Yujiang Province, Xiaozhou City, Yujiang University, in Zijin Xiyuan Community not far from Zijin Campus, Professor Xue Song from the Institute of Mathematical Sciences of Yujiang University is taking a walk in the community.
As the youngest doctoral supervisor at Yujiang University and one of the youngest researchers of the Hundred Talents Plan, Professor Xue Song, who is only 38 years old, can be said to have a bright future. It cannot be said that his current achievements are entirely due to With a good family background, Xue Song actually belongs to the category of young genius.
After receiving nine years of compulsory education in China, he was sent to the other side of the ocean by his parents to attend Princeton International School of Mathematics and Physics. In his first year there, he won the first prize of AMC12 and was invited to participate in AIME. After getting high grades, he also achieved good results at UO.
Originally, he also received an invitation to join IMO that year, but due to his parents' opposition and because he felt tired from taking exams, he simply chose to give up his qualification to represent the United States in IMO.
But even so, he was directly recommended to the School of Mathematics at Princeton University, where he completed his undergraduate studies in three years. He was valued by Manjul Bhargava, a well-known mathematics professor at Princeton, and became a student of this famous number theorist. , began studying for a master’s degree and a Ph.D.
Manjul Bhargava's main research directions are higher-order number theory and algebraic geometry, and he once won the Fields Medal for his contributions in this area.
Xue Song followed this tutor and was mainly engaged in the study and research of integer theory, covering a wide range of topics from quadratic forms to elliptic curves. His doctoral thesis was about the in-depth results of the distribution of integers in integer theory. After graduating from the Ph.D. , for various reasons, Xue Song chose to return to China for development. And joined Yujiang University five years ago.
Professor Xue's ability is indeed outstanding. When his peers were still having headaches on how to pass 3.3, he jumped directly twice in a row. Not only did he get the title of associate professor, but also with a paper published in the "Annual Review of Mathematics", Got a spot in the Hundred Talents Program.
They are the talents that Yujiang University will focus on cultivating in the future. If nothing unexpected happens, they will definitely become academicians in the future.
For mathematicians, especially mathematicians who study number theory, a walk must be more than just a walk. The brain usually does not rest, but thinks about some messy things. Suddenly, the mobile phone in the pocket suddenly turned on the continuous vibrating mode.
Xue Song stopped thinking, took out his mobile phone, and found that the graduate student group under him on WeChat was in trouble. After several students @ him, they started discussing it directly in the group. "Boss, you are in the algebra and number theory department." The question in the tree house was actually solved by that rookie! Go and have a look!"
"Yes, boss, that rookie really figured it out! The answer is actually correct, we just verified it." "It's amazing, what kind of rookie is this? Is this some big guy's trumpet playing a joke on us?" Bar?"
"Although I also think it is possible that some big shot came to joke with everyone, but to be honest, do you think a big shot could have written those words? And he calls himself a young master? If his identity is exposed by then, he must How embarrassing!"...
Xue Song probably browsed through the content of the group chat, but did not reply in the group, but turned around and walked home. Although you can log into the forum directly with your mobile phone, if it comes to the question he asked, it is more convenient to use a computer.
When he asked the question, of course he knew how big the solution would be if someone really figured it out. At least it would be tiring to do it manually, and you would have to get a computer.
In fact, he chose to bubble up on the forum and ask such a question because of a small breakthrough in his recent research. Simply put, he found a method that can prove a type of question similar to the one he asked.
The equation has integer solutions. This is also a paper he has submitted to Acta Mathematica, "A Class of Diophantine Equations Aritric Fractional s: Existence of Integer Solutions". The main content of the paper is to prove a class of Diophantine equations with symmetric fractional sums
Existence of integer solutions.
The equation he gave is one of the more representative equations of this type. Here I need to explain a little mathematical knowledge to you.
In mathematics, proving that a certain type or even a certain equation has an integer solution is not the same thing as directly finding the numerical solution.
