Riemann's cat

Recently, media reports of 89-year-old Sir Michael Francis Atiyah publishing a paper claiming to prove the Riemann conjecture reminded me of this novel I saw on Sci-Fi King in junior high. The in-depth math, physics concepts and descriptions of observing the ultimate truth that triggers the end of the world are impressive. Through this article, I was first exposed to classic public cases such as the Riemann Conjecture, Schrödinger’s Cat, and the Principle of Human Selection. It’s kind of enlightening. At the end of the novel, the protagonist abandons the publication of the results in order to save the world, choosing to commit suicide and destroy the manuscript. And while in reality Sir Attia’s twilight challenge was awe-inspiring, multiple sources claim the proof is likely to be wrong (can’t even call it proof), lamenting the fact that perhaps the world avoided a crisis of destruction [smile].

I. An unexpected call.

When the phone rang, I never dreamed that the ringing would smash my peaceful world to pieces.

“Hello,” I said slowly into the microphone as I picked up the phone.

“May I ask if it’s Jang Sung-yuan?” A familiar voice came from inside the phone.

“It’s me. Who are you, please?”

“I’m Tian Xiaoyu. How are you?”

My goodness. Woo! Immediately, a washed-out pale face and disheveled and somewhat yellowed hair appeared in my mind. It’s been about fifteen years, right? My best friend in middle school. The math geek of the class. The two of us competed in geometric proofs in front of the blackboard over and over again. It was because of his mathematical excellence that destroyed my confidence as a mathematician that I finally chose physics and ended up at a small polytechnic in Rochester, USA, as a physics teacher.

“Xiaoyu! Where are you?” I shouted.

“I just arrived in Luo City. Got your phone number from Ah Ching.” Ah Ching was a classmate of ours. I contacted him some time ago.

“Wow, you’re in Luo City? Where do you live? I’ll see you go.”

He gave me the address. It’s an apartment block not far from my house. I put down the phone and said to my wife who was cooking, “Faye, I’ll be right back after I go out.”

“Who is it?” Wife asked as she put down the spatula.

“A classmate of mine in middle school.”

“Female?”

“Just jealous? Male.”

“Who’s jealous of you,” said the wife with a deflated mouth. “It’s time to eat, hurry back.”

“By the way, you cook more. Maybe I’ll pull my classmates over for dinner.”

“There’s food for you classmates. Go and get back.”

I hurriedly kissed my wife, went to the garage, started the car, and drove to Xiao Yu’s.

Xiao Yu’s apartment area was hidden under a thick shade of trees, and the red brick buildings looked old, but relatively tidy. The roof of the building was glowing yellow with a dash of the lingering sun. I parked the car in the parking lot underneath Xiaoyu and took three steps and two to get to the door hole, pressing the number of Xiaoyu’s room at the door. A moment later, a “ding” was heard. I hurried to pull the door open. Only to hear Xiao Yu shouting from the second floor hallway, “Cheng Yuan!” I looked up, and Xiao Yu’s familiar wasted body emerged from the dark hallway. “Soooo!” I shouted back and rushed up the stairs, taking the hands Xiao Yu handed me. He had a pair of black-rimmed glasses, his hair was unkempt, and a slightly wrinkled white shirt was tied into a pair of dark gray pants. There was a faint smell of sweat on his body. “Come in and sit.” Xiao Yu said, pulling me into the room. The room was simple, a single bed, a table, a stool. Against the wall lay a large suitcase and a smaller travel bag. The water was burning in the kitchen. Xiao Yu said embarrassedly, ‘’Sorry, just arrived, nothing. Have a seat.” He pointed to the chair.

I sat down, and Xiao Yu sat down on the bed. “Dude,” I said, “haven’t seen it in fifteen years, right? How about that?”

Xiaoyu hehei laughed: ‘’Still alive. No, I came to see you. Are you okay?”

“It’s a sloppy life. You didn’t come here to say hello to me first either.”

“Too busy to leave, I still didn’t get your phone until I got on the plane.” The water boiled in the kitchen. Xiao Yu got up and went to the kitchen and turned off the electric stove.

“What are you doing to eat?” I followed his gaze into the kitchen.

“Instant noodles.” Xiao Yu was a little embarrassed.

“‘’A big professor still eating this? Go, go to my house and get you a nice meal.”

“I just got off the plane here and I’m so filthy, how can I go to your place.”

“You wash up then, I’ll wait for you.”

Xiao Yu thought for a moment and said, “Okay, you wait for me.” He opened his suitcase and took out his clothes and went to the bathroom to shower.

I sat there alone, thinking about Xiao Yu’s past. Xiaoyu is known throughout our school as the top math student. His sophomore year of high school he competed in the International Olympic Mathematics Competition and won a silver medal. If he hadn’t been dizzy with a cold the day of the game, he would have taken the gold medal. The rest of us had nothing but admiration for him. My math was okay too, but I chose to study physics because I felt I could never surpass Xiao Yu in math. After high school, he went to Tsinghua University to study physics. Xiaoyu, on the other hand, went to the mathematics department at the University of Science and Technology of China. We corresponded a lot back then. Then I came to the United States to study physics. Gradually, the connection with him faded. Some news about him from classmates and online. After college, he went to graduate school at the CCSU Math Institute. But then it seems the career didn’t go well. After graduation he went to a lesser-known university to teach mathematics for many years, and he was not heard of as having accomplished anything in mathematical studies. I occasionally meet with old high school classmates and talk about Xiao Yu, all feeling sorry for him. It’s amazing to think that after all these years Xiao Yu hasn’t solved some world-famous math problem. At that time, we actually thought that Goldbach’s conjecture should have been in Yu’s pocket.

Xiao Yu came out from the shower and changed into a grey shirt, looking much fresher. I brought Xiao Yu to our house. The scent of vegetables came to me as soon as I entered the door. As if struck by the fragrance of vegetables, Xiao Yu propped his hand on the doorframe and closed his eyes, taking a sharp breath and said, “Ah, it really smells good.”

The wife and eight-year-old son came to the door and said, “Welcome, welcome.”

I was busy introducing everyone: “This is my old classmate, Xiao Yu. This is my wife, Sheffy, my son, Zhang Jian. Jian Jian, call uncle.”

“Uncle.” The son yelled and went back in front of the TV to play the game.

Wife took us to the dining room. There were many dishes on the table, red and green. Xiao Yu said, “Wow, sister-in-law is really something.”

“Do it blindly. Just don’t be too hard on yourself.” Wife said with a smile.

“Sister-in-law, then don’t be modest. These dishes are just as good as they look. On the plane, I get tired of eating those things after two bites. Now my stomach is saved. Oh.”

The wife laughed and said, ‘’Haha Xiaoyu is quite interesting, come and have a seat. Son, come and eat.”

We sat down at the dinner table and I said, “How about some beer for Xiao Yu?”

“This one,” said Xiao Yu as he scratched his head, “don’t want it, do you?”

“Come on, have some.” I picked up two beers. “Years away. A toast to our brother and sister.”

Xiao Yu and I clinked glasses and took a sip of beer. He looked around our house and said, “Man, you’re having a good time.”

“Just mess around. How are you doing, Yu?”

“It’s a long story.”

I said to Fei, “Xiaoyu is the top math student in our class, who won a silver medal in the Math Olympiad.”

“Alas, a good man does not speak of his bravery anymore. Now it’s just a little teaching job, too.”

“By the way, Xiaoyu, all our classmates were counting on you to be the first to rise to prominence that year. After all these years, with your level, how come you’re still hanging out at that little school?”

Xiao Yu took a big sip of his beer and said, “Wrong choice.”

I smiled and said, “At your level, you should be able to make things even if you choose the wrong direction, right? Not to mention, not knowing a different direction for a decade?”

Xiao Yu shook his head and said, “It’s a long story. You know Riemann, right?”

“The German mathematician Riemann? Of course I know. It’s very famous. Riemann geometry is the mathematical basis of general relativity, and Riemann integration, which we who study physics have to learn.”

“Ever heard of the Riemann Hypothesis?”

“That’s something I haven’t heard of. What is the assumption?”

“The Riemann hypothesis is actually a conjecture that Riemann made over a hundred years ago.” Xiao Yu took a bite of shredded green pepper chicken and continued, “Let’s put it this way, if you ask a random mathematician what the most important guess in mathematics is right now, nine times out of ten the answer you get is the Riemann Hypothesis.”

“Really?” I was a little unsure, “I thought the most famous conjecture by now was the Goldbach conjecture. Isn’t that the jewel in the crown?”

