Top academic

Chapter 67: Can you do it? I'll give you a bonus of ! (Subscribe, monthly ticket)
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 Hundred Talents Program researchers, Professor Xue Song, who is only 38 years old, has a promising future.

It cannot be said that his current achievements were entirely due to his good family background. In fact, Xue Song was a young genius.

After completing nine years of compulsory education in China, he was sent by his parents to study at Princeton International School of Mathematics and Physics. In his first year, he won the first prize in AMC 12 and was invited to participate in AIME.

After getting extremely high scores in AIME, I achieved good results in USAMO.

Originally, he received an invitation to join IMO that year, but due to his parents' opposition and the fact that he felt tired of taking the exam, he simply chose to give up the qualification to represent the United States in IMO.

But even so, he was directly admitted to the School of Mathematics at Princeton University, where he completed his undergraduate studies in three years. He was noticed by Manjul Bhargava, a well-known mathematics professor at Princeton, and became a student of this famous number theorist, beginning his master's and doctoral studies.

Manjul Bhargava's main research direction is higher-order number theory and algebraic geometry, and he has won the Fields Medal for his contributions in this area.

Xue Song mainly studied and researched integer theory with this mentor, covering a wide range of topics from quadratic forms to elliptic curves. His doctoral thesis was about the deep results of integer distribution in integer theory.

After graduating with a doctorate, Xue Song chose to return to China for various reasons and joined Yujiang University five years ago.

Professor Xue's abilities are indeed outstanding. While his peers were still racking their brains over how to pass the 3+3 exam, he made two leaps in a row. Not only did he get the title of associate professor, he also secured a place in the Hundred Talents Program with a paper published in the Annals of Mathematics.

He is also the talent that Yujiang University will focus on cultivating in the future. If nothing unexpected happens, he will definitely strive to become an academician in the future.

……

For mathematicians, especially those who study number theory, walking is definitely more than just a walk. The brain usually does not rest, but instead thinks about all sorts of random things.

Suddenly, the phone in my pocket went into continuous vibrate mode.

Xue Song stopped thinking, took out his mobile phone, and found that the WeChat group of his graduate students had exploded. After a few students @ him, they started discussing it directly in the group.

"Boss, the problem you gave in the Algebra and Number Theory Tree House was actually solved by that rookie! Go check it out!"

"Yes, boss. That newbie really figured it out! The answer is actually correct. We just verified it."

"This is incredible. How can this be called a rookie? Is this some big shot's fake account playing a joke on us?"

"Although I also think it's very likely that some big shot is joking with everyone, but to be honest, do you think a big shot could write those words? And he called himself a little master? If his identity is exposed, it will be so embarrassing!"

……

Xue Song glanced through the content of the group chat, did not reply in the group, but turned around and walked home.

Although you can log in to the forum directly with your mobile phone, it is more convenient to use a computer if it involves the question he asked.

He certainly knew how big the solution would be if someone could find it. At least it would be very tiring to calculate manually, so he had to use a computer.

In fact, he chose to post this question on the forum because of a small breakthrough in his recent research. Simply put, he found a way to prove that a type of equation similar to the one he asked has integer solutions.

This is also a paper he has submitted to Acta Mathematica, "A Class of Diophantine Equations Arising from Symmetric Fractional Sums: Existence of Integer Solutions."

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 class or even a certain equation has integer solutions is not the same as directly finding the numerical solution.

The former uses mathematical reasoning and proof techniques to analyze the structure of the equation and use mathematical induction to confirm that this type of equation has at least one integer solution.

Solving the equation is done through specific calculation steps, such as using equation solving techniques such as combining like terms, transposing terms, factoring, etc., to calculate the specific numerical solution to the equation.

In other words, although Xue Song has determined that this equation has integer solutions, he actually does not know what the numerical solution is. The only thing he can be sure of is that the numerical value is very 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, and of course after it was proved it became Fermat's Last Theorem.

At the Second World Congress of Mathematicians held in Paris, France in 1900, the famous mathematician Hilbert proposed one hundred famous problems in his opening speech, the tenth of which was about Diophantine equations.
The original text is: Is there a general algorithm that can determine whether any given Diophantine equation has integer solutions?

In 1970, in response to the tenth question, former Soviet mathematician Yuri Matyashevich proved that there is no such universal algorithm, giving a definite negative answer to Hilbert's tenth question.

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 the scope of what traditional algorithms can solve and plays a fundamental and important role in computational theory.

Therefore, the Diophantine equation is still regarded as one of the world's difficult problems in number theory, especially in higher dimensions and more complex cases.

Now, someone has actually solved this equation directly with bare hands?

