Of course, Qiao Yu didn't dare to answer the phone. He hesitated just now to give the instructor face.

He can't keep pretending that he doesn't know about the conflict between his mentor and his master. In that case, he's not pretending to be stupid, but he's treating his mentor and grandpa as fools. It's something that Qiao Yu rarely does, but it's a bold thing. , which he often does.

So after Tian Yanzhen said those words with a half-smile, Qiao Yu answered the phone without hesitation in front of his instructor. "Hey, grandpa, morning... ah, no, good at noon."

"No, I'm still with my supervisor... Yes, yes, that's right, Director Tian. He called me early in the morning... Yes, I'm reading the paper... I'm still there. , he is right next to you, do you want to talk to him?

"Oh, okay... Well, yes, it's my mother... Yes, my mother, to be honest with you, that's what happened. Director Tian also asked me this question just now... Other than that, there’s nothing else...Yes, I didn’t tell Director Tian before.”

"Yes, after I checked the paper last night, I only sent an email to you and Director Tian. Apart from telling my mother that I was writing this paper, I have never talked about it with anyone else. !

"...That's it, thank you so much, grandpa...Well...I understand this...I'm not proud, really...by the way...that's you Don’t you really need to have a few words with Director Tian? Well, okay..”

Qiao Yu put the phone down from his ear, then confidently handed it to Tian Yanzhen, who was just sitting there, looking at him with a complicated expression, and said: "Director Tian, ​​Grandpa Shi, I want to have a chat with you.

Tian Yanzhen was stunned, but he still took the earphones, calmed down, put the already hot phone to his ear, and said in a deep voice: "Hello, Mr. Yuan." "I always thought you were lucky. The best among students! Now it seems that it is indeed true!"

Tian Yan was really moved when he heard the familiar voice.

Ten years ago, he would probably have argued with the old man opposite him about this sentence, but now Tian Yanzhen really feels that he is quite lucky.

His achievements are a little higher than those of the Chinese mathematicians of the same generation. At this age, the students he accepts are also better than those of the same generation of mathematicians... not just a little bit. They are even much better than the students of the old man opposite.

Tian Yan really doesn't think that doing scientific research is luck, but accepting students is really mostly luck.

If it weren't for the email Xue Song sent him and forwarded Qiao Yu's paper, he went to the CMO site on a whim. When he met Qiao Yu, he read the learning experience on this guy's computer and waited until after IMO. , maybe it’s too late.

Therefore, when Xue Song was transferred to Yanbei, in addition to letting him take Qiao Yu with him, he also wanted to reciprocate the favor. But the reason why Tian Yanzhen didn't want to argue at all was that he could hear the sour taste in his voice. .

Yes, others may not be able to hear it, but he can.

So Wen Yan replied: "What the teacher said is that I have been quite lucky these years. Especially last year, I accidentally thought about going out to have a look, but I came across a piece of jade. I would like to thank the teacher for his help." carving.

The person on the other side was silent for a moment and said: "Although your knowledge is still a little bit behind after all, since my grandson is willing to worship you as his teacher, I would like to ask you to put more thought into it. You are now your age, so you should fight less for fame and wealth. The right way is to cultivate students in a down-to-earth manner.

Tian Yanzhen immediately replied: "Teacher, please rest assured, Yanbei really has a training plan for Qiao Yu. I believe that his future achievements will surpass all of us. Huaxia can produce such a talent and will not be inferior to anyone else." It is not easy to become a mathematician, Yan Zhen will do his best. And..."

At this point, Tian Yanzhen changed the subject and began to give examples: "Actually, teaching this kid doesn't need to be so detailed. That day I taught him about the quantization problem in mathematics. It only took him ten minutes to understand it and he could use it. to the examples in the paper.

This is reflected in the proof process of Lemma 3.4 of the quantum homology category group in this paper. You can take a closer look at these two lemmas and you will probably be able to understand the meaning of those ten minutes.

The person on the other side was silent again for a long time, and then a word floated into Tian Yanzhen's ears: "Then take care of yourself, I'll die." "Teacher, take care of yourself."

When the phone was handed back to Qiao Yu, the person on the other side had already hung up the phone. Tian Yanzhen looked Qiao Yu up and down and joked, "Do you recognize a grandpa?"