“The Goldbach conjecture is indeed an important conjecture, but that is a rather peculiar one in mathematics. Little connection to other issues and areas. The Riemann hypothesis, on the other hand, has had a profound impact on modern mathematics. There are probably thousands of propositions or ‘theorems’ in mathematics that start with ‘If the Riemann hypothesis holds then we have such and such a conclusion’. These conclusions are the brainchild of countless distinguished mathematicians, some presumably the result of a lifetime of some mathematicians. But these results are based on the Riemann hypothesis. They are like some pretty gorgeous soap bubbles inside math. If, one day, anyone disproves the Riemann hypothesis, it will be like a gale blowing in the math world that will blow all those soap bubbles. The efforts of countless mathematicians would have all been in vain. That’s why this conjecture is called the Riemann Hypothesis. Because there are so many things that depend on that assumption. Did you know that at the 1900 World Congress of Mathematicians, the German mathematician Hilbert proposed 23 problems that 20th century mathematicians should study, the eighth of which included the proof of the Riemann hypothesis, and in 2000 the US Clay Institute of Mathematics published seven millennial mathematical problems. A $1 million reward is offered for each question. The Riemann hypothesis is one of them, and the only one of Hilbert’s 23 questions.”

“Oh? So famous,” Xiaoyu’s narration made me come to be interested. “How come I don’t know the Riemann hypothesis at all? Looks like I’m pretty much alone. So what exactly is Riemann’s hypothesis saying?”

“Look at you guys, talking about math as soon as we meet,” said Faye, pointing to the dish on the table with her chopsticks, “eat the dish, eat the dish.”

“Yeah, let’s not go cold turkey on such a delicious dish.” Xiao Yu laughed and sandwiched a fried shrimp, eating it to his heart’s content. “The Riemann hypothesis is not as clear as Goldbach’s conjecture in a sentence or two. That’s probably why it’s not as well known as Goldbach’s conjecture. I can talk to you in detail after dinner if you’re interested.”

“Yeah,” I said, “By the way, you’re not working on the Riemann hypothesis, are you?”

“Yeah,” Xiaoyu laughed bitterly, “it’s the Riemann hypothesis that’s brought me down like that. I learned about this conjecture in my freshman year of graduate school and ended up getting stuck in it and couldn’t pull it out. Not interested in other minor subjects. My teacher warned me many times to not touch the issue, but, I just couldn’t listen. This kind of math problem that no one has solved in over a hundred years is not something that anyone can solve all at once. In the end, if my mentor hadn’t pulled me along, I would have barely gotten my PhD.”

“Can’t you just switch to a different subject work?” Faye said.

“Yeah, I was supposed to change.” Xiao Yu sighed and fell into a moment of contemplation. Eyes fixed on the dishes on the table, but eyes stared into infinity. I looked at the languid man and knew he was thinking about the past.

“That’s the kind of person Xiao Yu is,” I said to Fei, “whatever problem he wants to solve, it has to be solved. I still remember one time in middle school, Xiao Yu spent the whole night in the comforter playing with a flashlight for a geometric puzzle, and the next day he fell asleep in math class and was severely criticized by his teacher.”

“I see, only such people can make it big.” Faye said with a glare.

“Still, it looks like those of us with little ambition are living comfortably. Haha.” I try to seem relaxed about it. Xiaoyu was still there brooding when I called out to him, “Xiaoyu, stop thinking about this and eat your food.”

Xiao Yu was stunned and seemed to snap out of it: “That’s right, just eating.”

II. A Section of Mathematics Course

After the meal, Xiao Fei cleaned up the bowl and chopsticks, and his son went to work. I put Xiao Yula to my study room upstairs and asked him to tell me about Liman’s hypothesis.

“Please give me a pen and paper,” said Little Yu, “I’ll give him a paper. Xiaoyu writes a mathematical formula on the paper:

$1+ \frac{1}{2}+ \frac{1}{3}+…+ \frac{1}{n}+… $

“Do you know what this is?” asked Little Yu.
“Oh, I know. Is this infinite quest and not a blend?” I said. I learned in calculus when I was a university.
“Yes,” said Xiaoyu. “This level is divergent. That is to say, it is infinite.”
“Yes, “ I said.
“Now I turn it a bit and turn each of the denominators into the second party,” said Little Yu. He wrote under this formula:

$1+\frac{1}{2^s}+\frac{1}{3^s}+…+\frac{1}{n^s}+… $

“The number of this level…” I said, trying to recall the math I had learned in college years ago.

Xiaoyu looked at me and said, “If S changes, this magnitude is a function of S. Riemann represents this function with the Greek letter ζ(S) (Xiaoyu wrote this on paper), so now we call it Riemann ζ function. This magnitude is convergent if s is a real number greater than 1, i.e. its sum is a finite number. And when s is less than or equal to 1, this magnitude is divergent, i.e., ζ(s) is infinity. When S equals 2, for example, do you know what the sum of its parts is?”

I thought for a while, 2 is bigger than 1, so ζ(2) is a finite number. “I don’t know. How much is it?”

“The square of the π is divided by 6!”

“π? you mean the circumference π?”

“Yeah.”

“Wow! How does this tie in with π?”

“That’s the magic of math. This result was first discovered by the 18th-century Swiss mathematician Euler. Sort of a great achievement for Euler.”

“So when S equals 3 and how much is it?” I asked.

“Good question! The answer is: no one knows. All we know now is that it’s an unjustified number.”

“Oh, Riemann guessed it was about the sum of the steps?”

“Huh,” Xiaoyu laughed, “No no, Riemann guessed it was much more complicated than that. As Riemann considers this magnitude, imagine what would happen if this power s were allowed to take the compound value.”

The plural is familiar to me. We use it a lot in physics. But the powers of the plural are not familiar to me. Xiao Yu wrote on the paper.

$s = x + iy$

He explains, “We know that each complex number can be written as a real number x plus an imaginary unit i, which is the square root of negative 1, multiplied by another real number y. If s is a complex number, the magnitude of the value of the s-second of a real number n is actually determined by the real x of s.” He pointed to the order above and said, “So this Riemann ζ function is also a finite number when x is greater than 1, except that its sum is a complex number at this point. And its value is infinity when x is smaller than or equal to 1.”

He then drew a right-angle coordinate system on the paper and marked the x-axis and y-axis. He wrote: “It should be known that each complex x+iy can be represented by the point (x,y) on a plane. According to the explanation I just gave, this Riemann ζ function is only defined when x is greater than 1.” He drew a perpendicular dashed line in that coordinate system through the point on the x-axis corresponding to x=1, splitting the plane in half. He goes on to say, “That is, this ζ function is defined on the right side of this line, while on the left side of this line, including this line, it is undefined.”

I looked at the paper, trying my best to keep up with his explanation. “So, this ζ function is a continuous function?”

Xiao Yu said approvingly, “Yes! Not only is it continuous, but it’s also resolved in the right half of the plane of the line.”

The solution function, which we also use in physics, means that this ζ function has a derivative at every point in the plane on the right half of the line x=1.

Pointing to the left half of the line, Xiao Yu said, “Although the ζ function is not defined on this half, Riemann used a very basic trick in compound functional theory to extend the ζ function into a function that resolves throughout the plane. Specifically, he defines a function that resolves across the entire plane using an integral formula that overlaps with this level above on the right half of the line. This function, which has been analytically extended, is actually the real Riemann ζ function.”

“Oh,” here I’m a little puzzled, “why would Riemann do that?”

Xiao Yu laughed, ‘’This one involves the problem of number theory. Riemann studied this ζ function for the purpose of using it to study the distribution of prime numbers.”

I know that prime numbers are those natural numbers that have no other factor other than themselves and 1 and are greater than 1. Like 2, 3, 5, 7, 11, 13, 17, etc.

“How can this function be related to the number of primes?”

“This actually has to start from Euler. Prime numbers can be said to be the atoms that construct all numbers in mathematics. However, the distribution of prime numbers in natural numbers seems to be irregular. Almost any problem about prime numbers is Mathematical problems. For example, you know Goldbach’s conjecture, which says that every even number greater than 2 can be written as the sum of two prime numbers. But to this day no one knows whether this proposition is correct. Our Chen Jingrun proved that Every even number can be written as the sum of a prime number and the product of two prime numbers. There is still one step away from fully proving Goldbach’s conjecture. But this step is hardly like reaching the sky. The ancient Greek mathematician Euclid proved that prime numbers have infinity There are many. For more than two thousand years after him, this is almost the only general property of prime numbers that people know. When Euler played with the ζ function, he found that when s is a real number greater than 1, the ζ function can be written as an infinite product related to prime numbers. After he got this simple equation, he immediately realized that in order for this equation to be true, the number of prime numbers must be infinite. So Euler used the ζ function to give Euclid A new proof of the infinite prime number theorem. Using this equation, Euler also proved that the sum of the reciprocals of all prime numbers is infinite. In this way, more than two thousand years after Euclid, the ζ function finally Makes people’s understanding of prime numbers a step further.

“From this, people know that this ζ function is in fact closely related to the number of primes. However, only over a hundred years later, because of the work of Liman, people finally realized that the ζ function was crucial to the research of prime numbers.”
“Because Rieman has introduced the power of the compound?” I asked.
“That’s exactly what it is! Rieman’s idea is that since Euler can derive the new nature of the number of elements from the real power of the Ζ function, all the real numbers are just on a one-dimensional line. Then, if I turn this power into the plural, what results? All the plural are full of a two-dimensional plane! This multi-dimensional dimension will certainly tell us more information about the number of primes. So, Liman worked hard for a few days, wrote a short, only eight pages of paper, the title is: less than the number of primes of a given value. However, this short text has become an epoch-making paper. In this article, Liman has established a close connection with the zero point and the distribution of the ζ function.”

