"You have two hours to answer the questions!", the teaching assistant helped him take the answer sheets and scratch paper and other test supplies and put them on the table, then retreated to the couch and picked up a magazine to flip through it.

It seems that Professor Nan is ruthless and does not intend to let himself pass this exam! Lu Qiujian did not intend to admit defeat, and began to look at the first question, only to see that the question reads: All completely polynomial non-deterministic problems can be converted into a class of logical operation problems called satisfying problems. Since all possible answers to such problems can be calculated in polynomial time, is there a deterministic algorithm for this kind of problem that can directly calculate or search for the correct answer in polynomial time?

There are two ways to solve this problem, the first is to find an algorithm for a particular completely polynomial non-deterministic problem, all of which can be solved because they can be transformed into the same problem, and the other is that such an algorithm does not exist. Then it is mathematically necessary to prove why it does not exist.

However, when current mathematicians encounter similar problems, they usually only use the exhaustive method to solve them, and there is no way to solve this kind of problem in a short time.

Question 2: Please show that for a particularly perfect type of space, such as a projective algebraic cluster, the components called the Hodge closed chain are actually the (rational linear) combination of the geometric components called the algebraic closed chain.

This is a problem of algebraic geometry that involves the correlation of the algebraic topology of a nonsingular complex algebraic cluster with its geometry expressed by the polynomial equation that defines the subclusters.

No, no, no, this is not a problem that can be solved in a short time, forget it, let's continue to look down, Lu Qiujian smiled bitterly and moved his gaze to the third question.

Question 3: Any single-connected, closed three-dimensional manifold must be the same as a three-dimensional sphere.

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

Let's look at the fourth problem: the frequency of prime numbers is closely related to the properties of a well-constructed zeta function ζ(), and all meaningful solutions to the equation ζ(s)=0 are in a straight line.

Prime numbers are 1, 3, 5 and other numbers that cannot be divisible by any positive integer other than 1 and themselves, and their place in number theory is similar to that of the atoms used to construct everything in the physical world;

Oh my God, can't you give me a topic that I can scratch my head of? Lu Qiujian wailed in his heart, doubting his IQ for the first time in months.

The fifth question is even more exaggerated, the need to complete this proof not only requires advanced mathematical knowledge, but also requires extremely profound research in physics, Lu Qiujian has not yet systematically studied physics, and it is impossible to solve this problem, even he glanced at it and decided to give up and study the next problem.

The sixth question involves using differential equations to describe the motion of fluids, and for Lu Qiujian, this problem is not much different from the five questions above, anyway, he has not thought of the idea of solving the problem at present.

Hey, do you have to hand in a blank paper this time? Lu Qiujian had such a ridiculous idea in his mind, even if the previous owner of this body was from elementary school to university, wasn't that exam a good idea? Could it really be planted today?

In the hope of what happened, Lu Qiujian wiped his sweat and turned to the last question: given an Abelian cluster on a global domain, guess that the rank of its Modal group is equal to the zero order of its L function at 1, and the first coefficient of the Taylor expansion of its L function at 1 has an exact equation relationship with the size of the finite part, the volume of the free part, the period of all prime sites, and the sand group.

After reading the last question!! Lu Qiujian lowered his head in frustration, even if he could pass one question correctly, he would not be able to pass the test this time! These seven questions either require an extraordinary amount of calculations or require ingenious ideas for solving the questions, how could Professor Nan think of using such a question to test himself? Even he himself can't do any of them, right?

The assistant heard the sound of Lu Qiujian banging on the table in distress, raised her head slightly and glanced at him and then became obsessed with the magazine again, this is the student who can't figure out the test paper during the exam, and she has seen a lot of students who have been reading for a long time but don't know where to start, she has long lost her curiosity, anyway, she will collect the test paper when her time comes, and leave the rest to Professor Nan!

I remember when I was at Beijing Normal University, a classmate in the Department of Mathematics laughed bitterly and joked to myself: I studied chaos, and then I learned to make wontons. Lu Qiujian has not only become a wonton now, he has mixed tastes in his heart, these seven questions have pressed him into a round cake, plus the five flavors in his heart, he is almost a five-kernel mooncake that adults dislike and abandon!

No, no, no, you can't just admit defeat! Lu Qiujian was a little depressed and returned to his senses, no matter how frustrated he was, these problems still had to be solved one by one, even if it was not for the purpose of being able to participate in the NCAA competition, he had to re-verify his mathematical level, compared to the plan he wanted to complete, the difficulty of these problems now was simply not worth mentioning!

Meanwhile, Professor Nan and Dyson were already in the café behind the Institute for Advanced Study in Princeton, where the two tasteless guys were in stark contrast to the personable Edward Witten.

The three of them had a heated discussion about the topic in Professor Nan's office just now, perhaps because he was studying physics, and Edward Witten sided with Dyson, trying his best to refute Professor Nan's various views, and Professor Nan quickly fell behind in a one-on-two situation.

"So the two of you have already found a way to solve this problem?", seeing that the situation was unfavorable, Professor Nan made a killer move.

"And did you find it?", Dyson retorted immediately after being frustrated.

"At least Yau Chengtong and Hamilton's research has broken through the forbidden area of this problem, and now they are close to kicking the door!", even though he knew that this kick could be missed, Professor Nan still said stiffly.

Naturally, such an argument will not be fruitful, 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 papers!", I don't know how many questions Lu Qiujian has made now? He thought to himself.

Ahem, these problems are more difficult to describe in words, you just need to know that these problems look amazing!

Thanks to the sun and the moon and the same light, Xiao Fan, dragonfly wings, unfashionable pigs, book friends 151114070946457, atheism cool, ~. Meow a mi, and I'm a dragon maniac tip. You guys are so powerful, so soon to 6000 recommendations, look for it and add more, love you!