The top student must be diligent.

Chapter 96: Inspiration Springs [First Order Request]

I thought I could take the first class after entering college well, but who could have thought that I would have to leave early halfway through the class?
Xiao Yi returned to the dormitory, feeling a little helpless.

Maybe this is the price of being too good at math?
There is always something to lose, such as a complete college life.

cough cough...

This kind of words should not be said out loud, otherwise there will be retribution.

"Okay, it's time to get down to business."

Sitting in his seat, Xiao Yi turned on his computer and took out paper and pen.

Decades ago, when personal computers had not yet appeared, paper and pen were the most important tools for mathematicians. Today, decades later, personal computers, which can easily browse almost all the knowledge in the world, have obviously become another most important tool for mathematicians.

Of course, paper and pen are still the most important.

"What is the parity problem of the sieve method?"

Xiao Yi began to face this most critical issue in his mind.

[If A is a set whose elements are all products of an odd number of primes, or all products of an even number of primes, then sieve theory cannot provide a non-trivial lower bound on the size of A without introducing other conditions, and any upper bound will deviate from the true value by a factor of 2 or more.]

"To put it more simply, sieve theory has a very hard time distinguishing between numbers with an odd number of prime factors and numbers with an even number of prime factors."

"This also stems from the nature of the sieve method, which is to keep multiplying upwards. Under the estimation of a large width, problems will arise."

"But...if we can classify them again on this basis, and find the characteristics of those numbers that have exactly two prime factors..."

"We will achieve a greater victory in our fight against the parity problem!"

"However, it is impossible to achieve this from a screening perspective alone."

“So, something new had to be introduced.”

"And the new thing is..."

Xiao Yi thanked Faltings for his advice in his heart.

If Faltings had not suggested that he first study the Elliott-Halberstam conjecture, he probably would not have been able to come up with the current theory of self-morphism of etale algebraic varieties.

Naturally, he could not use this theory to make further progress at this point in his career.

Inspiration came to him like a tide, and the tip of the pen finally touched the paper.

The limits of the sieve method began to be broken, and the limits of the twin prime conjecture also began to be conquered.

……

In the next few days, students in the 2020 Hua Luogeng class discovered that Xiao Yi was not attending classes with them.

According to Ye Cheng and the others, Xiao Yi left the dormitory at 7 o'clock in the morning these days and returned to the dormitory just after 11 o'clock in the evening.

It looks like he's doing some research again.

Anyway, what they knew was that there were a lot of sticky notes and the like on Xiao Yi's desk and on the wall. As for what was written on them...

They just couldn't understand it at all.

For a moment, although the classmates in their class felt a little sorry that they could not attend classes with Xiao Yi, they still felt a little secretly happy in their hearts.

At least……

No need to suffer a dimensionality reduction attack.

……

Time passed quietly, and recently, a video suddenly became popular on Bilibili.

The title is: [Xiao Yi's three solutions to this problem, can you think of them? ]

Station B is also known as B University. There are many people studying on it. Naturally, there are also many people studying mathematics. Some videos that specialize in discussing difficult mathematical problems often get good views.

After all, there are a lot of students nowadays. When they suddenly come across a math problem while watching a video, they might try to see if they can solve it themselves.

However, the content of this video is slightly different from those videos that specifically explain the topic in that it takes place in a college classroom.

This question was asked by a mathematics professor at the China University of Science and Technology. The protagonist in the video is Xiao Yi, who made headlines on various domestic and foreign online platforms some time ago for solving a world-class mathematical problem. In this video, he solved the problem using three methods.

This immediately attracted many netizens to click in.

Although, they are definitely not as powerful as the God Xiao, they also want to test the gap between themselves and God Xiao.

"If I can also use these three methods to solve the problem, does that mean I = Xiao Yi?"

In a mathematics laboratory at Beijing University, Chen Beihua, who was slacking off openly, thought happily in his heart.

Xiao Yi used three methods to solve this problem, and he also used three methods to solve this problem.

He = Xiao Yi.

Just tell me if there is anything wrong!
He used his identity as a doctoral student in mathematics at Shangjing University to testify that the equation was completely true.

Whoops, just kidding.

Of course, as a doctoral student in mathematics, he is still quite confident in his heart. As a functional analysis expert, his foundation is quite solid.

Besides, how difficult can the questions given in class be?
As soon as you click on the video, a lot of barrages appear.

[I want a market here]

[Can this question also be solved in three ways? ]

【Come in to see my idol】

[The uploader is actually a student of Hua Luogeng's class at HKUST? And he is also a classmate of Xiao Shen? I'm so envious]

【…】

Looking at these comments, Chen Beihua raised his eyebrows.

It seems that this question is indeed very difficult?

Finally, he focused his attention on the blackboard in the video and looked at the question.

"Hmm? It's actually a limit problem related to prime numbers? It looks like something interesting."

Chen Beihua rubbed his chin.

He paused the video, thought for a moment, then took out a pen and started writing.

After a moment, he completed the first solution.

"Well, the most important thing is the transformation at the beginning. This is the key point."

"Then we will use the prime number theorem and Stolz's theorem. This question is quite interesting."

"However, the second method..."

Chen Beihua was in trouble.

It is quite difficult to break through previous thinking and find a second solution to a problem.

The natural inertia of the human brain makes it difficult to break through this inertial thinking and find a second way to solve the problem after completing a problem.

If brain cells had their own thoughts, they would probably think: Is there something wrong with this person? The problem has been solved, why bother thinking of a second solution?

Therefore, if you want to come up with a second solution, you must first overcome this inertia of the brain. However, as a doctor of mathematics, Chen Beihua's thinking ability is relatively stronger than that of ordinary people, so after spending about ten minutes, he thought of the second method.

"Finally done!"