“Zero?” I didn’t react for a moment.

“These are the points that make the value of the zeta function equal to zero. For the zeta function, there are some zeros that are obvious. These zeros are -2, -4, -6,…, -2n,…, etc. These zeros are called ordinary zeros. In addition to these ordinary zeros, Riemann also found that the other zeros are complex numbers, and all fall on the plane from $x=0$ to $x=1$ in a band between the two vertical straight lines. So this band-shaped area is called the critical zone. It is the distribution of these non-trivial zeros that directly determines the distribution of prime numbers. Riemann made a very bold conjecture based on his own calculations: he thought that all the non-trivial zeros of the ζ function all fell on the line $x=\frac{1}{2}$! This is the Riemann hypothesis that has haunted mathematicians for over a hundred years. This vertical line $x=\frac{1}{2}$ is called the critical line.”

“Well.” I felt that my role was like the function of Riemann’s ζ function in terms of prime numbers. I’m afraid that I would have to spend some time to digest it. I asked, “Can you tell me a little about the relationship between Riemann’s assumptions and the number of primes?”
Xiao Yu glanced at me and said, “You are still a trained scientist, and the questions you ask are all right.”

I laughed and said, “My brother is a complimenter. It seems that your teacher must be very good.”
Xiao Yu also laughs: “Of course, so many years of mathematics teacher is not white. Here, I told you that Eurola has established a simple equation of the relationship between the real ζ function and the prime number. It follows the idea of Eurola and has established an equation between his complex Ζ function and the distribution of prime numbers. However, his equation is much more complex than the equation of Eurola, one of which involves the non-trivial zero point of the ζ function. If it can be proved that all the non-trivial zeros are on x=1/2 this critical line, then it can be thoroughly understood from this equation.”
“Oh, that’s what I see.”
At this time, Xiao Fei got some watermelons up and said to Xiao Yu, “Little Yu, eat some watermelons. You’re going to lecture here for a long time, and you should take his tuition.”
Xiao Yu said with a smile, “Ha-ha, I’m paying you the money.”
Xiao Fei also laughed. “Chengyuan, he’s just arrived. He hasn’t come back yet. Don’t be too tired of her.”
Yu said: “It’s okay. I’ve been sleeping on the plane for 10 hours.”
I said, “Don’t worry, Yu is not made of mud.”
Xiao Fei stared at me and went downstairs.
“Where have you been talking about?” I asked.
“Let’s talk about the relationship between Riemann’s hypothesis and the distribution of prime numbers.” Little Yu took a watermelon and said, “To talk about the relationship between them, I’m afraid we have to talk about the German mathematicians from another giant cow.”
“Gauss? Math Prince. It seems that every big mathematician has something to do with it?”

“How else can it be a core problem in mathematics? It’s like this. As you probably know, Gauss was a mathematical genius from an early age, and at the age of 15 he became interested in the distribution of prime numbers. He spent a lot of time counting the number of prime numbers less than a certain number. He found that there were 4 prime numbers less than 10, 2, 3, 5, 7. 25 prime numbers less than 100; 168 prime numbers less than 1,000; 1,229 prime numbers less than 10,000, and so on. He wanted to use this statistic to find a pattern in the distribution of prime numbers within a certain range. He considered the question: when you count the numbers one by one, what is the average number of prime numbers you will encounter. For example, if there are 4 prime numbers between 1 and 10, and you get 2.5 by comparing 10 to 4, so on average you encounter one prime number for every 2.5 numbers between 1 and 10. By analogy, an average of 4 numbers within 100 meets a prime number, an average of 6 numbers within 1000, and an average of 8.1 numbers within 10,000, so Gauss probably counted up to 100 million, right? He found that the average number of digits between 1 and a certain number N was close to the natural logarithm $\lnN$. He then dared to make a calculation. So he made a bold guess: as N gets larger and larger, the average number of numbers between 1 and N will encounter a prime number for every number $\lnN$.”

I understand this time. I said: “This discovery seems too simple. It seems that I can also find it myself?”
“Yes. But the problem is that success is always left with a heart. In fact, he did not immediately publish his findings. And after a few years of discovery, there was a French mathematician, Levied, and made the same finding.”
“It’s like Newton and Lenbitz discovered calculus at the same time.”
“Yes, this kind of thing happened in science too much,” said Little Yu. “We continue to say the discovery of the gaussian. The number of prime numbers less than N is marked by π(N). The Gaussian discovery, when N is very large, π(N) is close to N divided by the natural logarithm of N.” Little Yu wrote on the paper:

$π(N) ~N/\ln(N)$

“This is the discovery of the gaussian and Levins. This conjecture was confirmed by the two mathematicians in ninety-nine years. Do they know how they proved it?”
“Make use of the Rieman hypothesis?” I guessed.

“Almost. No one can prove the Riemann hypothesis. But they proved a very weak form of the Riemann hypothesis. They proved that the Riemann ζ function has no zero on the vertical line $x=1$. Use it. This result, they proved the conjecture of Gauss and Lagrange. This famous result is now called the prime number theorem. However, the prime number theorem is only an asymptotic result. If the Riemann hypothesis can be proved, this prime number can be given. The exact error of the term on the right side of the theorem.”

I was silent for a moment and said, “So, what evidence is it that it is right?”
“There’s a lot of evidence,” said Little Yu. “The most direct evidence is that it’s calculated. There are numerous non-trivial zeroes of the Riemann Ζ function. But it’s very difficult to calculate these zero points specifically. However, with the help of computers, mathematicians have calculated more than 10 trillion non-trivial zeros, all falling on $x=1/2$ this straight line!”
“Wow! I’ve verified so much!” I marveled at it. “So the Rieman hypothesis will definitely be right?”
“No one knows,” said Little Yu. “Even if there are more than 10 megabytes of zeros, it can’t be ruled out after 10 megapas. And once it is found that a zero point is not on this line, the Rieman hypothesis is overthrown. That’s probably a big earthquake in the mathematical world. In fact, who checks out 10 megazeros of the mathematician’s original intention is to find a zero point out of x=1/2 this critical line. Of course, he failed.”

After recalling Little Yu, I lamented: “The math is really wonderful. What do you do so many years?”
“Yes,” said Xiaoyu.
“I know what you’re capable of. With your level, you have done so many years, and you must have made some famous halls.”
“To be honest, I came to the United States this time for this.”
“Oh? Is there any progress?”
Xiao Yu approached me, lowered his voice and said, “Don’t talk to others. I think about the problem for more than a decade. I think I finally found the right way to prove Liman’s hypothesis.” He raised his body and then said, “It’s just that there are too many domestic chores and I have been quiet. Now, I have finally applied for a chance to go abroad and want to make a study in An’an quietly in the United States and attack the Liman hypothesis.”
“Well, I believe you can get that million dollar bonus. When you’re out, you can get some light on me.”
“I hope so.” Xiao Yu looked at the table and said, “Oh, it’s not too early. I have to go back.” We stood up. After saying goodbye to my family, I sent him back to his apartment.

III. Principle of Human Choice

Three weeks passed. I finished the final exam and delivered the student’s achievements. I was relieved from the busy schedule. After two days of rest at home, I remembered Little Yu. So, on a Saturday afternoon, I drove the car to the dormitory of Xiaoyu.
On these days, I occasionally contacted Little Yu with telephone and email. He knew that Dr. White, his boss, was very loose to him. He did not ask him to take the class on time every day. However, Xiao Yu had a strict requirement for himself, and he was on time every day.
Little Yu’s room did not add anything. However, according to the physics principle, the entropy in the room was increased irreversibly. Several pairs of shoes were not disciplined at all, and at least four dirty socks were placed on the floor of the room. The bed was piled up into a pile, and several pieces of clothes were still in bed. The table was full of scattered drafts, and several pieces of paper fell on the ground. Xiao Yu said with embarrassment, “I’m sorry, the room is chaotic.”
How dare it be? It’s too messy. I stood at the door and said, “Little Yu, I’ll take you out and turn around.”
“Where are you going?”

“There’s a highland park near here. It’s beautiful. Let’s go there for a walk.”
“This, I’m doing a complicated calculation,” said Little Yu, pointing at the paper on the table.
“Come on, take a break. Come to the United States and learn to live in enjoy.”
Yu was still hesitating. I pulled up and said, “Let’s go.” Little Yu had to take the door and walked out of the apartment with me.
The Highland Park is on a hill. It’s not five minutes from the start of a small apartment. There are thousands of clove trees planted on the lawn on the hillside. Now it is the end of the clove season, but there are still many kinds of lilac flowers on the tree. I park the car on the roadside at the top of the hill. We got off the car and walked along the path in the flowers.
“Do you have any progress in your research?” I asked.
“It’s a big progress.” Little Yu suppressed his complacency. “I’ve already proved that the Riemann ζ function has no zero point when x is greater than 0.99 and less than 0.01.”