Are you a newbie who just applied to join the forum?
Xue Song just felt his head was buzzing.

……

The Chinese mathematics community is so small, and there are even fewer people studying number theory.

So the Algebraic and Number Theory Tree House is actually a very niche forum. It relies entirely on word of mouth for publicity and has no profit needs. It is just a gathering place for domestic professors and graduate students who study algebra and number theory to have daily discussions.

It is unlikely for ordinary people to break in. Even if they accidentally click in and want to register, they can only grope in the dark when faced with fifty multiple-choice questions randomly selected from the question bank.

You should know that the forum’s question bank 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 moderators of the forum, they will be included in the question bank.

Given that everyone has different personalities, some professors really like to make things difficult for people, so over the years, the question bank has accumulated a lot of all kinds of messed up questions.

Let me put it this way, some time ago he recommended one of his new master's and doctoral students to join the forum. It took him two days and five rounds of questions before he successfully passed the assessment and got 92 points.

Of course, this does not mean that he is a poor student. After all, success depends not only on ability but also on luck. Some of the multiple-choice questions are designed to set traps, and he would be misled and choose the wrong answer if he is not careful.

Therefore, as long as you can successfully register, even if you have the title of a rookie, at least you have already gotten started with number theory.

But the problem with the rookie title is that Xue Song has no idea who the other party is!

Yes, in this forum, Xue Song knows at least 70-80% of the guys who are called math geeks or above, if not all of them in real life. It’s just that he doesn’t have a very good relationship with some of them in real life, and they don’t have much intersection in real life.

Even if you don't know someone, you can find the real person by just asking around in the circle.

But it’s different for rookies who have just applied.

The small forum only has an IP recording function that was left over 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 the 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 and quickly logged into the forum.

The first thing I saw was the post that the rookie had just posted.

After all, the title is highly recognizable, and has been manually pinned to the top by a forum moderator he knows.

Xue Song certainly knew that this was not aimed at him. In fact, if he were here, he would have directly pinned this post to the top. Otherwise, what was the difference between him and some so-called seniors who stood in the toilet without taking a shit in his eyes?
I clicked on the post and saw the results given by the other party.

The result was copied and directly inserted into the equation and calculated using a computer. Given the simplicity of the equation itself, the programming work was also quick, and the result was verified in less than ten minutes, and it was indeed correct.

For ordinary people, this may seem unnecessary, after all, more than one student in the WeChat group said that it has been verified.

But for a qualified mathematician, the step of calculating by oneself is naturally indispensable.

While feeding the computer with the calculations, Xue Song also roughly scanned the post posted by this rookie, as well as the replies below.

To be honest, the comments from his students are quite pertinent. The text in this post does not sound like something a serious academic figure would say, even on the Internet.

Especially the sentence "…but please don't get angry yet. Now that I'm on this forum, there will be many opportunities for you old guys to get angry in the future! I'm afraid that you'll get angry and hurt your health now, and you won't be able to set questions properly in the future." He felt embarrassed just reading it!

If he is really a big shot, and the name of the forum is exposed in reality, and he is an old guy and an uncle... How awkward it will be when everyone meets him in various meetings in the future, it will be a social disaster.

If he is just an ordinary student, he is probably a graduate student who has just passed the master's exam and has not yet officially started studying with his supervisor. Maybe this guy's supervisor told him about this forum and asked him to join it first without explaining too much.

Because this guy is obviously not familiar with this forum. Even if he knew a little bit, he probably wouldn't dare to speak 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 no exaggeration to say that they are the backbone figures of this generation of Chinese mathematics community.

This kid offended a lot of people with just one sentence.

So the comment section was indeed very lively at this time.

Although only more than a hundred floors have been built, almost all the IDs that were active during this period have been blown out.

"Boy, you're awesome! You have personality, I like you 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 to me, and let you know how cruel 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 ask for help?"

"Whose child is this? He has such a strong personality! Just admit it now, don't force me to call everyone to ask! He's too strong! He's really stronger than me!"

"You actually figured it out?! And it's correct? Old Xue, are you kidding us with your trumpet?"

……

Xue Song curled his lips, feeling speechless.

Is he such a boring person? Besides, he is too young and energetic to say such immature words.

However, as one of the moderators, he immediately retrieved the login IP record of this rookie from the background, and sure enough, it was the IP from Xingnan Province. It was currently shown to be online, but no operations were being performed.

It seems that there are no big guys who study Diophantine equations living in Xingnan Province.

Then it is very likely that this guy is a graduate student who has not yet registered.