The former uses mathematical reasoning and proof techniques to confirm that this type of equation has at least one integer solution through the analysis of the equation structure and the use of mathematical induction. The solution is through specific calculation steps, such as merging similar terms, shifting
Terms, factoring and other equation solving techniques to calculate specific numerical solutions to equations.
In other words, although Xue Song has determined that this equation has an integer solution, he actually does not know what its numerical solution is. The only thing that is certain is that this numerical value is very huge! In fact, the Diophantine equation is in the field of number theory
It is an unsolved problem.
For example, Fermat's conjecture is one of the most famous Diophantine equations. Of course, after being proved, it became Fermat's last theorem.
At the Second World Congress of Mathematicians held in Paris, France in 1900, the famous mathematician Hilbert raised the famous one hundred questions in his opening report, of which the tenth was about the Diophantine equation.
The original text is: Is there a general algorithm that can determine whether any given Diophantine equation has an integer solution?
In 1970, in response to the tenth question, the former Soviet Union mathematician Yuri Matyashevi proved that there is no such universal algorithm and gave Hilbert's tenth question a very definite negative answer. But
This does not mean that the Diophantine problem has no research value.
In fact, this negative conclusion just proves that the Diophantine equation is extremely complex in some cases. It can even be said that it goes beyond what traditional algorithms can solve and is of fundamental importance in computing theory.
Role. Therefore, the Diophantine equation is still regarded as one of the world's difficult problems in number theory, especially in higher-dimensional and more complex cases.
Now, someone has solved this equation directly with bare hands? Is he still a rookie who just applied to join the forum?
Xue Song felt like his head was buzzing...
The Chinese mathematics circle is so big, and there are even fewer people studying number theory.
Therefore, the Algebraic Number Theory Treehouse is actually a very niche forum. Its promotion relies entirely on word of mouth, and there is no need for any profit. It is a gathering place for domestic algebra and number theory professors and graduate students to have daily discussions. Most people are not very familiar with it.
You may break in, even if you accidentally click in, and want to register, you will be blinded by the fifty multiple-choice questions randomly selected from the question bank.
You must know that the question bank of the forum is extremely rich.
Because starting from a math veteran, each upgrade requires the upgrader to provide two multiple-choice questions to the forum assessment question bank. After being reviewed and approved by at least three of the forum moderators, they will be included in the question bank. In view of the different personalities of each person, some professors
I really like to embarrass people, so after so many years of accumulation, the question bank has all sorts of messy questions.
Let's put it this way, some time ago he recommended a new graduate student of his to join the forum. It took him two days and five rounds of questions before he successfully passed the assessment and scored 92 points.
Of course, this does not mean that he is not a capable student. After all, his success depends not only on his strength, but also on his luck. Some of the fun questions are multiple-choice questions that are specifically designed to dig holes. He will be misled if he is not careful.
, choose the wrong answer.
So as long as you can register successfully, even if you hold the title of a rookie, you will at least have an introduction to number theory. But the problem with the title of rookie is that Xue Song has no idea who the other party is!
Yes, Xue Song knows at least 70% or 80% of the guys in this forum who have the title of math geek or above. Not to mention all of them in real life. It’s just that some of them don’t have a very good relationship in real life.
, there is no intersection in real life. Even if you don’t know someone, you can find the real owner by just asking around in the circle.
But things are different for rookies who have just applied for clearance.
The small forum only has an IP recording function left a long time ago. You don't even need a mobile phone number to register. As long as you have an email address that can send and receive emails normally, and can receive a verification code automatically sent by the server, you can register.
There is no real-name requirement, which is really frustrating!
.....
Although there were a lot of messy thoughts in his mind, ten minutes later, Xue Song had already sat in front of the computer in the study room and quickly logged in to the forum. The first thing he saw was the post that the rookie had just posted.