"Ahem..." Qiao Yu coughed twice and immediately replied: "Director Tian, ​​that's Grandpa Shi. Oh, by the way, I just simplified it out of habit. I'm your student, let's learn In mathematics, it has become a biological instinct to simplify complex formulas when you see them can be simplified. Well, do you think this explanation is reasonable?

It does sound very reasonable.

But Tian Yanzhen just stared at Qiao Yu quietly, until he almost felt embarrassed by the young man. Tian Yanzhen couldn't hold it back, and the corners of his mouth gradually turned up. So he simply nodded and said: "It does make sense. So what did your grandfather just say to you?"

Although Qiao Yu answered the phone in front of him, he could only faintly hear the voice on the other end of the phone. He could only guess the details.

Qiao Yu answered honestly: "It's almost the same as what you asked, that is, have you discussed it with other people? Oh, by the way, grandpa said he would help me find someone to use Huaqing's Supercomputing Center to help me do some Verification, and said that until it is widely recognized by the mathematical community, my conclusion can only be regarded as a conjecture for the time being, so let me not be too proud yet."

Tian Yanzhen nodded and said: "Mr. Yuan is right, your article is very valuable, but before it is widely recognized, it can only be regarded as a conjecture for the time being! But as long as it can be verified by supercomputing, even if it is Conjecture, it has also been proven that at least in the known curve library, your conclusion is correct.

This is the same as when you use some of the conclusions of the BSD conjecture in your paper. Although the BSD conjecture has not been fully proved, some of the conclusions have been recognized, and everyone should still use it!

In addition, your ideas have many innovations, especially the content of geometric constraint parameter conjecture. Therefore, I think that after the supercomputer has verified that this article is correct, it will be no problem to submit it to the four major journals. Do you have a favorite journal that you particularly want to publish? "

Qiao Yu shook his head and said: "No, I only know the Big Four, which you mentioned to me before, saying they are the most influential journals in mathematics. I don't know the specific differences between these four journals. I understand. How about you decide who to vote for?

Tian Yanzhen pondered for a moment and said: "Then vote for Ann Math. The editorial office of this annual mathematics journal is at Princeton University. Do you still remember Professor Zhang who attended the seminar last time? He is now at Princeton's Advanced Research Institute. He serves as a professor in the college.”

Seeing Qiao Yu's confused look, Tian Yanzhen explained: "This is not to say that your paper cannot meet the standards of Ann Math. The main reason is that you are afraid of interference from factors outside the scope of academic research. Especially since you are only sixteen this year. Years old. You are still a complete newcomer to the world of mathematics. It will go more smoothly if you have someone other than your tutor to vouch for your academic performance."

Qiao Yu subconsciously asked: "What does academic guarantee mean?"

Tian Yan really smiled and replied: "Academic guarantee is a very serious matter. For example, in your paper, if no one can find a counterexample within a period of time and it is valid for almost all known curves, then it is possible Convert conjectures into theorems.

In other words, you have solved a world-wide problem in mathematics. At this time, a mathematician of sufficient importance stands up and tells everyone that you solved this problem independently. You did not borrow the help of others. This is an academic guarantee.

As the corresponding author, I can also vouch for your academic work, and Mr. Yuan will not mind vouching for you if you want to come. But in recent years, we have mainly been engaged in Chinese mathematics activities, and our international influence is not very large. If Professor Zhang is willing to provide you with With a guarantee, doubts will be much smaller.

Of course, it may not only be Professor Zhang, but also the visiting Professor Robert who wants to do this. In short, the more professors come forward to vouch for you, the fewer unexpected situations that may arise outside of academia. After all You are only sixteen years old!"

Yes, when he said these words, Tian Yan was really lucky that he made that phone call to Zhang Shuwen that day. Therefore, this paper appears to have a coherent context.

Because he did not expect that Qiao Yu could complete a paper that was qualified to be submitted to the four major universities in such a short period of time. He asked Qiao Yu to come to Yanbei in advance in the past six months to save him some time and lay a solid foundation in advance. This guy handed in a different answer sheet!

Tian Yanzhen believed that Qiao Yu would succeed more than anyone else, but he never thought it would happen so soon! He just celebrated his sixteenth birthday!