“Wait, what did you know before?” I asked.
“It was known that the ζ function was not zero when x is greater than or equal to 1 and less than or equal to zero.”
“That’s to say: You improved 0.01… than before.”
“Don’t underestimate this 0.01. For more than a hundred years there’s no person able to translate the boundary of this critical zone into even a Dinking point. That’s why mathematicians can translate this critical zone boundary into this conjecture as quasi-Liman hypothesis. I have actually demonstrated the quasi-Liman hypothesis!”
“Then… is that a major breakthrough?”

“Of course!” Little Yu lowered his head and walked down from a bunch of purple cloves. “I have to write it out, and it is estimated that it can be published in the world’s top math magazine.”
“Then you’re going to write your manuscript quickly.”
“I don’t want to write yet.”
“Why?”

“I told you that my approach could be the right way to completely justify the Riemann hypothesis. If I make it now, then others will know my method. Maybe someone would have robbed me of the Rieman hypothesis.”
“So you want to keep it secret now?”
“Yes. You know, it took him seven years to prove the result of the Fairman’s Great Theorem. He didn’t tell him that it was just for fear of others to know what he had done. I had spent more than ten years of gold time in Liman’s conjecture, so it was so. Now I can finally see the dawn of a little end. I’m not a Sage, of course, I don’t want to see someone else grab me in front of me. So, you must keep it for me. It’s your wife, and it’s better not to tell you.”
“Of course.” I assured him.
We saw a wooden chair on the roadside. I sat down and sat down. The chair was facing down the slope. The front was an open green lawn. Looking up, the white clouds and the blue sky were intertwined, and the sun was shyly hiding behind a large cloud of clouds. The cold wind was a habit, and the fragrance of the clove flowers was filled with the wind. A young couple led a small curly dog from behind us. They greeted us in a friendly manner. In the distance, the tall and low buildings were hidden in the green trees, like some sail shadows in the green ocean. The world was particularly gentle in the quiet.

“It’s good to see the scenery here,” said Little Yu.
“Yes.” I attached and said.
“It seems that you are very happy. I haven’t had such a calm and calm feeling for a long time. Looking at the landscape, I feel that living in this world is really a happiness.”
“Do you know that this world is really exquisite?” I thought of my own bank. “There are some important constants in physics, such as the Pritz constant, the fine structure constant, and so on, if it is a little different from the current values, the world will be different. We are often confused by this matter: all the settings in this world, such as those physics constants, seem to be prepared for us. Why is it that? In order to answer this question, some physicists put forward the principle of human selection. It is believed that those constants are precisely because the universe requires observer, that is, our human existence. Otherwise, no one will ask these questions.”
“Interesting,” said Little Yu. “But how do I think this explanation is a little inverted?”
“There is a point. So not all physicists agree with the principle of human selection. But the principle of human selection is indeed based on the physics we know and cannot be considered as a merecentrism. In quantum mechanics, we know that observers are likely to have an impact on quantum. For example, when you observe it, it is impossible to know which place it is. You can only know the probability it appears in a place. In order to explain this probability, physicists put forward multiple universe theories. They believe that the universe is divided into countless parallel universes at every moment. When you observe the moment of electrons, the world is divided. The electrons you see are just the samples of it in this world.”
“Well, I’ve heard a bit before,” said Little Yu. “So what’s the relationship between this multi-smic theory and the principle of man-selection?”

“It is natural to explain the principle of human selection using the principle of multiple universes. The reason why our universe is now is because in countless parallel universes, only the universe in this way can produce our human observer.”
“The things you’ve studied are becoming more and more mysterious. It’s also something that we’ve studied in mathematics.” Little Yu sighed. “It’s lucky that I didn’t learn physics. Thinking about the strange ideas in quantum mechanics, I’m very big. Ha-ha.”
“I don’t know the existence of your mathematics depends on the observer.” I joked.
“Nonsense. How is that possible? The Mathematics Theorem is based on rigorous logic reasoning, and you can’t change them into your parallel universe.” Xiao Yu said with a smile. He then said, “By the way, my wife will come to see me from the country. If you can help me to pick her up.”
“No problem.” I said. I know that Xiaoyu’s wife is in Chinese. They don’t have children. “Hehe, your wife takes a plane to help you tidy up the room.”
“Hehe.” Little Yu smiled and did not speak.

IV. The arrival of Wu Fang

Xiao Yu’s wife, Wu Fang, arrived at one night after two weeks. I drove the car and took her to the airport to pick her up. On the road, Xiao Yu told me that his research had also made new progress. He had narrowed the critical zone from 0.01 to 0.99 to 0.27 to 0.73. I said, “It seems that the progress is not small.”
“Of course, that’s what I think. I think I can finally be sure that I am on the right path. That’s the result itself as a major breakthrough in the Rieman hypothesis. I believe that this is the first time that humans have proved so close to Liman’s hypothesis.”
The airport is not far away. From a small apartment to the airport for only 10 minutes. However, Wu Fang’s aircraft was delayed for two and a half hours. When we received Wu Fang, it was at 11:20 p.m.
Wu Fang was not tall, her skin was white, oval, and she looked very beautiful. Her eyes were very attractive. Her black hair was casually tied to a ponytail. Dressed in a gray pants, a light blue dress. When she saw her, she jumped into his arms.
“This is my wife, Wu Fang. This is my old classmate, Zhang Chengyuan.”
“Brother Cheng Yuan.” Wu Fang shouted.
I said with a smile, “Little Yu, I think you want to fall asleep.”
Wu Fang laughed happily and said, “I’m afraid he’s thinking about his mathematics?”
Xiao Yu is busy saying: “If you want it, the wife needs to think about it.”
We said with a smile, he went to pick up the luggage. Wu Fang held Xiao Yu’s hand, and the two were very close. It seemed that Little Yu was very good at mathematics. His wife looked beautiful and wise.
“Today’s plane scares me, “ Wu Fang said.
“What’s the matter?” Little Yu asked with concern.
“When our planes were in the Pacific, all the instruments were out of work.”
“How could such a thing happen?” asked Little Yu. “What’s the reason?”
“It’s strange that even the driver doesn’t know what’s the reason. It’s not long. The radio on the hindplane said that they never met this kind of thing. Some passengers also said that they had not encountered a flying dish. But no one saw a flying dish.”
“What time is it?” I asked.
“It’s about seven or eight hours ago,” Wu Fang replied.
Seven or eight hours ago, about three or four o’clock in the afternoon. When Xiao Yu heard Wu Fang’s words, his face changed. I asked, “What’s the matter?”
“Nothing. The critical belt of my 0.27 to 0.73 is about to come out at this time.”
“Ha-ha, it’s really a coincidence. It seems that your mathematics has found an impact on Wu Fang’s aircraft,” I said with a smile.
“It’s just a coincidence.” Little Yu smiled. It was a little unnatural. We got the luggage and said with a smile, walking towards my car.
After sending them back to the apartment, I came home. The wife and the children were asleep. I used to open the computer and browse the news. Suddenly, there was a news that sucked my eyes like a magnet:
The world’s aircraft instrumentation has failed at the same time.
News says that in the east of the U.S. today at about three a.m.
Seeing this, I feel that there is a burst of cold in my body. What does this really have to do with the research of Little Yu?