After all, the title was highly recognizable and had been manually pinned to the top by a forum moderator he knew.
Of course Xue Song knew that this was not intended to target him. In fact, if he were here, he would directly pin this post to the top. Otherwise, what is the difference between him and some so-called seniors who in his eyes are standing in the pit and not shitting? Point.
After opening the post, I saw the results given by the other party.
Copy the results, directly put them into the equation and use computer calculations. Since the equation itself is very simple to construct and the programming work is very fast, the results are verified in less than ten minutes. It is indeed correct. For ordinary people, this may seem like It's unnecessary, after all, more than one student in the WeChat group said it had been verified.
But for a qualified mathematician, this step of self-calculation cannot be omitted.
When throwing it to the computer for calculation, Xue Song also roughly scanned the post posted by this rookie and the following replies.
To be honest, the evaluations of his students are also fair. The text content in this post is indeed not like what a serious academic leader can say, even on the Internet.
Especially that sentence... But please don't be angry. I'm here in this forum, and there will be many opportunities for you old guys to get angry in the future! I'm afraid you'll be so angry now that you won't be able to answer questions in the future." He felt embarrassed when he saw it!
If you are really a big boss, if the name of the forum is exposed in real life, it belongs to an old guy and an uncle... It will be so embarrassing for everyone to meet at various conferences in the future, and it will be a direct social death.
If it is just an ordinary student, it is most likely a graduate student who has just passed the master's degree and has not officially started studying with his tutor. Maybe this guy's tutor just told him that there is such a forum and asked him to join it first, without explaining much. .Because this guy is obviously not familiar with this forum. If he knows a little bit about it, he probably wouldn't dare to talk nonsense to those IDs.
After all, most of the active high-level IDs here are relatively young master's and doctoral supervisors in the field of number theory in major universities and research institutes. It is not an exaggeration to say that they are the backbone of this generation of Chinese mathematics.
This guy offended a lot of people with just one sentence. So the comment area was really lively right now.
Although only over a hundred floors have been built, almost all the active IDs during this period have been exploded.
"Boy, you are awesome! You have a personality and I like it very much. Just don't let me know who you are! If I find out, I will definitely ask your mentor to bring you over and let you know how ruthless the old guys can be." "Oh, I'm despised! But you win this time! I'll give you a chance to tell the truth. Did you find someone to help?"
"Whose child is this? He has such a personality! Hurry up and admit it, don't force me to call and ask everyone! He's so strong! He's really better than me!" "He actually figured it out?! Or is he right? Lao Xue , are you kidding us with your trumpet?"
Xue Song curled his lips and felt speechless.
Is he such a boring person? Besides, he is still young and energetic, so he won't be able to say what he said in the second grade.
However, as one of the moderators, he immediately retrieved the rookie's login IP record from the background. Sure enough, it was still the IP from Xingnan Province. It currently showed that it was still online, but no operations were performed.
It seems that the big guy who has not studied the Diophantine equation lives in Xingnan Province.
Then it's highly likely that this guy is really a graduate student who hasn't signed up yet.
Without wasting any more time looking at other people's replies, Xue Song thought for a moment, opened the forum's private chat system, and sent a message to the rookie whose online name was Yu Jian Xiao Qian Qian: "I am Xue Song from Yujiang University. , is it convenient to leave your contact information?" Yes, Xue Song finally fell in love with talents.
Although I don’t know whether Yu Jian Qianqian asked his mentor for help in the process of solving this equation, but the fact that this guy can solve the numerical solution is enough to show his high mathematical talent. Although the other party most likely already has a mentor, but Maybe just study for a master's degree with a tutor?
You can still strive for it at the doctoral level. And Xue Song is very confident.
I dare not say anything else, but in the field of Diophantine equations, there are really few people in China who can match his research. And he also believes that since this kid can solve this equation, he must also know about him. It's a pity. Unfortunately, after this message was sent out, it was like a stone sinking into the sea, with no response at all.
