Xueba's life simulator

Chapter 152
When Zhou Ming uploaded his paper titled "Any even number greater than 2 can be written as the sum of two prime numbers" proving Goldbach's conjecture to arXiv in less than a quarter of an hour, the other side of the ocean at the University of California in Los Angeles A young professor at UCLA is browsing arXiv as usual.

In fact, many professors like to follow arXiv, but most professors do not personally browse arXiv every day. After all, the articles on arXiv are of mixed quality. Reading these articles every day is mostly non-nutritive. It is not only time-consuming, but also harmful. No more useless work.

So although most professors like to pay attention to arXiv, they generally let their graduate students pay attention.

After all, postgraduates, whether they are abroad or in China, are free laborers. They are not in vain, and they can also say that this is to cultivate their ability to read and write papers. very big.

Afterwards, they ask graduate students to tell themselves the useful information they have read from arXiv, so that they don't have to go to arXiv to watch a lot of unnutritious content, but they can quickly harvest the latest research results at the forefront of science and technology.

But this young professor at UCLA is different. He is Tao Terence, and he usually likes to browse arXiv by himself.

The last time Zhou Ming uploaded his paper proving the twin prime conjecture to arXiv, Terence Tao didn’t see it immediately because he was busy at that time, and then he saw this article on arXiv through his students Tell him, he just knew.

This time at Princeton University, it was reported that Zhou Ming proved Goldbach’s conjecture and invited mathematics professors from Princeton University who were interested in Goldbach’s conjecture to attend his academic report at HKUST. Terence Tao had heard about it before.

But for this matter, most people are skeptical about this matter because they have not seen Zhou Ming's proof process.

Tao Zhexuan went to arXiv immediately after hearing the news.

Because in Tao Zhexuan's view, since Zhou Ming uploaded it to arXiv immediately after proving the twin prime number conjecture, Zhou Ming will definitely post his article proving Goldbach's conjecture to arXiv this time.

But Terence Tao was disappointed that after browsing arXiv, he did not find the paper submitted by Zhou Ming on proving Goldbach's conjecture.

Although Tao Zhexuan couldn't find it, no matter how busy Tao Zhexuan was after that, he would take time every day to quickly browse the mathematics, especially the new articles on number theory on arXiv that day.

To this day, shortly after Zhou Ming uploaded his complete proof of Goldbach's conjecture to arXiv, Terence Tao quickly noticed that he finally saw what he wanted to see,
"Although it's a little strange to ask why he should have proved it long ago, but he didn't announce the proof process until now. Maybe it's because he was still perfecting the paper in the past two days, but this is no longer important."

When Tao Terence came across the article titled [Any even number greater than 2 can be written as the sum of two prime numbers], his heart was moved, because this title was the Euler statement version of Goldbach's conjecture.

With excitement and trembling, Tao Zhexuan quickly looked at the author, he wanted to know if the author of this paper was the person he thought in his heart.

When he found that the name written on the author's name was indeed what he had guessed, it was Zhou Ming, the prover of the twin prime number conjecture, the excitement in his heart was already evident.

After Tao Zhexuan saw Zhou Ming's name, he couldn't wait to open the paper immediately, and began to read the abstract on the first page word by word.

Meanwhile, Peter Sarnak, sitting in his office at Princeton University, was preparing for a routine review of manuscripts sent to the editorial board of the Annals of Mathematics.

Since Zhou Ming has already been paid special attention by the editorial board of "Mathematics Yearbook", the manuscripts he sent can skip the review without queuing up. As long as there are editors who read them, they will see the manuscripts he submitted at first glance. .

"Huh?" It was precisely because of Zhou Ming's special position on the editorial board of "Mathematics Yearbook" that Peter Sarnak saw Zhou Ming's name at the first sight when he checked the manuscripts he sent. [Any even number greater than 2 can be written as the sum of two prime numbers].

