There is a joke on the Internet about mathematics civil science.

What it's about is that someone posted a post on the Internet, saying that he spent decades creating an important mathematical theory, and then simultaneously posted his proof process on the Internet.

It turns out that a mathematician actually took a serious look at it and told him in the forum that this theorem has actually been proved by mathematicians for more than 80 years. Anyone who has studied mathematics as a graduate student will know this theorem and everyone will directly use the conclusion.

Regardless of whether this joke is true or false, it at least illustrates that to learn mathematics these days, you first need to have a solid foundation.

This is also the reason why after Tian Yanzhen discussed with Xue Song, he developed a series of systematic courses for Qiao Yu so that his knowledge could be systematic. But when Tian Yanzhen discovered that Qiao Yu had just read Peter Schulz's "

After writing the thesis and having his own ideas and opinions, he gave up the decision.

The reason is actually very simple.

For example, you will often see people on the Internet claiming to have proved Goldbach's hypothesis. It is no exaggeration to say that my guess can be proved hundreds or thousands of times a year by math enthusiasts around the world. But they claim to have proved the Riemann hypothesis.

Mathematics enthusiasts can immediately reduce the number by 90%. As for P=NP?, the turbulence problems involved in the N-S equation, etc., there are even fewer. This is the threshold of mathematics.

If you can’t even understand the problem itself and cannot accurately describe it, let alone solve it.

As for the things studied by Peter Schulz, there are no mathematics enthusiasts on the Internet who would like to touch upon them, and there are even very few mathematicians who want to touch upon them.

This threshold is too high, and it is difficult to find opportunities to express different opinions or raise arguments, because most people cannot even understand the core ideas of their research, let alone make criticisms or suggestions.

In a sense, Peter Schulz's research on mathematics itself challenged many mathematicians' traditional views on such issues. But everyone has to admit that his achievements, such as the construction of complete coprojective geometry,

It does provide new tools and methods for solving previously difficult problems.

But this guy Qiao Yu actually understood Peter Schulz's paper.

To be honest, in the eyes of Tian Yanzhen and Xue Song, this is a very unmathematical thing. But it also allows them to see Qiao Yu's infinite possibilities. At this time, Qiao Yu's performance is probably among the infinite possibilities.

A certain possibility.

It only took one night to find a method that seemed to greatly simplify the accurate estimation of the upper bound of the rational number points of special curves.

Of course, it can only be seen here, because Qiao Yu directly used the framework set up by Peter Schultz, created five mathematical tools in one go, and successfully solved this problem. But the problem is, although he felt that these were

The mathematical tools he just created must be correct, but he is currently unable to fully prove any of them from mathematical logic. In other words, he cannot prove any of these mathematical theorems that are expected to solve certain world problems, so it is very difficult for him to prove them.

It is difficult to say whether these theorems are really true.

So theoretically, he just proposed five less popular mathematical conjectures.

Regardless of whether it is useful or not, at least the manuscript paper is filled with three large sheets, which can be used to discuss with everyone during the lecture.

And with these things, Qiao Yu felt that he was no longer showing basic courtesy. This was simply courtesy, showing the highest courtesy in China to the professor who came to give the lecture.

After all, he not only studied the other party's paper, but also found a set of methods that seemed to be able to solve similar problems, which is enough to prove that he has been thinking very carefully for a period of time. As long as you don't care about this little detail, you can't prove it for the time being.

If so, it would be perfect.

And it only took him more than an hour to construct this set of tools.

Qiao Yu finally realized the joy of those great mathematicians coming up with a conjecture for nothing.

It’s probably the mentality that I think this mathematical theory is what it is, but I can’t prove it, so anyone who wants to prove it can just try it.

Qiao Yu has even imagined that when he becomes a world-recognized great mathematician like Riemann and Fermat in the future, he will also come up with a mathematical conjecture that is so awesome and useful that people feel that they will die in the morning.

.Then he proved it secretly and privately, then hid the manuscript and left it in his last words.

Next, he went to cooperate with a wealthy and well-known mathematics research institution like the Clay Institute. Both parties spent a large amount of money to offer rewards. Whoever could prove his conjecture could take the money away immediately.

!When everyone's enthusiasm was mobilized, but it was found that it could not be proved, he would just watch the excitement, and from time to time he would speak to encourage everyone, or drop some vague clues.

