The End of Technology

Today is actually a big day in China, June 9th, the last day of the 2007 college entrance examination.

Ning Zi was in a quiet little bedroom, looking at the message from March in a daze.

Father Ning has already calmly accepted the fact that his son will go to a sports university. Anyway, in his eyes, his son is the best. But Ning Zi obviously doesn't have the understanding that I am the best.

He couldn't even understand March's words.

"I just solved a world-wide problem?"

"Meow, yes, we used the simplest and most convenient mathematical method to solve a world-wide mathematical problem, which can also be said to be a world-wide problem in computer theory. How do you like it? Isn't this feeling great? Great? Congratulations on taking a step closer to becoming a world-renowned scholar."

Ning Zi couldn't help but look at the math problem he had just solved again.

This is a solid geometry question.

The main part of the question is: If more than half of the vertices of an n-dimensional cube are dyed red and the rest are dyed blue, will there always be some red points with neighbors of the same color? If so, what is the maximum number of red dots around it?

The description of the problem was very abstract, so he used a more realistic form when solving the problem. He started with a three-dimensional cube and then pushed it to a higher-dimensional cube. The process of solving the problem was not too complicated. He used the Cauchy interleaving theorem that March instilled in him at night to deduce. Through this theorem, the matrix is ​​connected to the eigenvalues ​​of the sub-matrices of the matrix as a mathematical tool.

Then a set of 2n×2n order matrices was constructed, and then the problem was easily proved using mathematical induction. It took about three hours before and after. The difficulty in the middle was that when using Cauchy's interleaving theorem, the mathematical matrix that constitutes the cube needs to be redefined.

Can this also be considered a world problem?

But soon Mao Mao sent another message: "Meow, the prototype of this question is: for a Boolean function f, in the case of a certain input x (x is a Boolean variable of n bits), there are more than s Boolean The result will be reversed only when the variable changes. That is, the sensitivity of the Boolean function f when the input is x is s(f, x). The maximum value s of all sensitivities s(f, x) is called the sensitivity of the Boolean function f Degree. Prove: There is a positive constant C, yes bs(f) ≤ s(f)^C. And now you have perfectly proved that bs(f) ≤ 2s(f)^4. Congratulations, Ning Jie Yong The simplest and most easily verifiable method proves the Boolean function sensitivity conjecture."

Ning Zi was stunned for a moment, and then, without even waiting for him to take action, Master March had already turned out various introductions about the sensitivity conjecture of Boolean functions. Ning Zi watched carefully, transformed countless data in his brain, and then discovered that he seemed to have really solved this problem.

Ning Zi was unprepared for suddenly solving a world problem in one afternoon.

In fact, when he saw this topic, he never thought that it was a world problem. I only treated this question as a normal training question, and now that I have successfully completed it, it feels like a dream.

After all, this is different from his last paper.

It can be said that the last paper was forcibly instilled in him in March, but this difficult problem was solved by him through the accumulation of study in this month and drawing inferences from one example. He had not been given similar training before March. At most, it only had the derivation process of Cauchy's interleaving theorem, which impressed him deeply.

After hesitating for a long time, Ning Zi asked, "What should we do now?"

"Meow, of course you decide the topic you choose. You can write a paper now based on the answers you just answered. Of course, I will only guide you this time, and you need to write the main part yourself. It is just in time to practice your writing skills. . I suggest you still submit to the last journal. After all, your last paper has not been published yet, and you are still a newcomer to the academic world. But to the editor-in-chief of the last journal, you are very popular."

Ning Zi nodded, this was indeed a good suggestion. But then he asked: "Why not directly submit it to a Chinese journal?"

"Meow, because of my understanding of your world, the current mainstream understanding is that the results that are recognized by foreign countries are the best. So if you want to conquer the country, the easiest way to solve it is to make those foreign people bow down first. First, let those famous people abroad praise you so that you can obtain enough resources at home without relying on anyone, so that you can develop more smoothly. Hey, who told you that human lifespan is limited? Time does not wait. You!"

March sighed as before.

Obviously this kitten is very dissatisfied with the limitation of human life span, and he has expressed his feelings about this matter more than once.

"Meow, you should also understand why I chose you, right? In fact, you are very talented, including your spatial imagination and ability to summarize problems. I have studied you for a long time, and your thinking is actually very meticulous and your intuition for solving problems is very good. Accurate. The score in the college entrance examination is not high, purely because the systematic question-answering training here is not scientific. Simply put, the teacher's level is too low, and he has not found the right method for cramming teaching!"

"Meow, so you have to believe in yourself. Not only do you have to believe in your own abilities, but you also have to believe in my judgment. Although I always say that you are stupid, compared with other stupid people, your stupidity is also different from others. It’s different. It’s the kind of stupidity that’s pretty smart, you know?”

Um……

In fact, Ning Zi felt it was a little weird.

He could feel that Lord March was praising him. Although this was rare, this mode of praise always made people a little uncomfortable.

The evaluation of "reasonably smart but stupid" is probably, should, probably, a very high evaluation for March, right?

After all, he had seen this kitten's poisonous tongue. In his eyes, the two academicians were probably just idiots who didn't have much medicine to cure them. With the comparison, I feel quite comfortable.

"Well, I know I'm pretty good, so why should I start writing my thesis now?"

"Meow, write it. This time you write it yourself. I won't help you revise it, but I will give you review opinions. You can continue to revise according to my opinions until I am satisfied. Speaking of which, I miss the time when I became the world Do you know what it feels like to be the first reviewer? At that time, I was the darling of countless mathematics journal editors. They lined up, knelt there, said nice things, and begged me to help them review various mathematics papers. Meow, so You should feel honored.”

"I'm very honored! Really!" Ning Zi responded, then created a new file and began to carefully sort out the format of the previous paper in his mind.

Speaking of which, this is the real first paper in his life, and it cannot be overemphasized!

I expressed my emotion.