For other people, they read the manuscript first and then the people. The reason why they read the people first and then the manuscript for Zhou Ming is because Zhou Ming did not have low-quality papers from last year to the last time he sent manuscripts. .

Another reason for paying special attention to Zhou Ming is that they don't want to miss any manuscript sent by Zhou Ming.

Wouldn't it be embarrassing if Zhou Ming's articles were circulated through arXiv, but the manuscripts Zhou Ming sent to them are still under review and have not reached the editors of the editorial board?
After Peter Sarnac saw the manuscript sent by Zhou Ming, the first thing he did was not to open it immediately to see the proof process, but to send it to Deligne and hand it over to Deligne review.

In this way, they can also announce to the outside world as soon as possible whether Goldbach's conjecture has been proved by Zhou Ming from Huaguo.

After sending Zhou Ming's manuscript to Deligne's mailbox, Peter Sarnak clicked on the manuscript and began to watch it seriously.

Paris, France, Ecole Normale Supérieure.

There is a six-hour time difference between Luzhou and Paris, so although it is already evening in Luzhou, it is still afternoon in Paris.

Harold Hoofgot was drinking afternoon tea in the office at this time, but his graduate student hurriedly opened the door of the office without knocking.

"What's the matter? You're in a panic." Harold Hoofgot put the cup in his hand on the coffee table aside, and he glanced at the not-so-young young man who broke into his office with a hasty look on his face. man, asked him.

"Professor Hoofgot, I just saw a paper proving Goldbach's conjecture on arXiv."

Although this man is only in his 20s, he is a doctoral student of Harold Hoofgot, but he has already shown signs of being extremely smart, and he looks even older than the ageless Hoofgot, At this time, he was talking to Harold Heofgot with an excited expression on his face.

This Harold Hoofgot is a Peruvian mathematician born in 1977. He received his Ph.D. from Princeton University in 2003. Doing postdoctoral research and starting in 2003 as a researcher at the French National Academy of Sciences and the Ecole Normale Supérieure in Paris, this mathematician's main research area is analytic number theory.

The reason why his students came to his office in such a hurry after knowing that Goldbach’s conjecture was proven was that he published two papers in May 2013, and he was here The weak Goldbach conjecture was declared to be completely proved in two papers.

The content of weak Goldbach's conjecture is: any odd number greater than 7 can be expressed as the sum of three odd prime numbers.

Speaking of Harold Hoofgot's proof of the weak Goldbach conjecture, this matter is different from proving the strong Goldbach conjecture, because this road is exactly the same as that of proving the strong Goldbach conjecture. There are two paths.

People's proof of the weak Goldbach's conjecture is this. As early as 1937, the Hongsu mathematician Vinogradov proved that the conclusions of Hardy and Littlewood can be obtained without relying on the generalized Riemann conjecture. directly proved that.

However, since Vinogradov's original proof used the Siegel–Walfisz theorem, it is impossible to give a "sufficiently large" lower bound.

后来，维诺格拉多夫的一位学生在1956年证明了出了下界3^3^15，也就是说他的证明说明了3^3^15以上的奇数都可以写成三个素数之和。

At this point, the uncertain definition of large enough is over. Future generations only need to prove that all odd numbers less than 3^3^15 can be written as the sum of three prime numbers to prove the weak Goldbach conjecture.

However, the number 3^3^15 has 6846169 digits, which is too large. It is completely infeasible to verify all numbers smaller than this number.

直到几十年后的2002年，王洪泽和香江大学的一位教授将3^3^15降至到e^3100，约为2*10^1346，这位王洪泽便是和王圆、潘彪他们一起来周明这里的那位。

2*10^1346这样的数字仍然太大，超出了当时计算机能够验证的范围，但相比较于3^3^15已经足够小了。

Later, in 2013, Harold Hoofgot used the Hardy-Littlewood-Vinogradov circle method, sieve method and index sum in the article [Minor arcs for Goldbach's problem]. And other traditional methods, the lower bound is reduced to about 10^30.

