"You have two hours to answer questions!" The teaching assistant helped him get the answer sheet and draft paper and other exam supplies on the table, then he stepped onto the sofa and picked up a magazine and looked it up.

It seems that Professor Nan is cruel and unwilling to let himself pass this exam! Lu Qiujian did not intend to admit defeat, and began to start with the first question. The question said: All the complete polynomial non-deterministic problems can be converted into a type of logical operation problem called satisfaction problems. Since all possible answers to such questions can be calculated in polynomial time, is there a deterministic algorithm for this kind of question that can be directly calculated or found out the correct answer in polynomial time?

There are two ways to solve this problem. The first is to find algorithms one by one for a specific complete polynomial nondeterminism problem. All such problems can be solved because they can be transformed into the same problem. Another possibility is that such algorithms do not exist. Then we must prove from a mathematical theory why it does not exist.

However, when mathematicians encounter similar problems, they usually only use exhaustive methods to solve them. There is no way to solve this problem in a short time. Lu Qiujian plans to take a look at the following questions first.

Question 2: Please prove that for the so-called projective algebraic clusters, the components called Hodge's closed chain are actually (rational linear) combinations of geometric components called algebraic closed chains.

This is an algebraic geometry problem, involving the correlation between the algebraic topology of non-singular complex algebraic clusters and the geometry it expresses by polynomial equations that define subclusters.

No, no, this is not a problem that can be solved in a short time. Forget it, let’s continue reading. Lu Qiujian smiled bitterly and moved his eyes to the third question.

Question 3: Any single-connected, closed three-dimensional manifold must be homoembred on a three-dimensional spherical surface.

This is a topological problem. Lu Qiujian thought about it. A closed three-dimensional manifold is a three-dimensional space without boundaries; single connection means that every closed curve in this space can be continuously shrink into a point, or in a closed three-dimensional space, if each closed curve can be shrink into a point, this space must be a three-dimensional sphere.

Let’s take a look at the fourth question: The frequency of prime numbers is closely related to the properties of a carefully constructed zeta function ζ(), and all meaningful solutions of the equation ζ(s)=0 are on a straight line.

Prime numbers are 1, 3, 5, and so numbers that cannot be divided by other positive integers except 1 and itself. Their position in number theory is similar to that of the atoms used in the physical world to construct all things; the definition of prime numbers is simple, but their distribution is mysterious and abnormal.

Oh my God, can't I give me a question that I can nod my mind? Lu Qiujian wailed in his heart, for the first time in the past few months, he had doubts about his IQ.

The fifth question is even more exaggerated. It requires not only to complete this proof, but also to have extremely profound research on physics. Lu Qiujian has not systematically studied physics, so there is no way to solve this problem. Even if he glanced at it, he decided to give up and study the next question.

Question 6 involves using differential equations to describe the motion of a fluid. For Lu Qiujian, this question is not much different from the above five questions. Anyway, I have not thought of a solution at the moment.

Alas, are you going to hand in the blank paper this time? Lu Qiujian had such a ridiculous idea in his mind. Even if the master of this body had been from elementary school to university, that exam was not easy to get. Could it be that he really was going to fall into trouble today?

With the hope of failure, Lu Qiujian wiped his sweat and turned to the last question: Given an Abel cluster in an overall domain, guess that the rank of its modal group is equal to the zero-point order of its L function at 1, and the first term coefficient of its L function at 1 has an exact equation relationship with the finite part size, free part volume, period of all primary positions, and sand group.

Dead!!! After reading the last question, Lu Qiujian lowered his head in frustration. Even if he answered one question correctly, he could pass it. He would not be able to pass this time! These seven questions either require extraordinary calculations or require ingenious problem-solving ideas. How could Professor Nan think of taking such questions to test himself? Even he himself could not do any of them, right?

When the assistant heard the sound of Lu Qiujian knocking on the table in distress, he raised his head slightly and looked at him, and became addicted to the magazine again. This was when the exam was not done. She had seen many students who had read it for a long time but had no idea how to start. She had long lost her curiosity. Anyway, when the time came, she would go to collect the exam papers, and leave the other things to Professor Nan!

I remember when I was in the Peking University, a classmate from the mathematics department, who was also in the mathematics department, teased himself with a wry smile: I studied Chaos, and then learned wontons. Lu Qiujian has not only become wontons now. He has mixed feelings. These seven questions have pushed him into round cakes. In addition, the five flavors in his heart are almost like adults to abandon the five-nut mooncake!

No, no, no, you can't give in! Lu Qiujian was a little depressed and returned to rationality. No matter how frustrated he was, these problems still have to be solved one by one. Even if it is not for being able to participate in the NCAA competition, he still has to re-verify his math level. Compared with the plan he has to complete, the difficulty of these problems is simply not worth mentioning!

Meanwhile, Professor Nan and Dyson had already arrived at the cafe behind Princeton Advanced Studies, where two guys with no clothes were dressed in stark contrast with the elegant Edward Witten.

The three of them had a heated discussion on the topic in Professor Nan's office, perhaps because they were studying physics. Edward Witten stood on Dyson's side and tried his best to refute Professor Nan's various views. Professor Nan quickly fell at a disadvantage in a one-on-two situation.

"So have you two found a way to solve this problem?" Seeing that the situation was unfavorable, Professor Nan used his trump card.

"So have you found it?" Dyson immediately retorted after being frustrated.

"At least the research of Qiu Chengtong and Hamilton has broken through the penalty area for this problem, and it's almost time to kick it!" Professor Nan said stubbornly even though he knew that this kick might be knocked away.

Such a dispute will naturally not have any results. Professor Nan looked at his watch and was about to get up, "Okay, it's time for me to go back and correct the test paper!" He didn't know how many questions Lu Qiujian had done now? He thought to himself.

Ahem, it is difficult to describe these problems in words. You just need to know that these problems look very powerful!
Chapter completed!