Without wasting time reading other people's replies, Xue Song thought for a moment, clicked on the forum's private chat system, and sent a message to the rookie with the online name Yu Jian Xiao Qian Qian: "I'm Xue Song from Yujiang University. Can you please leave me your contact information?"

That’s right, Xue Song was finally moved by his love for talent.

Although it is not known whether Yu Jian Xiaoqian sought help from his mentor in the process of solving this equation, the fact that this guy was able to find a numerical solution is enough to show his high mathematical talent.

Although the other party probably already has a supervisor, maybe he or she will just study for a master's degree under that supervisor?

You can still strive for a doctorate degree.

And Xue Song is still very confident.

I dare not say about other fields, 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 know his.

Unfortunately, after this message was sent, it fell into oblivion and there was no response at all.

His cell phone rang again. It was a call from a professor from the School of Mathematics at Yanbei University.

"Hey, Brother Zhiyuan, long time no see."

After answering the phone, Xue Song casually said hello.

"Hey, Lao Xue, we're chatting in the group, why haven't you said anything?"

"Oh, I have set all the groups to do not disturb."

"Okay, stop playing that game with me. Tell me, did you accept a new student whose family lives in Xingnan Province?"

Xue Song smiled bitterly.

It seems that other people's judgment is similar to his.

"Stop joking. If he were really my student, given my personality, I would have shown him off to you in the group a long time ago. Am I really afraid that you would poach my best student?"

"Haha, that's right. Do you think it could be Mr. Xiao's new student?"

Xue Song naturally knew that the "Old Xiao" mentioned by Weng Zhiyuan was Professor Xiao Liang from Huaqing University, and that the Young Elite Scientists project he applied for last year was about integer theory.

However, the relationship between Xue Song and Xiao Liang was not very good, and it seemed that they were not very happy with each other. They were almost attacking each other.

There is no way, mathematicians are ordinary people too. Wherever there are people, there are rivers and lakes, grudges, hatreds and struggles.

"How should I know? Isn't he just across from your school? Can't you just go and ask him?"

"Hey, I was just asking casually. This little guy suddenly showed up. He was obviously online, but he pretended to be dead and didn't reply. How rude. Now that we know who it is, let's criticize him together. By the way, let's check the group chat. It's been so lively for a long time. Okay, no more words, I'm hanging up now."

Xue Song hung up the phone, took a deep breath, but still couldn't help but open the WeChat group.

Sure enough, the topic in the professor group revolved around this rookie.

Indeed, many people were asking whether he had accepted a new disciple, but he didn't need to answer because Weng Zhiyuan, who had just called, had already helped him answer everyone's questions in the group.

"I just called to ask, and Lao Xue said he didn't know this rookie either, so he couldn't possibly be his student, otherwise he would have boasted to us a long time ago."

"That's interesting. You've asked around, and everyone says he's not their student. Don't tell me this guy is an undergraduate?!"

"Impossible, right? If he is an undergraduate student, then he is extremely talented. He was able to solve such a difficult problem in just ten days? Is there an undergraduate student in your Yanbei Mathematics College who can reach this level?"

"Haha, I think some kids might have that ability, but they can't join this forum for now!"

Seeing Weng Zhiyuan, such a shameless man, say these words, Xue Song couldn't help himself.

“@老翁, are you sure that the undergraduate students of Yanbei School of Mathematics can independently solve the numerical solution of my equation? Okay, there are many similar equations. I will select five for you undergraduate students of Yanbei School of Mathematics to try.

"For one month, if anyone can find a numerical solution to one equation, I will personally reward him with 100,000 yuan! There is no upper limit! If all five problems are solved, I will directly reward him with 500,000 yuan!"

"Haha, Lao Xue, I was just joking, why are you so angry? Calm down, calm down. On the other hand, if undergraduates can't do this, it seems that no one in China has done in-depth research in this area, right?"

Weng Zhiyuan changed the subject directly.

Although he is at Yanbei University, he is currently only a lecturer and is in a stage where he must either be promoted or leave. It is not easy to argue with a professor like Xue Song who has a bright future.

"That's right, but everyone can really try to solve this kind of equation. Since someone can solve it, we should be able to do it too."

"Yes, you can try it!"

Some people started pulling, trying to ease the atmosphere in the group.

However, some people are too lazy to pay attention to all this and are still immersed in thinking about who that rookie is.

"Well, it can't be those big guys, right? No, with their status, they shouldn't say such things! And everyone respects them very much."

Following these words, the group gradually grew colder.

But the question was not answered, and Xue Song put down his phone. He really wanted to know who had solved the equation in just ten days.

I just checked the forum again and still received no response from the private message.

Whoever this guy is, he is so rude!
(End of this chapter)