It wasn't until after he died and his last words were exposed that mathematicians all over the world knew that this conjecture was actually a theorem and had been proved by him long ago. Alas, he just didn't tell everyone when he was alive, just for fun. And then that

Naturally, a bonus will be paid to him. Even though he dies, it can be left as a legacy and passed on to the next generation.

Really, just thinking about this makes Qiao Yu very emotional, and even makes his blood boil. And in reality, he is only three steps away from realizing this fun thing.

The first step is to become a world-famous mathematician; the second step is to come up with this conjecture, and the third step is to prove it completely and without error! See, mathematics is that simple.

Thinking of the dumbfounded looks of all the mathematicians, Qiao Yu couldn't help but smile knowingly, looked at his masterpiece again, stood up, stretched hard, and then picked up the phone.

Today's study ends here. Qiao Yu knows very well that the things he has just come up with out of the blue are impossible to prove with his current ability. But it doesn't matter, he has not yet published Peter Schulz's related papers.

After reading it. Maybe you will be inspired after reading it and solve this problem accidentally?

Qiao Yu took a look just now and found that Professor Robert had a paper published in the "Journal of the American Mathematical Society", which was one of the top four mathematics journals in the world that Lao Xue had mentioned to him. In other words

In other words, the old man hasn't completely solved this problem yet, and his papers can be published in the world's top journals. If he can really solve this kind of problem, he must be more qualified to be published.

Although this is not the kind of mathematical problem that will shock mathematicians all over the world after being solved, but since so many mathematicians are interested in this thing, it shows that the influence is definitely there. At least it can be considered as equal to the one opposite. Is that the genius student named Zheng Zhiqiang trained by the school?

In fact, it is not all due to competitiveness. The main reason is that Qiao Yu has always believed that he has to do his best to realize the awesomeness he has boasted about. If he slacks off because he encounters some difficulties, then how can he realize his dream? Today he was because of The genius on the other side had done so well before that he gave up the idea of ​​competing with the opponent. Then tomorrow, wouldn’t he give up the idea of ​​acquiring the entire community because it is too difficult to make billions or tens of billions? Then he and his grandfather are always ready What's the difference between a drinking buddy who just likes to brag?

Men, when faced with difficulties, must face difficulties in a literal sense, not in a phonetic sense. I turned on my phone and looked at the time. It was only 10:23.

So Qiao Yu clicked on WeChat, thinking of sending a message to Qiao Xi, just for fun. But the moment the crappy software was opened, a bunch of messages popped up in the friend group.

I clicked on it and took a look, and sure enough, it was Yu Yongjun who kept @ him for almost the whole day. He probably just couldn't help but @ him when he was free.

What can I say, Qiao Yu has indeed not been in the group these two days. On the one hand, he feels that he has tight time and heavy tasks, and on the other hand, he already feels that it is not good to bully the kid in the group all the time...

Well, although everyone is actually the same age, he is now a college student, and those two guys are still hanging out in high school, so doesn't this gap show up?

Qiao Yu now thinks that those people on the Internet who say that college students are clear and stupid, and that high school is the pinnacle of wisdom in life, are either making fun of themselves, or they went to a fake university. If nothing else, just the library of Yanbei University Which high school in the country has a better documentation system?

This thing can really improve your horizons.

During the two months he was in high school, he stayed in the study room of Tieyi Middle School every day, trying to find some useful information. It often took a lot of time to find resources through search engines, and many times he finally found the resources. It's not that high quality and it's a complete waste of time.

After arriving in Beijing, I searched through the internal literature search system of Yanbei University in this small room and found a large list of extremely high-quality resources in minutes! I couldn’t finish it, I couldn’t finish it at all!

But since these two guys are so pious, he must bully them...

Qiao Yu decided to click in and take a look. He had to respect his friends' psychology of being abused. Oh, it's been two days and they are still discussing his paper.

Yu Wei is still so powerful. He only took a picture of half of the name of the paper. Compared to him, this guy actually found the entire text of the paper. Of course, this does not mean that this guy was scared. In the group chat, there were still As tough-talking as ever.

To sum up, this guy had dozens of arguments with Yu Yongjun in the WeChat group. What he meant was that at most Qiao Yu had an idea for this paper, and most of the article must have been completed, modified, and polished by others... .