However, his cell phone rang again. It was a call from a professor at the School of Mathematics at Yanbei University. "Hey, brother Zhiyuan, long time no see."
After answering the phone, Xue Song said hello casually.
"Hey, Lao Xue, we are chatting in the group, why haven't you said anything?" "Oh, I have set Do Not Disturb in all groups."
"Okay, don't play this trick with me. Tell me, did you recruit a new student from Xingnan Province?" Xue Song smiled bitterly.
It seems that other people's judgments are similar to his.
"Don't make trouble. If you are really my student, according to my temperament, I have already shown it to you in the group. Am I still afraid that my good talents will be poached by you?" "Haha, that's right. Do you think so? Lao Xiao’s new student?”
Xue Song naturally knew that the old Xiao mentioned by Weng Zhiyuan was Professor Xiao Liang of Huaqing University, and the outstanding youth project he applied for last year was about integer theory.
However, the relationship between Xue Song and Xiao Liang is not very good. There is a point where they don't like each other. They just don't attack each other. There is no way, mathematicians are also ordinary people. Where there are people, There are rivers and lakes, there are grievances and struggles.
"How do I know? Isn't he right across from your school? Why don't you just go and ask him?"
"Hey, I just asked casually. This little guy suddenly appeared. He was obviously online and pretended not to reply. It's so rude. You know who it is. Let's criticize together. By the way, it's okay. Check out the group , it hasn’t been this lively for a long time. Okay, no more words, I’m hanging up.”
Xue Song closed the line, took a deep breath, and couldn't help but open the WeChat group. Sure enough, the topic in the professor group revolved around this rookie.
Indeed, many people are asking if he has a new disciple, but there is no need for him to answer, because Weng Zhiyuan, who just called, has already helped him to clear up everyone's doubts in the group. "I just called and asked, Lao Xue He said he doesn't know this rookie, so he can't be his student, otherwise, he would have shown off to us long ago."
"That's interesting. You've asked around and everyone said you're not one of their students. Don't tell me that this guy is still an undergraduate?!"
"Isn't it possible? If you are an undergraduate, you are simply gifted. Can you solve such a difficult problem in the world in ten days? Are there any undergraduates in Yanbei Institute of Mathematics who can reach this level?"
Haha, I think some kids might have that ability, but they can’t join this forum for the time being!”
Seeing Weng Zhiyuan say this shamelessly, Xue Song couldn't help it anymore.
"@老哥are you sure that undergraduates at Yanbei Institute of Mathematics can independently solve the numerical solution of my equation? OK, there are many similar equations. I will choose five for you undergraduates at Yanbei Institute of Mathematics to try. One month
As long as he can solve a numerical solution to an equation, I will personally reward him with 100,000 yuan! There is no upper limit! If he solves all five problems, I will directly reward him with 500,000 yuan!"
"Haha, Lao Xue, wasn't I just joking? Why are you so impatient? Calm down, calm down. Then again, it's unlikely that undergraduates will be able to do that, and no one in China seems to be doing research in this area.
Is it very in-depth?" Weng Zhiyuan directly changed the topic.
Although he is at Yanbei University, he is still only a lecturer and is in the promotion-or-leave stage. It is really difficult to compete with a promising professor like Xue Song. "Yes, but everyone can really try to solve this kind of equation.
, since someone can figure it out, we should be able to too."
"Yes, you can try it!"
Someone started to pull some strings, trying to ease the atmosphere in the group.
However, some people don't bother to pay attention to this at all, and are still immersed in the topic of thinking about who the rookie is.
"Well, it can't be those big guys. No, given their status, they shouldn't be able to say that! And everyone respects them." With these words, the group gradually became colder.
.
But the question was not solved, and Xue Song also put down his mobile phone. He really wanted to know who had solved this equation in just ten days. But he went to the forum again, and there was still no news in the private message.
Chapter completed!