuming f is a function whose domain is an integer and when n tends to infinity, f (n) tends to infinity, then for almost all n, the smallest value in the 3n+1 sequence starting from n is less than f(n)".

This is the most important result in the hail conjecture.

Finding that the draft book in his hand was full, Qin Ke stopped writing and shook his sore wrist.

Today's attack on the hail conjecture is still fruitless.

Similar situations have occurred countless times.

To this day, he and Ning Qingyun are still at the stage of finding proof ideas, but Qin Ke doesn't feel discouraged. Didn't it take more than half a year for Polignac to figure it out?I have only studied the hail conjecture for four months now, so there is no possibility of any major breakthroughs. As long as I continue to accumulate experience and judge which paths are not feasible, I will always find the most correct path.

Putting away the drafts, Qin Ke casually picked up the magazines on the magazine rack and flipped through them. These magazines were basically about travel and fashion, and he was not very interested.

He picked up the coffee and took a sip, but heard Qin Xiaoke and Ning Qingyun next to him discussing the content of an old movie "Butterfly Effect". God knows how their topic got so wrong.

"Sister Ning, do you think it is possible to travel through time and go back to the past? My brother also said before that because of the 'space-time paradox', it is impossible for people to go back to the past in the same world, unless it is the past of another parallel world. , has nothing to do with the current world, and cannot affect this world."

Ning Qingyun was very patient with Qin Xiaoke, she said softly: "Yes, from the perspective of quantum physics, parallel worlds explain the existence of 'the cat is alive' and 'the cat is dead' at the same time in 'Schrödinger's cat' A self-consistent statement can also ensure that the Schrödinger equation can be established and the wave function does not collapse. Therefore, the "butterfly effect" is actually a story of traveling through different parallel worlds. Every change jumps out of the original timeline and enters a new one. parallel world."

Qin Xiaoke looked ignorant and serious: "Sister Ning, you speak just like my elder brother. I can't even understand you, but it feels very powerful. You are indeed a match made in heaven. Well, sister-in-law."

Ning Qingjun's face was burning hot, especially the words "Hello, sister-in-law" always reminded her that Xiao Ke actually knew that she and Qin Ke had had a very intimate relationship, and saw Qin Ke next to him smiling at her. Winking, she couldn't help blushing and went over to gently pinch his waist: "Xiao Ke also asked whether the 'Butterfly Effect' in that movie will definitely appear, you can answer for her."

Qin Ke enjoyed the little intimacy with Ning Qingyun very much. He held the girl's soft little hand, pulled her to sit beside him, and waved to Qin Xiaoke, waiting for the little girl to approach. laughed:
"'Butterfly Effect' is a word belonging to chaos, which is described by an abstract concept, that is: a very small change in the initial conditions, if it is continuously amplified, it will cause an extremely large difference in its future state. It belongs to right and wrong Inherent properties of linear dynamical systems are ubiquitous phenomena in nonlinear systems..."

When Qin Ke said this, he suddenly remembered that there is also a typical example in mathematics to illustrate the butterfly effect, which is the "cotangent sequence".

For example, 1, 1.00001, and 1.0002 are continuously cotangented, and the cotangent values ​​are very close at the beginning, but after the 10th cotangent, the difference between the three sequence has appeared a huge divergence, that is to say, after enough After the cotangent of times, the final value can be regarded as random and chaotic.

Such a small difference at the beginning, but the result is completely different... Hey, isn't this just the opposite of the "hail conjecture"?
In the hail conjecture, no matter how big the difference is in the natural numbers at the beginning, such as 2 and 1 million, they will eventually fall to 1, that is, no matter how big the difference is at the beginning, the result will tend to be the same.

Obviously, both the "cotangent sequence" and the "hail conjecture" are based on clear mathematical rules, but the results are diametrically opposed. One result is random, while the other is fixed.Why such a big difference?

A flash of light flashed in Qin Ke's mind.

By the way, can you find a way to prove the hail conjecture by delving into the reverse derivation of the "cotangent sequence"?

Qin Ke was lost in thought.

Qin Xiaoke said strangely: "Brother, halfway through what you said..."

Ning Qingyun hurriedly held her back: "Xiao Ke, don't disturb your brother, he seems to have thought of something important."

Qin Ke thought about it for nearly 10 minutes before taking out a new draft and counting it.

"The cotangent sequence can be regarded as an infinite number of observations of a continuous random variable X, which is described by a distribution function:"

"F(x)=1/2+1/πarctan(x/α), (cothα=α),..."

Qin Ke wrote faster and faster, until the boarding notification sounded repeatedly, and he reluctantly stopped writing.

He is about [-]% sure that this idea is feasible.

Yes, through the research on the "cotangent sequence" just now, Qin Ke thought of an idea, that is, try to start with the visualization graphics of different natural numbers. The hail range of each natural number is fixed, and there are corresponding values, as long as Converting it into two-dimensional coordinates, it is possible to use the mathematical method system of "Lime Number Theory Hypergeometric Mapping Method" to solve it.

Of course, this is only a possibility, and the research on the laws of visual graphs involving different natural numbers and different hail ranges... will be a long and arduous task.

But this is the biggest harvest recently, at least there is a more likely direction, and the rest, let's study and refine with Ning Qingyun slowly.

Qin Ke stretched, stood up and smiled at Ning Qingyun and Qin Xiaoke: "Let's go, let's go board the plane."

……

Jizhou is a famous historical city with many cultural attractions.

Qin Ke and Ning Qingyun took Qin Xiaoke to visit places of interest in the morning, and chatted with the old academician Wang Heng in the afternoon and evening, taught him the "Oriental Yuan Cultivation Method", and listened to his mathematics teachings.