What else could he say? Originally, it was an advance plan that looked to the future, but in the blink of an eye, it was only used in more than a month. It can only be said that things are unpredictable, and this kid Qiao Yu is even more unpredictable. Inadvertently, a person popped up surprise.

"Is that so? If there is no academic guarantee, it will be very troublesome?" Qiao Yu nodded suddenly and asked.

Tian Yanzhen hesitated for a moment. Originally, he felt that there was no need for Qiao Yu to be exposed to some of the dark sides of academia, so as not to dampen the child's academic research enthusiasm. But since he can already achieve results, God knows what surprises there will be in the future, so it is better to let him He knew in advance.

"Academic arena is also an arena. Many people are researching in one direction. Generally speaking, whoever publishes first will own the results. But sometimes the problems in mathematics are very special. If you claim to have proved a certain thesis, it may be because of the proof process. If there are some flaws or ambiguity, someone will question it.

There will also be people who fill in the flawed parts and then claim to have proved the problem. They even think that they may even fabricate the story that their previous work was about to yield results, but the original research was leaked at a critical moment.

So this world is not friendly to new academics. Can you understand?"

Qiao Yu nodded and said: "I understand. In fact, Professor Xue mentioned something to me before, but what he said was that the laboratory was used to let people loose... That, the results that have been made, including all research manuscripts Is it possible to encounter this kind of situation under other circumstances? Shouldn’t most professors be gentlemen?”

Tian Yanzhen smiled: "Don't overestimate the average moral standard in academia. You can check the academic integrity analysis report when you have time. In fact, theoretical mathematics is pretty good, compared with theoretical physics and application. Compared with some studies, forget it, let’s not talk about others...

Hey, in short, if someone is willing to endorse your academic achievements, you should remember to be grateful. Because they are risking their academic reputation to prove it for you. Especially when you are just starting out, these are timely help.

The higher the academic reputation you accumulate, the more people will be willing to vouch for your academic work. Until you become a well-known mathematician, at that time no one will need to endorse you. In turn, you will be able to endorse others. .

But you should pay more attention at this time. As I just said, academic guarantee is an extremely serious matter. If you guarantee him, if he really commits academic fraud, it will also affect your academic reputation. You share the honor. It’s not much, but it’s true that if one loses, both will suffer.”

Qiao Yu nodded seriously, indicating that he had learned the lesson.

He heard Lao Xue say something before, and he thought that Professor Xue was probably not involved in top academic circles, so the things he encountered were a little more complicated. But after hearing Director Tian say the same thing, Qiao Yu also realized Yes, probably the higher you go, the more competition there will be.

Listening to what Director Tian meant, the academic world not only has this kind of thing about stealing the achievements of newcomers, but also has many tricks... This only increases Qiao Yu's determination to catch both sides and be tough on both sides.

Having the two banners of Huaqing and Yanbei behind him means that when he makes achievements in the future, the big guys on both sides will help him support him. If he wants to steal his achievements, he must first weigh whether he has enough weight. They all say mathematics. Home is the only area where you can fight alone, but now it seems that before you have enough strength, you have to stay together as a team.

Tian Yanzhen then added: "This is why Mr. Yuan and I have repeatedly asked you whether you have discussed this issue with others. But you don't have to worry too much. At least your achievements this time will not be coveted by anyone.

Your method is very new, and just when you first proposed this idea, we held a seminar. Not only did Professor Zhang Shuwen and Professor Robert participate in the seminar, but the entire process was videotaped. With this evidence, even if someone has a wrong idea,

It is also enough to win the trust of the international academic community.”

Qiao Yu raised his hand, and then said sincerely: "Teacher is wise!" After all, that seminar was Tian Yanzhen's final decision to hold it.

Tian Yanzhen smiled, okay, it was just a spur of the moment idea that day, and he even wanted to show off his status as a closed disciple. At that time, he never thought that Qiao Yuzhen could complete this project. It can only be said that he did it unintentionally.

However, Tian Yanzhen didn't explain anything, but changed the subject: "In addition, under the current situation, I can't treat you as an ordinary student. So you should study step by step according to your own way, but you also

It’s time to think about what to do next.”

