Chapter 67 Can you do it? I'll give you a bonus of half a million! (Please subscribe, please vote)
Yujiang Province, Xiaozhou City, Yujiang University, in the Zijin Xiyuan Community not far from the Zijin Campus, Professor Xue Song from the Institute of Mathematical Sciences, Yujiang University Taking a walk in the neighborhood.
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 his good family background. In fact, Xue Song belongs to the category of young geniuses.
After receiving nine years of compulsory education in China, his parents sent him to the other side of the ocean to attend Princeton International School of Mathematics and Physics. In my first year there, I won the first prize of AMC12 and was invited to participate in AIME.
After achieving extremely high results in AIME, he also achieved good results in USAMO.
Originally, he received an invitation to join the IMO that year, but due to his parents’ opposition and because he felt tired from the exams, he simply chose to give up the qualification to represent the United States in the IMO.
But even so, he was directly recommended to the School of Mathematics at Princeton University. He completed his undergraduate studies in three years and was valued by Manjul Bhargava, a well-known mathematics professor at Princeton. He became this A student of a famous number theorist, he began to study 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 integer distribution in integer theory.
After graduating with his doctorate, Xue Song chose to return to China for various reasons. And joined Yujiang University five years ago.
Professor Xue’s ability is indeed outstanding. When his peers were still having headaches about how to pass 3+3, he jumped twice in a row. Not only did he get the title of associate professor, but he also won an article published in " The paper published in the "Annals of Mathematics" received a spot in the Hundred Talents Program.
They are the talents that Yujiang University will focus on cultivating in the future. If nothing else happens, they will definitely become academicians in the future.
......
For mathematicians, especially mathematicians who study number theory, taking a walk is definitely more than just a walk. The brain usually does not rest, but thinks about some messy things.
Suddenly, the mobile phone in my pocket suddenly turned on continuous vibrating mode.
Xue Song stopped thinking, took out his mobile phone, and found that the graduate student group under him on WeChat was directly in trouble. After several students @ him, they started discussing it in the group.
“Boss, the question you asked in the Algebra and Number Theory Treehouse 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? Are we kidding?”
"Although I also think it is possible that some big shot came to joke with everyone, but to be honest, do you think those words could have been written by a big shot? And he calls himself a young master? If his identity is exposed by then, he will have to 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.
The question he asked, of course, he knew how big the solution would be if someone really found the solution. At least manual calculation is very tiring, and you must 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 "AClassofDiophantineEquationsArisingfromSymmetricFractionalSums:ExistenceofIntegerSolutions" that he has submitted to ActaMathematica.
The main content of the paper is to prove the existence of integer solutions to a class of Diophantine equations with symmetric fractional sums.
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 to calculate the specific numerical solution of the equation through specific calculation steps, such as using equation solving techniques such as merging similar terms, moving terms, factoring, etc.
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 value is huge!
In fact, the Diophantine equation is an unsolved problem in the field of number theory.
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, the tenth of which 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 mathematician Yuri Matyashevi proved that there is no such a universal algorithm and gave Hilbert's tenth question a very good answer. A definite no.
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. effect.
So 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?
Still a newbie 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.
So 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 daily discussions between domestic algebra and number theory professors and graduate students. .
Ordinary people are unlikely to break in. Even if they accidentally click in and want to register, they will be blinded when faced with 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 the 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.
Given that everyone has different personalities, some professors really like to make things difficult for others, 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 good student. After all, his success depends not only on his strength, but also on his luck. Some of the fun questions were multiple-choice questions specifically designed to dig holes. If he was not careful, he would be misled and choose the wrong answer.
So as long as you can successfully register, even if you have the title of a rookie, you will at least have an introduction to number theory.
But the problem with the rookie title is that Xue Song doesn't even know who the opponent is!
Yes, in this forum, Xue Song knows at least 70% to 80% of the guys with titles such as math geeks and 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 reality, and they don't have much intersection in real life.
Even if you don’t know someone, you can find the real owner by just asking around.
But it’s different for newbies who have just applied.
The small forum is just an IP record 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, you can receive the verification code automatically sent by the server. Just 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.
What comes to mind is the post just posted by that rookie.
After all, the title is highly recognizable and has been manually pinned to the top by a forum moderator he knows.
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 just standing in the pit and not taking a shit?
When I clicked on the post, I saw the results given by the other party.
Copy the results, put them directly into the equation and use computer calculations. Considering that the equation itself is very simple to construct and the programming work is also very fast, the result was verified in less than ten minutes and it is indeed correct.
For ordinary people, they may think this is unnecessary, after all, more than one student in the WeChat group said that it has 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 replies below.