Old academician Wang Heng is the leading master of number theory in China. Now that Qin Ke and Ning Qingyun have the status of teachers and students, they naturally give them careful guidance.

And Qin Ke and Ning Qingyun's mathematical talents are top-notch in the country, and they can even draw inferences about other cases from one point of view, making Academician Wang feel more comfortable as he teaches, so he gave all the summaries of what he has learned in the past ten years. .

Ning Qingyun benefited the most, because her original gentle and dense mathematical thinking is similar to that of Academician Wang Lao. By studying the handwritten notes of Academician Wang Lao, she has mastered the theory of "Wang School". This time, with the personal guidance of Academician Wang Lao, I have made a qualitative leap, and I have fully grasped the essence of the "Wang School" number theory and integrated it.

In time, when she graduates from Professor Tian Jianlan, she will become the only mathematician in the world who can combine the knowledge of "Wang School" and "Chen School" in number theory.

Even the old academician Wang Heng sighed with relief: "I have taught you everything I have thought and realized in the past ten years since I retired. Especially Xiao Ning, you are the only one among my dozen or so disciples who have received all of my knowledge. The academic essence is passed down. Even if I close my eyes and die tomorrow, I will have no regrets."

Qin Ke is different from Ning Qingyun. His flamboyant and forceful personality determines that he cannot fully accept Academician Wang's "gentle" mantle of number theory.

Relying on the incomparably rich mathematical knowledge passed down to him by the system, Qin Ke is taking the path of learning from others, not sticking to a certain school, all the schools of mathematics from ancient times to the present, he has easily picked up, and the knowledge of number theory taught by Academician Wang Lao is also the same , He just took the part that suits him and integrated it into his mathematical thinking system, and didn't absorb it all like Ning Qingyun.

However, the guidance of Academician Wang is also of great help to him. He has a deeper understanding and perception of the overall view of mathematics and the "big unification" in the field of number theory, which will have a positive impact on his future path of mathematics. influences.

During this period, Academician Wang also specially notified his proud disciples to come and gather together. Among them were many heavyweight figures in Xia Kingdom's mathematics field, and several academician-level bigwigs were also invited.

Academician Wang introduced Qin Ke and Ning Qingyun to them, calling them "the last two closed disciples", and hoped that the rest of the disciples would take good care of the two junior brothers and sisters.

This is the most important gift that Academician Wang gave to the two closed disciples besides what he has learned all his life. It makes up for the fact that Qin Ke and Ning Qingyun have risen too fast in the mathematics world, their foundation is too shallow, and the "Tsinghua School" behind them is too weak defect.

After this mutual recognition, at least in addition to the "Yan University School" and "Aurora School", the "Wang School", which has always been relatively neutral, will become a solid backing for Qin Ke and Ning Qingyun on the future path of mathematics.

To sum it up in one sentence, it is that Qin Ke and Ning Qingyun's apprenticeship this time is really profitable.

The four of Qin and Ke stayed in Jizhou for almost ten days, until they were about to go abroad to attend the AMS academic report meeting, and then reluctantly bid farewell to Academician Wang, and prepared to return to the capital.

With the support of his son, Academician Wang insisted on sending him out of the courtyard.

The setting sun was like blood, and the old man's body was a little rickety. Under the blowing of the evening wind, his silver hair was also dyed red by the setting sun.

Qin Ke's nose was a little sore, and Ning Qingyun's eyes were blurred with tears. Even after learning the "Oriental Yuan Cultivation Method", the old man was too old and too weak to prolong his life for a few more years.

Qin Xiaoke also had a good impression of this kind and amiable grandfather. She had no grandfather, only a serious and serious grandfather, so she was very close to the old Academician Wang who always smiled at her. The teardrops in Li couldn't stop.

Academician Wang stretched out his hands to rub Qin Xiaoke's beautiful hair, Wan Er said: "Little girl, learn to draw well, I also met your teacher Mai Huiqing and Ni Wanying once, and I will write a book when the time comes, so that they can learn to paint well." teach you."

Such caring words made Qin Xiaoke feel even more sad, the little girl bit her lip and kept crying.

Qin Ke pulled the little girl behind him, and repeatedly asked the old academician to persist in practicing the "Oriental Yuan Cultivation Method" and strictly follow the above recipes for diet therapy.

The old academician Wang Heng nodded in response, and said to the two earnestly: "Xiao Qin, Xiao Ning, you are going to go abroad to win another big prize soon. This is a good thing, but don't be proud, the road of mathematics will never end. In addition , I also know that there are many bad ethos in the mathematics world in Xia Kingdom today, with Qin Ke's character, maybe something will happen..."

He obviously thought of Qin Ke's exposure of Jiang Quansheng's academic fraud at the American Science Breakthrough Awards report meeting. Seeing what Qin Ke wanted to say, he waved his hand and continued: "But as long as you think it's right, do it. Just stick to it."

There was a frightening brilliance in the old man's always gentle eyes: "The world of mathematics needs a breath of fresh air. Lao Qiu and I will pay attention to you. As long as we old bones are still alive, no one can use those disgraceful means to get rid of you." Deal with you!"

After all, the old man smiled slightly on his dry and pale lips:
"Go, do what you think is right. The scenery of mathematics is beautiful. I hope you can stand taller than me in the future and see farther than me. The future of Xia's mathematics world is entrusted to you gone."

　Ask for a monthly ticket recommendation ticket at the end of the month!
　　
　
(End of this chapter)