Also, there are no new tools in this paper. It is just a flexible study and application of many known mathematical tools. In essence, it is no different from their participation in the Olympiad. It is just that they are a flexible application of high school knowledge, while the paper is only exposed to many universities.

Flexible use of mathematical tools.

Because of the above reasons, Yu Wei believed that the reason why Qiao Yu did not appear was that he had already understood a generic paper and had nothing to show off. As for Yu Yongjun's expression, it was simple.

In fact, his long and extremely damaging language expressions can be translated into one sentence: If you say that my eldest brother is not good, then it is Chi Guoguo's jealousy, otherwise You Can You Up! Seeing that his younger brother was bullied, Qiao Yu felt that he should still

Occasionally educate Yu Wei, otherwise this guy will have some unrealistic illusions over time.

"Ahem, you two are really good at chatting? I've been too busy these past two days to be in the group, but you guys actually chatted hundreds of times? Have you studied the questions well? In this state, I doubt whether you can be selected this year.

IMO!" It was still Yu Yongjun who was the first to rush out: "Damn it, boss, you are finally willing to take the initiative. When you are not around, this guy Yu Wei will turn against Tiangang!"

Qiao Yu: "I can't help it. Haven't I been too busy when I first arrived at Yanbei University? Don't you know how strict Director Tian's requirements are? I have to attend a lecture given by a professor from New York University tomorrow, so I have to finish the lecture today.

At least two papers, hey, is it easy for me?"

Yu Yongjun: "Holy shit, is it so high-end? Reading papers and attending lectures? This university life is a bit different from what I imagined!" After the two chatted for a while, Yu Wei also popped up: "Heh.

.Blow, you keep blowing!"

Qiao Yu: "Classmate Yu Wei, I know you are in a hurry, but don't be in a hurry now. Let's do this. Later, I will suggest to the instructor that we come to Yanbei University for the first phase of special training this year. Then I will let you personally

You will know after you experience my life at Yanbei University. In short, I forgive you first, because people simply cannot imagine life beyond their own knowledge."

Yu Yongjun posted a picture of himself laughing, and then said: "Yu Wei, are you still not honest?"

Yu Wei: "Your family runs the Chinese Mathematical Society? If you say you want to go to Yanbei, why don't you go to Yanbei?"

Qiao Yu: "Hey, you don't understand. Let's put it this way, you were right about the paper I sent you yesterday. I don't think the level is high either. I'm just better than you. It's not interesting. I

I really don’t want to show off to you, but I’ll tell you that I just found a way to solve a world-wide mathematical problem.

Let's put it this way, as long as I show these things tomorrow, in order not to delay my research time, the special training in March must also be held at Yanbei University. After all, it will save me the time of running back and forth, because this is

You’re saving time for mathematicians around the world, understand?”

Yu Wei: "???You went to Yanbei University to major in bragging, right?!"

Yu Yongjun: "Well, boss, although I think you are indeed very awesome, at least much better than that guy Yu Wei, but to be honest, you did brag a little too loudly this time, right? How about we

Let’s collect it first and start by solving a small problem?”

Qiao Yu: "Hey, summer insects cannot talk about ice. You first search for the problem of accurate estimation of the upper bound of the number of rational points on the algebraic curve, and then search for the theory pioneered by Peter Schulz. And I, your eldest brother

, is the first person who tried to combine the two to solve this problem, understand?"

Yu Wei: "..." Yu Yongjun: "..."

Qiao Yu: "Forget it, I don't have time to explain to you. I have to go to bed early today and have to attend a lecture tomorrow. I know it is difficult for you to accept the gap between us now, but time will prove everything. So come on

Work hard! Try to pass the interview at Yanbei University in the future. After all, only when you come to Yanbei University can you know how big the gap is with me!"

After saying that, Qiao Yu directly quit the group chat and clicked on Qiao Xi's WeChat. There was no way, the situation was different, and some things were difficult to explain to these two guys.

"Mom, I have completely gotten used to life at Yanbei University. You don't know how friendly the people here are! Not only did they arrange a special private room for me, but Director Tian also said that all the mathematics professors in Yanbei would come to train me.

.By the way, I also met a senior brother today. He was nice and cute. Before leaving, he said that I was as important to him as air."

Qiao Xi replied quickly: "Hmm? I can understand other things, but why does your senior brother think you are as important to him as air? Are you sure this senior brother is normal?" Qiao Yu was a little confused, he was just right
To be continued...