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 the sentence "...but please don't be angry first. I came to this forum. You old guys will have many opportunities to get angry in the future! I'm afraid you will be so angry now that you will ask questions in the future. It’s not easy to ask.” He felt embarrassed when he saw it!
If you are really a big boss, if the name of the forum is exposed in reality, it belongs to an old guy and an uncle... It will be more embarrassing for everyone to meet at various conferences in the future. , directly social death.
If they are just ordinary students, most likely they are graduate students who have just passed the master's degree and have not officially started studying with their tutors. Maybe this guy's instructor just told him about this 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 younger master's and doctoral supervisors in the field of number theory in major universities and research institutes.
It is no exaggeration to say that they are the backbone figures of this generation of Chinese mathematics.
This guy offended a lot of people with just one sentence.
So at this time, the bottom of the comment area was indeed very lively.
Although only more than 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, I like it very much, just don't let me know who you are! If I know, I will definitely find your mentor and ask you to come over, let you know the old guys How cruel can you be?”
“Oh, I’m despised. ! But this time you win! Give you a chance to tell the truth. Did you ask for help? "
"Whose child is this? Hurry up and admit it, don't force me to fight each other. Ask on the phone! It’s so powerful! It’s better than me!”
"You actually figured it out?! Or is it right? Old Xue, are you kidding us with the trumpet?"
......
Xue Song curled his lips and felt Very speechless.
Is he such a boring person? Besides, he was still young and energetic, so he couldn't say anything about the second grade.
However, as one of the moderators, he immediately retrieved the rookie's login IP record from the backend. Sure enough, it was still the IP from Xingnan Province. It currently showed that it was still online, but there was no operation.
It seems that the big boss who has not studied the Diophantine equation is a resident of Xingnan Province.
Then it’s very 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, could you please leave me your contact information?”
Yes, Xue Song is still interested in talents after all.
Although it is not known 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, maybe he just studies for a master's degree with his mentor?
You can still fight for it at the doctoral level.
And Xue Song is very confident.
I dare not talk about other directions, but in the field of Diophantine equations, there are really few people in China who can match his research. And he also believed that since this kid could solve this equation, he must also know about him.
Unfortunately, after this message was sent out, it was like a stone sinking into the sea, and there was no response at all.
However, his cell phone rang again. It was a professor from the School of Mathematics at Yanbei University.
“Hello, brother Zhiyuan, long time no see.”
Xue Song said hello casually after answering the phone.
“Hey, Lao Xue, we are chatting in the group, why haven’t you said anything?”
“Oh, I have set Do Not Disturb in all the 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 it were really my student, according to my temperament, I would have shown it to you in the group. Am I still afraid that my good seedlings would be poached by you?"
"Haha, yes. Do you think he is Lao Xiao's new student?"
Xue Song naturally knew that the old Xiao Weng Zhiyuan was talking about was Professor Xiao Liang of Huaqing University. 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 quite like each other. Just barely attack each other.
No way, mathematicians are also ordinary people. Wherever there are people, there are rivers and lakes, and there are grievances, hatreds and struggles.
"How do I know? Isn't he just across from your school? Why don't you just go and ask him?"
"Hey, I just asked casually, and suddenly A little guy showed up and pretended not to reply even though he was online. It’s so rude. I know who it is. Let’s all criticize. By the way, it’s okay. Check out the group. It’s been a while. It’s so lively. Say too much, hang up.”
Xue Song closed the thread, 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 said that he doesn't know this rookie, so he can't be his student. Otherwise, he would have shown off to us long ago."
"Then That’s interesting. You’ve asked around and you’ve all 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?"< br>
“Haha, I think some children may have that ability, but they can’t join this forum for the time being!”
Seeing Weng Zhiyuan say this shamelessly Xue Song couldn't bear it anymore.
“@老公 are you sure that undergraduate students from 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 from Yanbei Institute of Mathematics Give it a try.
As long as he can solve a numerical solution to an equation within one month, 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, isn't this just a joke? Why are you so impatient? Calm down, calm down. Then again, it's unlikely that undergraduates will be able to do it, and no one in China seems to be doing research in this area. Is it very in-depth?”
Weng Zhiyuan changed the topic directly.
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 you can really try to solve this kind of equation. Since someone can solve it, we should be able to too."
"Yes, you can try it!"< br>
Someone started to pull some strings, trying to ease the atmosphere in the group.
However, some people are too lazy to pay attention to this 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 solved this equation in just ten days.
I just checked the forum again, but there was still no news in the private message.
No matter who this guy is, he is so rude!
(End of this chapter)