V. Encounters of wild cooking

One turn, two months later. Time went by as usual, and the world was as quiet as usual. People had long forgotten about the failure of the aircraft instrument. I did not talk about this with Little Yu and Wu Fang. Little Yu tried his calculations and deduced his calculations as usual, and did not care about the news outside his body. When he wanted to further narrow the critical belt of the Rieman’s ζ function, he always said there was no progress. He told me that he might have been too optimistic. When he wanted to further narrow the critical belt of the Rieman’s ζ function, he found that there were several obstacles that seemed to be insurmountable in front of him. He told me that he might have been too optimistic. When he wanted to further narrow the critical belt of the Rieman’s ζ function, he found that there were several obstacles that appeared to be insurmountable in front of him. He told me that he might have been too optimistic. When he wanted to further narrow the critical belt of the Rieman’s ζ function, he found that there were several obstacles that seemed difficult to overcome before him. He told me that he might have been too optimistic. When he wanted to further narrow the critical belt of the Rieman’s Ζ function, he found that there were several obstacles that appeared to be insurmountable in front of him. He told me that he might have been too optimistic. When he wanted to further narrow the critical belt of the Rieman’s Zeny function, he found that there were several obstacles that seemed difficult to overcome in front of him. He told me that he might have been too optimistic. When he wanted to further narrow the critical belt of the Rieman’s Ζ function, he found that there were several obstacles that seemed difficult to pass through. He told me that he might be too optimistic. When he wanted to further narrow the critical belt of the Rieman’s Zeny function, he found that there were several obstacles that seemed insurmountable, and that was just like a few steep mountains that blocked him from moving forward. Looking at him, he was probably too optimistic. When he wanted to further narrow the critical belt of the Rieman’s Ζ function, he found that there were several obstacles that seemed difficult to pass through. He told me that he might be too optimistic. I felt that the road was tortuous and the future was bright. After hearing it, Xiao Yu laughed. I felt that I had no confidence in what I said just now.
On a Saturday at the end of July, we pulled them to a park in Lake Ontario to cook. This is one of the famous five lakes in North America, where the city is located on the lake. The day before, a heavy rain took away a lot of summer hot. The park’s wild cooking land is famous in the city. A strong tree shade sets a lot of picnic tables and grills, all of which are available for use.
We found an empty table not far away from the lake. Today is a sunny day, but the lake is cool, blowing on the body is very pleasant.
Wu Fang and I put coal on the oven, lit the fire, began to barbecue. The son ran to a small amusement park on the edge, and Xiao Yu went to the beach in the lake to walk. He saw him wandering over there with his hands behind his back, and sprinkled a series of deep impressions on the beach.
Ms. Wu is obviously worried about her body. She comes to the oven side and helps us turn over the meat while talking to us: “Yuzhen is worried. He often works at three or four in the morning. I went to school early in the morning and forgot to have lunch several times in school.”
Xiao Fei looked at Xiao Yu’s walk and said, “He doesn’t seem to be thinner.”
Wu Fang said: “That’s not because I forced him to drink milk every day. Otherwise, I really don’t know how he can live.”
I said, “It’s thanks to your care.”
Wu Fang sighed and said, “I just don’t know how long he can stick to it.”
I comforted her: “Now he is just stuck there. If his problems are solved, it will be good.”
Wu Fang shook her head and said, “This problem is solved, and there will be another problem.” Wu Fang was a scholar and did not understand the advanced mathematics at all. However, she knew that Xiao Yu’s research was a major problem in mathematics. She also knew that Xiao Yu was not a general problem. She knew very well about the talent of Xiao Yu. Usually, she looked at Little Yu with a trace of admiration. However, her eyes were only concerned about fear and anxiety.
“There’s no problem with it.” I said. “When I read the doctor back then, I only slept for three or four hours every day in order to catch up the paper. It’s not coming back.”
Xiao Fei said: “Don’t mention you back then. But now you are sleeping lazy every day. Look at your stomach.”
“Didn’t this summer break?” I patted the bulging stomach and said, “It’s all yours.”
Xiao Fei said to Wu Fang: “The United States only knows the importance of the body. We can’t afford a big disease here.”
Wu Fang said: “Alas, forget it. Don’t think about it. You can eat more meat today,” said Wu Fang. On the oven, sausage and chicken were all baked, and the fragrance began to murder people’s intestines and stomach.
“We can eat it. Let’s call Little Yu.” Xiao Fei said to Wu Fang.
Wu Fang agreed and was going to call Little Yu, but he saw Little Yu walking in a hurry from the lake. Wu Fang used to greet him. They hand the hand back to our table. Xiao Yu took out a paper in his bag and said to us, “I’m sorry. I just had a wonderful idea. I have to check it out.”
“Do you want some roast meat?” Xiao Fei came to the table with a tray of roast meat.
“To eat it, I need a little time.” Little Yu took a paper and went to the table. Wu Fang picked several sausages and several pieces of chicken with a paper tray, and gave her a look at her. “You can eat it while you’re counting on it.”
Xiao Yu looked up at Wu Fang and said, “Thank you.” He buried his head and continued his calculations.
Little Yu’s time concept is obviously different from us. His “a little” time has been over half an hour and he is still counting on it. We have all the meat baked, and everyone is full. We are thinking that Little Yu will never be finished. Little Yu suddenly shouts loudly: “It’s it!”
As this shouts, a dazzling flash of lightning suddenly lit up in the sky, followed by a blast of thunder. All of them were shocked. Then, the sky gradually dimmed. The sun was still hanging high on the sky. However, the sun slowly lost its luster and became like which child was casually posted on a pale disc in the dark sky. I could easily watch it with naked eyes. The park’s tourists stood there and looked at the sky with surprise. My son was afraid to hide in his mother’s arms and said, “Mom, what happened? Is it the end of the world?”
Xiao Fei patted his shoulder and said, “No, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no
The vision was about five minutes, and the sky became brighter. The sun restored its previous brightness.
The tourists began to work, and many people gathered together. Xiao Fei and Wu Fang began to pack things. I asked Little Yula to the side and asked, “Little Yu, how old have you solved just now?”
“It’s very big. It can be said that in order to completely prove that the Liman hypothesis has cleared the obstacle, what’s wrong?”
“Little Yu, do you remember the failure of the aircraft instrument that Wu Fang came from that day? On that day’s news, the world’s aircraft instrumentation had failed at the same time. And that time was exactly the moment when you proved Rieman’s assumption of a breakthrough.”
“That’s just a coincidence.”
“Listen to me. The odd thing happened by accident. It happened twice and everything happened when you made a major breakthrough in the study of Liman’s hypothesis. I’m afraid it’s not that accident.”
“Are you saying that two strange things are because of my research?”
“There’s such a possibility.”
“That’s nonsense! I think this is theoretical research, how can we have a direct relationship with the real world? To say that my research has been applied to the world, it’s also said to be the past.”
“Tell me that Riemann assumes a more important position throughout the maths?”
“Well, you know that natural numbers are the basis of mathematics, and the number of primes can be said to be the basis of natural numbers. The Rieman hypothesis can help people completely deal with the distribution of plain numbers. It can be said that Liman hypothesis is at the core position of the whole mathematics.”
“You just said that the Liman hypothesis can be applied to the real world?” I thought that the theory was the most abstract mathematics. And Rieman hypothesis was the most sophisticated theory in the mathematical theory. I understand the significance of Liman hypothesis on mathematics theory. But to say that Liman hypothesis will have some practical application, it makes me feel unbelievable.
“Yes.” Little Yu answered. “Do you know what network security is based on?”
“My password?” I guessed.
“Yes, but not only the simple password of your own.” Little Yu stared at the lawn under his feet. “For example, when you pay your credit card or something, your bank’s transmission of your credit card information is encrypted and decrypted by a number of methods. This code system is called the RSA encryption algorithm. The success of this algorithm is based on the random distribution of the number of prime numbers in the natural number set. If you can prove the Liman hypothesis, and then understand the distribution of the quantity, people may find a method of quickly decomposing the number on this basis, which will have a very far-reaching and unpredictable impact on today’s password system.”
“Oh.” I really didn’t expect that pure and pure mathematical theory would be so applied. However, the words below made me more surprised.
“In fact,” said Little Yu, “Liman hypothesis may also have direct links with the quantum mechanics of physics.”
“Really? That’s impossible?” As a physicist, I know that there is a close link between mathematics and physics. For example, Yang Zhenning’s normative field theory is based on the modern differential geometry. However, it is incredible that there is no direct link between the mathematical theory and quantum mechanics.
“There is an interesting story here. When the mathematician at the University of Michigan
“Study on a random matrix Dai Sen?” I asked. The random matrix was an important tool to study complex physics systems such as heavy nuclei. Mr. Dyson was famous in the physics world because of the groundbreaking work in this area. I had seen him at the American Physics Year. He was a wonder that Dai Sen was a genius who studied mathematics alone.
“Yes,” said Little Yu. “Mr. Zhoula said to Montgomery: Dude, I took you to see a cattleman. As he said, he pulled Montgomery to Daisen. In fact, Montgomery had met with Daisen on the road, but it was only Harodharo’s greeting. Montgomery thought: “Don’t you need it? You know Zhou La is a stubborn man, and he said it was necessary to do it. Hard is to bring Montgomery to Daisen and introduce them to them. He probably thought it was not clear, he wrote down his statistical formula on the zero interval on the paper. Do you know Mr. Daisen suddenly opened his eyes and said, “Is this not the correlation coefficient of the distribution of the characteristic value of the random Eritrean matrix?”
Although I am not statistical physics, I have some understanding of the meaning of these words: the correlation coefficient is a statistical amount of the interval. The characteristic value of the random Eritrean matrix is the energy level of complex quantum systems. It is known that in physics, the three-body problem in classical mechanics is already a difficult problem to be solved so far. In complex quantum systems such as heavy nuclei, the number of proton neutrons is far more than three, and the quantum mechanics is followed. Therefore, the research is more difficult. In order to solve this problem, physicists use statistics to study. Matrix is the main tool of quantum mechanics, so the statistical quantum mechanics is used in the random matrix. The correlation coefficient distribution of the characteristic distribution of random Eritrean matrix refers to the distribution characteristics of the interval between different energy levels of complex quantum systems. However, it is really incredible to say that this distribution is the same as the distribution of the non-trivial zero point of Liman’s ζ function.
“This… I’m afraid it’s just a coincidence, right?” I hesitated.
“In 1980,” said Little Yu, “The Odeliz Section of the University of Minnesota, that is, the mathematician who has checked the ten-mile non-trivial zero, has made a numerical calculation of the energy-level distribution of various complex quantum systems. After averaging, it is found that the interval distribution of this level is exactly the same as the interval distribution of the non-trivial zero point of the ten megazero Ζ functions that he has calculated. It’s probably not a coincidence, right?”
“This… seems unlikely to be a coincidence.” I was shocked. The two things were obviously not at all. Why do they have such a consistent distribution? Could the abstracts invented by the mathematicians once again describe our real world? Number of theories and quantum physics? It’s too incredible! “So, is that the proof?”
“No,” said Little Yu. “In fact, no one can explain why these two distinct distributions are so consistent.”
At this time, Xiao Fei walked over the table and said, “Our things are clear. Let’s go home.”
“Well, “ I said to Xiao Fei. Then I turned to Xiao Yu and said, “I have some ideas, but I have to think about it carefully. I’ll talk to you tomorrow.” After saying that, we went to the parking lot together.