After a long sigh of relief, Chen Beihua smiled again.

It seems that I am not bad after all, being able to come up with such a cool second method.

But then, his expression turned difficult.

How to do this third method?
He racked his brains to come up with the second method. The third method... God knows how long it will take him.

After thinking about it tentatively, he finally gave up.

"Forget it, let's not think too much about it. It's good to be able to come up with two methods. At least it's equal to two-thirds of Xiao Yi!"

After comforting himself in his heart, he raised his head and clicked on the video that had been paused just now, wanting to see what Xiao Yi's three methods were like.

In the video, Xiao Yi left his seat and came to the blackboard.

"Come on! Let me see how long it takes Xiao Shen to solve this problem!"

Chen Beihua began to compare. It took him about three minutes to come up with the first method. How long would it take Xiao Yi?

However, the next moment, he found himself defeated.

After Xiao Yi went up, he started writing without even thinking.

Chen Beihua was stunned. It was written just like that? ?
Watching Xiao Yi complete the first method, he began to comfort himself: "It must be because I'm already a doctoral student and haven't been exposed to this kind of problem for a long time, so it took me three minutes to solve it."

"As for the second method, Xiao Yi needs to think about it for a while, right?"

As a result, the next moment, he saw Xiao Yi started writing a second method on a new line, and it seemed that... the second method used by Xiao Yi was even more "showy" than the second method he had just thought of.

The second method he used involved some more advanced stuff, which is definitely not something you can learn in freshman mathematical analysis.

However, Xiao Yi's second method only used the most basic methods learned by freshmen, and pushed them to the extreme, and finally completed the problem.

"This is really awesome..." After staring for a moment, Chen Beihua finally sighed in his heart.

Can't compare, really can't compare.

At least, his mastery of these very basic things has declined a lot.

This is very common. For example, he knows that some mathematics professors may even forget the formula for finding the roots of a quadratic equation.

After all, people are not computers, and it is difficult to remember things from many years ago unless they use them frequently.

"Then, how will Xiao Yi solve the third method?"

Giving up the desire to compare, he began to watch the video with the heart of an apprentice.

A moment later, Xiao Yi in the video also started writing the third method on the other side of the blackboard.

As Xiao Yi wrote the definition first, Chen Beihua was immediately surprised: "This is... the sieve method? I can actually think of using the sieve method to solve this problem..."

"Yes, that's totally fine. w(n) itself represents the number of prime factors a positive integer has... Damn, that's brilliant!"

Chen Beihua slapped his thigh, completely convinced.

He studies functional analysis, which has many applications, including number theory, algebraic geometry, etc., so he also understands the sieve method.

This is simply...

"Old Chen, what are you doing? You look so excited."

At this time, one of his fellow disciples saw him like this and walked up to him and asked.

"Oh, Lao Liu, I saw a video about Xiao Yi. Check it out. It's so awesome!"

Chen Beihua replied.

When Liu Dongchen heard this, he came over immediately and started yelling, "Old Chen, you are so mean. Don't you know that Xiao Shen is my idol? You saw his video but you didn't send it to me?"

Chen Beihua rolled his eyes: "I just saw this video, too."

Liu Dongchen is also one of the beneficiaries of Etale's theory of automorphism of algebraic varieties. Some time ago, he began to claim to be Xiao Yi's super fan, acting like a bootlicker, making everyone in his laboratory dislike him.

snort!
Isn’t it just relying on this theory to write a paper that can be published in District 1? What’s so great about that?
It's not the top.

Chen Beihua said he was definitely not being jealous.

"Let me check..."

Liu Dongchen came over and took a look.

"Hmm... Is this a limit problem? It should be freshman mathematical analysis. I remember that Xiao Shen just entered school this year."

"Oh my god, you even brought in prime numbers. Are you doing this kind of problem even in your freshman year? Do I need to use the prime number theorem to solve it?"

At first, he was a little surprised at the difficulty of this question. Then, Liu Dongchen saw Xiao Yi's first solution. He clapped his hands and said happily, "Yes, the prime number theorem is indeed required. It seems that my skills are still as good as before."

Chen Beihua sneered.

He was thinking the same thing just now.

Then Liu Dongchen saw the second method.

Then, just like Chen Beihua, Liu Dongchen was shocked by the basic methods that were used to the limit: "Oh my god! Can the squeeze theorem be used like this? If I had known this trick when I took the entrance exam, I wouldn't have lost points on the last question."

"And this, wow, can the Cauchy convergence criterion be used here? This equivalent substitution... is it too showy? He really deserves to be my idol!"

"Xiao Shen, my Superman!"

Finally, Liu Dongchen's attention turned to the third method that Xiao Yi was writing in the video.

"Walter? There is actually a third method, this this this... is this the sieving method? That's amazing..."

Just as Liu Dongchen was still expressing his admiration for his idol, Chen Beihua suddenly said, "Wait, don't talk!"

Liu Dongchen was stunned, "What's wrong?"

Chen Beihua pointed at what Xiao Yi was writing in the video, squinted his eyes and said: "Take a look, what is he writing now...?"

Liu Dongchen was puzzled, but then he looked over.

"Hey...wait! This is...this is..."

His expression gradually changed from confusion to thinking, and finally to stunned.

"Fuck, is he planning to classify the parity problem in the sieve method?"

"What did you say? What is this?"

Chen Beihua didn't react and asked hurriedly.

At first, he just felt that there seemed to be something in the few lines of formulas written by Xiao Yi, which seemed to be related to the sieve method, but he couldn't see the details.

However, Liu Dongchen himself is researching in this direction, so it is normal for him to see this.

But Liu Dongchen shook his head, then took out his phone and said, "I can only see a little bit for now. Wait a minute, I'll ask."

(End of this chapter)