When this number is reached, it is already possible to use computers in modern society to prove all cases less than 10^30.

Soon after, Harold Hoofgot's colleagues used a computer to verify that all odd numbers below this were consistent with the conjecture, thus completing the entire proof of the weak Goldbach conjecture.

"Although I asked you to pay attention to the latest results on arXiv, you also have to learn to distinguish which papers are achievements and which papers are rotten fruits!"

He thought he was going to say something about what his doctoral student hurried into his office and said to him. It turned out that it was such a thing, and Hoofgot didn't care much.

Hoofgot originally planned to let the graduate student leave his office directly, but in the end he asked safely, "Who is the author of the paper you mentioned that proved Goldbach's conjecture? "

"It's Zhou Ming." The student said.

As soon as he heard Zhou Ming's name, Harold Hoofgot was shocked immediately, and the casualness just now disappeared in an instant. He asked his graduate student seriously and seriously: "You said, Is it Zhou Ming who just proved the twin prime number conjecture not long ago?"

"Well, that's him." The student nodded.

As soon as he heard that it was indeed Zhou Ming, Harold Hoofgot hurriedly said, "Go and print out this paper for me to see."

……

Once Zhou Ming’s complete proof process of Goldbach’s conjecture was uploaded, it quickly attracted the attention of mathematicians all over the world. This happened at the University of California, Los Angeles, Princeton University, and the Ecole Normale Supérieure. It's happening all over the world right now.

People who had heard that Zhou Ming proved Goldbach's conjecture before, because they had not seen the proof process issued by Zhou Ming, they all held a disbelieving point of view, and they all thought it was either a rumor or Zhou Ming's own bragging .

However, when Zhou Ming's paper proving Goldbach's conjecture was published, most of those who didn't believe it also believed it.

Regardless of whether it is domestic or foreign, the news about Zhou Ming's proof of Goldbach's conjecture has completely spread in the academic circles, especially in the mathematics circles.

Li Zhizhi, who returned to his residence at night, had already taken a shower. He was wearing a pair of cotton shoes and sitting in front of the desk in his study, with a heater under his feet, while looking at a printout of various mathematical formulas densely written on it. Paper, while writing and drawing on the draft paper from time to time, typing a draft.

"It's almost eleven o'clock, go to bed early." Li Mingzhi's wife saw Li Mingzhi staying up late at night and sitting in the study immersed in writing something, he shook his head and advised.

"I'll go to bed right away, and I'll go after reading this page." Li Mingzhi continued to look at the content on the printing paper without turning his head, and said to his wife.

This printing paper is not Zhou Ming's original manuscript of the complete proof process of Goldbach's conjecture, but a printed paper compiled by Zhou Ming.

Li Zhizhi's wife was obviously used to his behavior. After Li Zhizhi finished speaking, she walked out of the study without saying anything.

After more than 20 minutes, Li Mingzhi, who finally finished reading this page, looked at the time and found that it was almost ten past eleven, so he took his foot off the heater, turned off the switch of the heater, and The study room came out.

After pouring a cup of hot water in the living room and taking a few sips, Li Mingzhi was about to go to bed when he heard his cell phone ringing.

"Why is there still someone calling me this late at night." Li Mingzhi frowned and thought, he walked into the bedroom, unplugged the charging cable that charged the phone, and then picked up the phone.

"Huh?" Li Mingzhi picked up the phone, and when he saw the caller ID, the frown on his forehead disappeared immediately, replaced by doubts, and then he seemed to have figured something out, with a smug expression on the corner of his mouth smile.

"Hey, Lao Li, I heard that Zhou Ming, who was only in his 20s this year at your university of science and technology, was recruited by you last year, just proved Goldbach's conjecture, do you know about this?
Didn't he just solve the twin prime conjecture?How did you solve Goldbach's conjecture so quickly? "

As soon as Li Zhizhi pressed the answer button, before he could speak, a voice came from the other end of the phone.

(End of this chapter)