VI. Riemann’s cat

The next morning, about 10 a.m., I drove the car to the apartment of Little Yu. Yu and Wu Fang were at home. Their room was clean and clean than the one in Xiaoyu. After a while, I sat down and said to Xiao Yu, “Little Yu, I thought of a night yesterday. I want to talk to you about my research thoughts.”
Wu Fang, who is looking for tea, said, “Can I hear it?”
I looked at Little Yu and said, “No problem.”
“Well, “ I said to Xiao Yu, “I have to talk to you about quantum mechanics first. Do you know the cat of Xue Dingyu?”
“What kind of cat is that?” Wu Fang asked.
“I know a little bit. But it’s not true,” said Little Yu.
“The cat is not a real cat,” I said to Wu Fang. “That’s the cat in an ideal experiment in physics. It’s like this: some of the results in quantum mechanics seem to be grotesque. One of them is: in the micro world, the observer decides the results of the observation.”
“What does that mean?” Wu Fang had finished the tea and gave each of us a glass of tea.
I gave a tea and said, “Wow, this tea is really good.”
“This is the West Lake Longjing brought by me from home. Zheng Zong,” said Wu Fang.
“No wonder it’s so fragrant.” I’m still drinking tea. “Where do you start? Do you know the second elephant?”
“Yes,” said Little Yu. “It’s microscopic particles, such as photons, and they have the properties of particles and waves.”
“Yes, “ I said. “In fact, all microscopic particles have the duality of wave particles. This fact is based on experiments. A well-known experiment is called double- or double-hole experiments. It is an electron-launching source that emits electrons from a baffle with two small holes away from the back of the baffle, and a electronic detection screen is placed not far away behind the baffle. Some electrons pass through the small holes and leave records on the test screen. If electrons are a single particle, it is like a bullet, and when many electrons are emitted, the records seen on the test screen should be two unrelated dots or dots. However, the actual situation is not so. When many electrons are emitted, the records seen on the test screen show the interference fringes of waves, like two waves passing through the two small holes and interfere with each other. Thus, it is known that electrons are of the nature of wave.”
“This is strange?” Wu Fang asked.
“Yes. The problem is that if only one electron is emitted to the baffle, the electronic does not necessarily fall behind the two small holes as a bullet and then to a point in the interference ripple. The magnitude of the wave size determines that we find the probability of this electron. So, this electron wave is a probability wave. So what is this electron coming here? There is no answer to this question. It is impossible for people to know how electrons fly past, and it is impossible to know which hole it is from. This electronic wave is like a ghost, which is inconceivable.”
“Isn’t it? Can’t people use something to measure how electrons fly?” Wu Fang asked.
“Good question,” I said. “It can be measured. But, for example, if you want to see which hole you’re going through, you have to launch a beam of light to this electron so that you can see it. The problem is that the light changes the initial experimental conditions. Once people see this electron with this beam of light, its behavior is completely transformed into particles, like bullets. That is to say, our observation has turned the electrons from an illusory ghost into an objective entity!”
“Wow! Is there anything else in the world?” Wu Fang exclaimed.
“The math is true,” said Little Yu.
I glanced at Xiaoyu and said, “Let’s continue talking about Schrödinger’s cat. Schrödinger is an Austrian physicist. In 1935, Schrödinger proposed an imaginary experiment in one of his papers. Put a cat in it. Enter a closed box, and then connect the box to an experimental device containing a radioactive nucleus and a container of toxic gas. Imagine that the radioactive nucleus has a half chance of decay in an hour. If it decays, it A particle will be emitted, and the emitted particle will trigger the experimental device to open the container containing the poisonous gas, thereby killing the cat. According to the principles of quantum mechanics, without observation, we cannot be sure of the nucleus Whether it is decayed or undecayed. To be precise, the nucleus is in a superimposed state of decayed and undecayed. However, if the box is opened after an hour, the experimenter can only see the’decayed nucleus and dead cat’ Or one of the two situations of’undecayed nucleus and live cat’. The question now is: When did this system cease to be in the superposition of two different states and become one of them? Open the box and observe In the past, was the cat dead or alive or half alive? Like the previous double-slit experiment, according to the interpretation of quantum mechanics, here is the observer who determines the life and death of the cat. In our physics jargon, it makes the cat The superposition of death and life collapsed, so that we can get the only result of this cat being alive or dead. The difference is that this closed box is no longer limited to the micro world, but in the macro world of our daily lives. The grotesqueness of quantum has come to our daily lives.”

I made a great deal of endorsement, feeling as if I was giving my students classes. I drank tea and saw Wu Fang’s beautiful face puzzled, while Xiao Yu was thinking about where he was.
After a while, Yu finally raised his head and said to me, “Do you want to say that I have made a study on the assumption that I have become an observer in the experiment of your cat?”
Little Yu is a mathematical genius who caught me so quickly. I added: “I think our cat can be said to be Liman’s cat.”
Wu Fang said, “I don’t understand. What do you mean?”
Looking at the window, Xiao Yu said: “It means that mathematics is similar to quantum mechanics. The mathematical truth is not present before people observe, but when people observe the truth of mathematics, it changes our initial conditions like that beam of light to electrons, so that the truth of mathematics becomes an entity from illusion. But what does this have to do with yesterday?”
“I don’t think that all the mathematical theorems can have a direct impact on the real world. But as you described yesterday, Liman hypothesis is the core guess of mathematics. But the energy level of complex quantum systems is indeed closely related to the distribution of those zero points. Perhaps they are interdependent relationships, one distribution change, and the other distribution will change. So, I think that our world depends on the uncertainty or illusory nature of Liman hypothesis. Once Rieman assumes that this Rieman’s cat is confirmed or fake, it will make it collapse. So, we now know that the world depends on the uncertainty or illusory nature of the Riemann hypothesis. It is clear that any change in the micro world will change the basis of our substance, so that our macro world will produce great changes. I used to tell you that from the perspective of human selection, our world is very delicate and fragile. Any change in the physical world, I think will only be an unprecedented disaster!”
“I’m afraid it’s just your idea, right? You don’t have any evidence to prove your theory,” said Little Yu.
“The evidence? What else do you have to explain yesterday’s strange events? What happened to the failure of the world’s aircraft instrumentation that day?” I said.
“But that can’t be a disaster?” said Little Yu. His face was a little pale.
“That’s because you haven’t completely demonstrated Liman’s hypothesis. The light that you shot to Liman’s cat is not strong enough, but you’re not able to completely collapse the overlap!”
“Hehe, what do you call me?” Little Yu sneered.
“The only thing that can be done: Stop your proof.” I know that this is a fatal blow to Xiao Yu, but I have to say.
“Come on!” Little Yu suddenly stood up. “You came here early in the morning to talk nonsense. You want me to stop my certificate? Are you jealous?”
“What are I jealous of you?” I was too angry. “My life is already so. How can you have any influence on me?”
“All your conclusions are nonsense. Mathematics is mathematics, mathematics and quantum mechanics are fundamentally different. The truth in mathematics is real, no matter what people have found them, they exist there. What I do is just to uncover a cloth covering the eyes on the truth. How can it cause a disaster? Your idea is absurd!”
“I admit that I have no strict proof of my thoughts. But the strange events that took place at the time of your breakthrough are unlikely to be coincidence. What if I say is true? Then your personal behavior will destroy our world. The victim will include you, including Wu Fang, including our family, including all other innocent people. Have you thought about this?”
“There’s no consequence at all! Your idea is entirely your imagination. You’ve been in the U.S. for a long time. Are you worried about losing these?”
“Well, stop arguing!” Wu Fang shouted beside him.
I calm down. It seems that I can’t convince Xiao Yu today. I said to Xiao Yu: “Well, I’m not arguing with you today. I told you my point of view. I hope you can think about it. Wu Fang, see you later.” After saying that, I left Little Yu’s home.