"Project?"

Qiao Yu was stunned. He seemed to have not officially started his undergraduate studies yet. According to his understanding, the formal registration for the subject should be at the postgraduate level.

So he immediately explained: "Well, Director Tian, ​​you may have a misunderstanding. I did this project mainly because Teacher Xue told me at that time that there was a genius opposite me who submitted a top conference paper when he was participating in military training as an undergraduate. I think the author is

Your students must not be worse than the other students.

Then I happened to encounter such an opportunity. I had some ideas and just tried to do it. At present, I feel that I should focus on learning. After all, I am still lacking in basic knowledge and I still need to work hard to make up for it.

Shortcomings.

Although Qiao Yu has been shamelessly thinking that he will be the one to carry the banner of Huaxia Mathematics in the future, this does not mean that he wants to put more burdens on himself at this stage. His idea is also very simple, and he completed this paper

, thus establishing his status in the minds of Director Tian and the opposite master, and he can relax for a while.

It is really simple for him to lay a solid foundation. In the past six months, he only needs to read books and papers every week, and participate in IMO special training with a relaxed attitude. After he comes back with a first place, he will enroll next year and start to officially enjoy undergraduate life.

.

Like Schultz, he completes his credits in two years, and then starts graduate studies. The key to doing projects is to enjoy two years of undergraduate life.

With the foundation laid by this thesis, he can't even think about how happy he will be as an undergraduate in the next two years. Think about it, with two giant Buddhas covering him, he can study at two universities at the same time.

Walk sideways in the School of Mathematics and the Institute of Mathematics.

By the way, he can enjoy the admiration of his peers around him. He can take professional classes if he wants to. If he doesn’t want to, the professor will not make things difficult for him. Instead, he will reflect on why he can’t keep him. After all, according to his understanding, even most of Professor Yan Bei’s

I haven’t published any articles in the top four mathematics journals either.

It's beautiful to think about such a life.

But it will be different if you are tasked with doing the project.

Looking at Senior Brother Chen, you can tell that once tasks are on his shoulders, he may not even be able to sleep well, let alone go out to play. He may not even be in a good mood to show off in front of his classmates. Mathematics research should be a very happy thing. But it’s different when you have to shoulder the burden of scientific research.

It is normal for the former not to achieve results, but it is a surprise if he achieves results.

If the latter fails to achieve results, he will feel that he has failed the teacher's expectations and the school's training; it is normal if he achieves results! Obviously, Qiao Yu hopes to live the carefree life of the former two years ago.

However, Tian Yanzhen was obviously not moved by his remarks. He said warmly: "Age is not a problem, and foundation is not a problem. The mathematical life in which people can really make achievements is very short, and time cannot be wasted."

If you don’t have that ability, that’s it. If you have the ability, of course you have to set a goal for yourself. Since you are so interested in the upper bound of rational number points on curves, why not try to solve problems related to BSD conjecture?

Of course, I don't mean that you must completely solve this conjecture immediately. For example, you can first study the rational point ranks of some specific elliptic curves, or study the properties of the L-function at s=1, including the multiplicity of zero points and the poles. Relationships and so on.

If you are interested, I will recommend a few papers to you today. You can go back and study them first. After deciding on the proposition, we will decide on a more specific direction when we meet next week.

Qiao Yu could see that Director Tian was serious. His dear mentor no longer wanted to talk about martial ethics!

I really wanted to go to the other side to complain to my grandpa, but suddenly I felt that if I complained about other things, my grandpa would most likely side with him. But for this kind of thing, not only might he not side with him, but he might even have to put more pressure on him. For a moment, my mentality was a little bit... collapse.

But then I thought about it, although I couldn't resist this matter, I still had to have my own opinion on the research direction.

After all, he was not that interested in studying curvilinear rational numbers, so he simply said: "Director Tian, ​​since I have to choose a topic, in fact, I have always wanted to do research on the distribution of prime numbers. Otherwise, I will directly do the Riemann Hypothesis Bar?

This time Tian Yan was really speechless as he stared at Qiao Yu...

Good guy, the BSD conjecture has already taken shape. If this guy refuses to do it, just change it to a more challenging one. Haha, Riemann Conjecture!
To be continued...