VII. The world is no longer the same

On the morning of the next morning, I called Xiao Yu’s house and Wu Fang took it. She told me that Yu Yu was lying on the table last night, and he went to the university a long time ago. I know that Xiao Yu was not persuaded by me, and he still continued his research. I can only hope that my thoughts are wrong.
However, at about 2 p.m., a flash appeared on the sky.
It’s not lightning, it’s flash.
At the beginning of the flash, I was sitting on the side of the window in the bedroom on the second floor. I saw a man and a girl, seven or eight years old, on the road out of the window pointing at the sky. I walked along their fingers to the sky, and the sky was full of red, orange, yellow and golden, shining like countless flames in the blue sky.
I felt cold in my heart. It seemed that it was true. I heard the sound downstairs and said, “Mom, come to see it. It’s all about fireworks!”
I rushed down the building, picked up the phone, and wanted to call the small office. However, there was only a squeaking noise in the phone. I said to Xiao Fei and Jian Jian who looked at the sky at the door: “You stay at home and don’t go out. I have to go to Little Yu.”
“It’s like this outside, don’t you go out?” said Little Fei.
“No, it’s very important. I’ll come back to you.” I rushed into the garage and drove to a small apartment.
The flash in the sky became increasingly dense. At the same time, the sky began to become red. On both sides of the street, people were looking up to the sky. I opened the radio in the car and wanted to listen to the news of the radio station. However, the radio was full of noise. Suddenly, a huge airliner whistled from the sky on the head. It was not a while, and only heard a loud bang from the direction of the plane flying. The earth suddenly shook and my car was shaken. A fire light was covered with smoke from the sky. Oh my God! I cried in my heart. A plane fell down! I looked up and looked at the sky, with a colorful flash of the sky. It was impossible to estimate that the aircraft’s instruments were all down. Those aircraft that were still on the sky were afraid that no one could survive.
I came to the apartment of Little Yu and saw the apartment door open. The downstairs was full of people, and there was a lot of discussion in the sky. I took great strides to the building. I saw Wu Fang hurriedly preparing to go out. I asked, “What about Xiao Yu?”
“He has gone to school and hasn’t come back yet.” Wu Fang said.
“Do you know where the office of Xiao Yu is?” I asked Zhou Bao and Wu Fang to walk down the building.
“I know, I’m going to go to him.”
“Get in the car, let’s go to find him.”
“This,” Wu Fang pointed to the flash in the sky and asked, “Is it because he?”
I nodded.
“What’s going on?” She pointed at the dense smoke nearby.
“It was a lost plane, because the instrument failed to fall down! These are all the credit of Xiao Yu.”
Wu Fang was stunned. “Really?”
“There should be no doubt now. I’m sure that Xiao Yu might have quickly figured out his assumption of Liman. It’s not allowed to come out. His certificate will change the basis of our substance and may destroy our world! God bless him not yet.”
Wu Fang stood at the door, and her white teeth clenched her lower lip and fell off with tears. I didn’t know how to comfort her. She said softly, “Let’s get in the car quickly. Maybe he hasn’t finished yet. We have to stop him quickly. I hope it’s still too late.”
Wu Fang went to the car, and I stepped on the accelerator. The car roared and ran to the University of Luocheng.
The road has begun to break. I saw a couple of cars collided when passing through a crossroads. Looking up, the green light here was also like the sky. I went through the edge. But at the next intersection, I could no longer move. The car there was seven vertical and eight squeezed together, and no one could move. I and Wu Fang had to abandon the car and rushed to the University of Luocheng.
The University of Rome is not far away, and Xiaoyu is usually walking to work. I and Wu Fang run in a chaotic street, and soon they arrive at the campus. Although I am not in the University of Luocheng, I often come here to know where the math system is. I and Wu Fang soon find this building. This is a six-storey building. Because it is summer vacation, there is no one in the building. The window of the building reflects the flash of the sky under the black sky curtain and is very mysterious. I and Wu Fang came to the gate, I pulled a glass door and pulled it. The door was locked! I looked around, there was a big stone not far away. I ran over and moved the stone back to the door.
“What are you going to do?” Wu Fang asked.
I didn’t answer. Raise the stone and hit the glass door. Just listen to the sound of “swoosh” and the glass crumbled. I pulled up Wu Fang and drilled it from the broken glass door.
“Tell me, where is the office of Xiaoyu?”
“In the fifth floor,” Wu Fang answered.
I went to the stairs with Wu Fang. This time, even if the elevator was still open, I wouldn’t try it.
We rushed to the fifth floor, Wu Fang pointed to an office. We ran to the past. The office door wrote “Xiaoyu Tian” several words. I suddenly patted the door. Xiao Yu opened the door from inside. I shouted, “Little Yu!”
Xiao Yu looks at us in surprise: “Cheng Yuan, Fang Fang, how are you coming? I’ll tell you a good news: I’m about to prove Liman’s assumption!”
I glanced at the office of Xiao Yu. It was found that the office of Xiao Yu was not big, there was no window, and the ceiling was illuminated by a fluorescent lamp on the top of the ceiling. Little Yu’s desk was filled with paper. It was obvious that Xiao Yu did not know what was happening outside.
I shouted, “You’re still here! You come here to see.” I took Xiao Yu and ran to the corridor.
“What’s going on?” Little Yu protested.
I didn’t answer and dragged Xiao Yu to the window at the end of the corridor: “Look outside!”
The sky outside had become black and red, like the night in the winter snowy city. Xiao Yu looked at the continuously dazzling light on the sky and asked in surprise, “What’s going on?”
“You don’t believe it? It’s all because of you! The plane’s off. All the communication facilities are out of work!” Just as he said, the lights on the corridor were suddenly destroyed. The lights outside the other buildings were also destroyed. “Well, now there’s no electricity now!”
Flash lighting the corridor outside. Our faces are changing in the five-color flash. Xiaoyu looks at us with eyes wide open, and the eyes are filled with confusion.
“There is no doubt now. Do you remember what I said yesterday? It was your research that changed the world. You have to stop research quickly!”
“But… I have completely demonstrated that Liman’s assumption is just the last step. I’ll just have three hours’ calculations…” Little Yu hesitated.
“Stop! You haven’t got a chance to come out of the world. We’ll all be doomed if you pass it out!”
“Xiao Yu, let’s listen to Brother Cheng Yuan.” Wu Fang held her clothes and said.
“I…” Little Yu also wanted to say something.
“Let’s see the outside! I saw a plane off! How many lives!” I said. Wu Fang nodded at the edge.
Xiao Yu suddenly crouched down and held his head. Wu Fang crouched down beside him and pushed him down. He said, “Let’s go home first.”
Little Yu stood up. He seemed to have lost all his energy at once and headed towards the office with Wu Fang.
The office is not far away from the window. Although there is no lamp
Xiao Yu put his notebook and paper into his big book bag. He walked out of the office with a book bag. He was dark in the corridor, and we groped for the next building. At the door of the building, Xiao Yu saw the broken glass and asked, “What’s going on?”
Wu Fang pointed at me: “He used stones to hit it. Otherwise we can’t come in.” Outside the dark red sky was still shining. It was only at 3:30 p.m., but it seemed to have arrived at 12 o’clock in the evening. The campus was quiet. Three of us walked out of the campus. The streets were littered with abandoned cars. There was a smoke of smoke in the air. There was no way many pedestrians were out there. Occasionally, some policemen walked around with the batons. On a road, I went in and tried it. The car was not on fire. I closed the door. We continued to walk to the small house.
When I arrived at Little Yu’s apartment, I and I said: “You’re all going to our house. I don’t know what will happen next. We’ll all be safe together.”
Wu Fang and Xiao Yu looked at each other and looked at each other. Wu Fang nodded and said, “Let’s get something.” They went upstairs to clean up the good stuff. Then we went to my home.

VIII. Wu Fang’s choice

Half an hour later, we went to my home. There was no lamp in my house, but the flash outside gave some light to my house. Fei and Jian Jian sat on the sofa in the living room. Fei saw us entering the door, and quickly stood up and asked, “Why have I been out for so long? The phone doesn’t make sense. I’m so anxious. What about your car?”
I spoke roughly about the situation. Tell her that they were temporarily living in my house. Xiao Fei helped them put the things in, and we all sat down in the living room.
“Xiao Yu,” I said, “You should trust me now?”
Yu slowly nodded and said, “I don’t want to go down.”
“But now it seems too late,” I pointed to the sky outside. “This strange event may not be as much as a few minutes ahead of the previous two. At least there is no sign of stopping now. Let’s hope not to get worse.”
“It’s bad enough now,” said Little Fei.
“If Koyu has finished his theory, our world may be completely destroyed.” I said. I don’t need to hide anything about Little Fei. I told Little Fei about the work of Liman’s assumption, and how my work would change mathematics, so as to change our world’s idea. Little Fei was a nurse, and he was not familiar with mathematics and physics. Listening to my words was like listening to the Tomes of Arcane. However, she finally heard a few words.
“Are you saying that all this is caused by Xiaoyu?” she asked.
I nodded.
Little Fei opened her eyes and looked at me later. She said, “How can I know? I’m just my math.”
“I told you yesterday, but you don’t listen.” I said.
“But what you said is too incredible.” Little Yu said.
“What should we do now?” Wu Fang asked.
“There’s no way,” I answered. “We’ll wait to see it.”
Television radio calls are all useless. We are like an island in the ocean, and we can’t know what happened outside the world. We can’t cook with electric stoves. There are still a lot of bread at home. Each of us eats a few pieces of bread and ham sausages. It is filled with stomach.
At night, the flash at the sky continued, but it was not so dense. The weather began to cold. When we slept, we had to find a long time-free cotton quilt.
The next morning, I looked out of the window and was covered with heavy snow. The quilt was lifted and felt a chill. I found the sweaters and leather coats worn in winter and pushed the door open. Outside, the ground, the house, the trees were covered with red snow. It was still summer season! The sky was dark red. The flash was basically stopped, and replaced by some slow-moving curtain-like green light, as if the demon was prepared to show you a great play in the sky. The polar light! This dimension generally does not see the polar light. I am in a daze that I have entered the scene of the science fiction movie “The Heaven”.

![][3]

Fei was also up. She came to the door with a cotton-padded jacket. She snuggled at me and said, “Chengyuan, I’m so scared.”
“Don’t be afraid, everyone is the same.” I replied. I think this day will be as cold as the “The Heaven”? Should we still burn books and heat? Will we finally freeze or starve to death?
“I’ll give them cotton jackets.” Little Fei said. They did not expect the weather to be so cold yesterday, so they didn’t bring the cotton-padded jacket. Xiao Fei went to the wardrobe to find out our redundant cotton jackets and sent them to Xiaoyu’s room. After a while, Yu and Wu Fang also wore their clothes and came to the door. Wu Fang shouted, “Why yesterday or summer? It’s winter today!”
“Mom.” Jian Jian shouted in his room. Fei Shanglou took care of the building and woke up. I looked at Xiao Yu and said with a bitter smile, “It seems that the world will not change again.”
Yu Dai looked outside and silent.
Xiao Fei came downstairs with Jian Jian. Jian Jian looked at the light in the north of the sky and said, “Dad, what is that?”
“That’s the Arctic Light.”
“Is it really the end of the world this time?”
I looked at Jian Jian’s wide eyes and did not know what to answer. It was almost the end of the world. But what should I say to the child? Xiao Fei crouched down and said to Jian Jian, “Child, this is just temporary. The end of the world is still far away.”
At noon, the sky was colder. The temperature in our house had fallen to 18 degrees Celsius. The sky was still dark, and the snow was still under constant. The Arctic light was still swaying in the dark sky. Because of the power cut, the heating was not opened. We put the stoves in the house for heating. However, everyone was frozen enough to choke. Xiao Fei, Jian Jian and Xiao Yu had been in the quilt for heating. Wu Fang called me to the study and said he wanted to talk to me.
“Xiao Yu is very frustrated,” she said.
“In fact, it can’t blame him. He doesn’t know that his research will bring such a big disaster. In fact, I don’t really believe it when I told him about my theory.”
“But, in fact, he brought us to the end of the world,” said Wu Fang.
“Perhaps, it’s not the end of the world. He has stopped studying, maybe the world will not be even worse.”
Wu Fang shook his head. “It’s impossible. Look at the thermometer’s pointer is still straight down. Soon, all of us will be frozen.” Her tears began to fall. She lowered her head and continued to tremble.
I walked over and patted her shoulder and said, “Don’t cry. The tears will freeze. If this is really the end of the world, let’s face it with strength.”
Wu Fang raised his head and wiped the tears with his hand. “I didn’t understand exactly what you said before yesterday. But I basically understood something. You said that the change in the world was due to the fact that Yu’s certificate changed mathematics, thus changing the world. Is it true?”
“Yes. Observers can change the entity this is actually the conclusion of quantum mechanics. I just spread it to mathematics.”
“That is to say, our world has turned into such a way that he became the observer of mathematics, which led to a change in mathematics. Is that true?”
“Little Yu is not an observer in the general sense. The general observer is not able to change mathematics. Little Yu’s work is proof of the most essential thing in mathematics. This makes him the first person to reach mathematics. That’s why he became the most profound observer in mathematics. Only in this way can the observer change mathematics.”
“You said… You said…” Wu Fang said, “If this observer disappears from this world, will our world recover to its original state?”
My brain seemed to be struck by a big stick. “This… I don’t know.” In fact, I have an answer in my heart. This may be the only way to save our world.
“You tell me. I have to know exactly.” Wu Fang looked at me with tears.
I looked out of the window and the snow was still there. I suddenly felt colder. I glanced at the thermometer. It was 25 degrees below zero.
“Do you know how I know Little Yu?” Wu Fang suddenly shifted the topic.
“I don’t know. How do you know it?”
“That’s the morning of the early winter. I ride a bicycle to school. There are some thin ice on the road. Although I am very careful, but when I ride to the edge of a pond, I still skied. I have brought the bicycle together into the pond. I will not swim at all. I have no one in the morning. I shouted out for help. When I was about to lose consciousness, one hand grabbed me. I dragged me from the cold thorn water to the shore. Rescue people, it was Xiao Yu. I was rescued, I was unconscious. Xiao Yu threw me on the ground cotton-padded jacket and wrapped me. He held me running a lot of land, finally stopped a car and sent me to the hospital. To this end, he also gave birth to a big disease and lived with me in the eight-day hospital.
“In the hospital, I know he is a math teacher at our university. He is different from the mathematicians in my imagination. He is smart, persistent and humorous. He later chased me and told me that chasing me to the end of the world would also bring me to the end of the world. I didn’t expect that he really chased me to the end of the world. And I want to…tell me.”
I felt my tears down and said, “I dare not guarantee, but… if there is only one way to save the world, that’s what it is.”
“I see. The world is no longer enough.” Wu Fang suddenly laughed, and her face was still with tears. She stood up and said, “I’ll call Little Yu. We’re going to go out.”
“Wu Fang, you think so. It’s not a joke.” I said.
“Nothing. We just took a walk. I’ll be back in a while.” She pointed to the window. On the sky, the polar light changed the color of red orange and yellow, and the sky was painted like an abstract painting. She said, “The world is still beautiful,” she said. “The world is still beautiful,” she said, with a sense of despair.
She went upstairs. After a while, she left the building with her hand. Yu Ren was led by her and walked out with her. It was like a dream. Wu Fang turned back to me and showed a brilliant smile to me. This was probably the most brilliant smile I saw in my life. They walked towards the distance with deep feet in the snow.
Xiao Fei covered the quilt and walked down. “Chengyuan, why did Little Yu go out?”
I nodded. “They don’t think the house is too boring. I’m going to go for a walk. I’ll be back in a few minutes.”
“How can I go out for a walk?” Fei shook her head and went back upstairs. I saw a thermometer, and it was thirty-two degrees below zero. My body was frozen, but I felt that my heart was even more painful than my body.

IX. Observers of the World

After Wu Fang and Xiao Yu went out for an hour, the snow stopped. The arc in the sky began to darken. I know that the incident had happened. But why hasn’t Wu Fang come back yet? I put on my boots and walked out of the door and walked along the direction they left.
Outside the cold spikes. It is estimated that there are more than 30 degrees Celsius. The snow has not completely covered the footprints. I followed the footprints and struggled forward. The footprints passed through the streets of our community, turning to the right, extending forward along the big road. Two pairs of footprints were close to each other. The road was passed through the 490 intercontinental highway. There was no one on the road, and there was no other footprint. The road was not far away from the 490 intercontinental highway. The footprints reached the bridge on the highway. There was no other footprints on the road. I went down to the bridge to see the snow on the highway and quietly lay a pair of mixed men and women. Blood stained the snow around them, like a red rose in the snow. I know what Wu Fang would do for Xiao Yu, but I didn’t expect Wu Fang to follow him. I grabbed the railing of the bridge and cried.
The thought of the most profound mathematician ever stopped. Because of his insight into mathematics, the world could not coexist with him. I don’t know what else this world can be more sad. I hope that Little Yu can find his home in another world. Wu Fang, help me take care of Xiao Yu in another world.
The sky began to shine, and the temperature began to rise. I know that our world has been saved.
I stopped crying and turned to go back to the community. I saw some people walk out of the house to see the sky.
I have to go back quickly. Little Yu’s manuscripts are still in my house. I want to go back and burn them down. These manuscripts must never let anyone go. They are not in the world.
They belong to the world of Xiaoyu.

——End——

[Note 1] Armateddon is coming, meaning “Hamijidoton!” Hamyjidoton was the final battlefield of good and evil in the end of the world of Christianity.

**Source: ** Science & Magic World April 2009 **Author: ** North Star

Brief introduction to the author:

North Star, real name is Ruhan Zhao，the author of science fiction literature, translator, fan, mathematics professor of New York State University of the United States, now living in the United States, has a small female, according to the May 2006 World Science and Transformation Expo. He has long served as the host of the empty plate of the Qingyun community, and often wrote about the foreign science fiction trends and science fiction awards, affecting the later generations of science fiction enthusiasts.

[3]: https://s1.ax1x.com/2018/09/28/iQJoXd.jpg “Poster for the film “The Day After Tomorrow”
[4]: https://s3.ax1x.com/2021/02/09/yachvR.jpg “Ruhan Zhao”