I thought I could give a good first class after entering college, but who would have thought that halfway through the class, I would have to leave early?
Xiao Yi returned to the dormitory, feeling a little helpless.
Maybe this is the price of being too talented in math?
There is always something to lose, such as a complete college life.
Ahem...
You can't say this kind of thing, otherwise you will get retribution.
"Okay, it's time to get down to business."
After sitting down in his seat, Xiao Yi opened his computer and took out paper and pen at the same time.
A few decades ago, before personal computers appeared, paper and pen were the most important tools for mathematicians. Today, decades later, personal computers that 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 prime numbers, or are all products of an even number of prime numbers, then without introducing other conditions, sieve theory cannot provide a non-trivial lower limit on the size of A. In addition, any upper limit will deviate from the true value by 2 times or more.]
"In simpler terms, sieve theory has an extremely difficult 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 essence of the sieve method, which itself is to continuously multiply upwards and estimate the range of problems, so problems will arise."
"But... if we can classify them again on this basis and find those properties that have exactly two prime factors..."
"We will have a greater victory in the fight against the parity problem!"
"However, from a screening perspective alone, it is impossible to achieve this."
"So, something new has to be introduced."
"And the new thing is..."
Xiao Yi thanked Faltings in his heart for his suggestion.
If Faltings hadn't suggested that he study the Elliott-Halberstam conjecture first, he probably wouldn't have been able to come up with today's etale algebraic variety automorphic theory.
Naturally, he cannot use this theory to make further progress at this critical moment.
Inspiration came to him like a tide, and the tip of his pen finally touched the paper.
The limits of the sieving method began to be broken through, and the limits that represented Twin Prime Conjecture also began to be overcome.
In the next few days of class, the students of grade 2020 Hua Loo-Keng Class discovered that Xiao Yi was no longer in class with them.
According to Ye Cheng and the others, Xiao Yi left the dormitory at 7 o'clock in the morning in the past few days, and then returned to the dormitory at early 11 o'clock in the evening.
It looks like they are doing some research again.
Anyway, what they can know is that there are a lot of post-it notes on Xiao Yi's desk and on the wall. As for what is written on them...
They couldn't understand it at all.
For a while, although the students in their class were a little regretful that they could no longer attend class with Xiao Yi, they were still a little bit happy in their hearts.
At least...
No need to suffer the blow of dimensionality reduction.
Time passed quietly, and recently, a video suddenly became popular on station B.
The title is: [Xiao Yi Three solutions to this problem, can you think of them?]
Station B is also known as Big B. There are many people studying here. Naturally, there are also many people studying mathematics. Some videos that specifically talk about mathematical problems often get a good number of views.
After all, there are many students nowadays. When watching a video and suddenly come across a math problem, they might try to see if they can solve it.
However, the content in this video is slightly different from those videos dedicated to the topic in that it takes place in a university classroom.
This question was asked by a mathematics professor at University of Science and Technology of China. The protagonist in the video is Xiao Yi, who made a splash on various online platforms at home and abroad for solving a world-class mathematics problem some time ago. In this video, he solved this problem using three methods.
This immediately attracted many netizens to click in.
Although, they are definitely not as powerful as Scholar Xiao, but they also want to test the gap between themselves and Scholar Xiao.
"If I can do it using three methods, does that mean I =Xiao Yi?"
Shangjing University, Chen Beihua, who was fishing openly in a certain mathematics laboratory, 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 something wrong!
He testified as a doctoral student in mathematics at Shangjing University that this equation is completely true.
Ahem, just kidding.
Of course, as a doctoral student in mathematics, he is quite confident, and as a person engaged in Functional Analysis, his foundation is quite solid.
What's more, how difficult can the questions asked in class be?
Once you click on the video, a lot of barrages will appear.
[I'm thinking of a trade fair]
[There are three methods that can be used for this question?]
[Come in to see my idol]
[The owner of the up page is actually a student of USTC Hua Loo-Keng Class? Are you still classmates with Scholar Xiao? Envy]
[...]
Looking at these barrages, Chen Beihua raised his eyebrows.
It seems that this question is really difficult?
Finally, he focused his eyes on the blackboard in the video and looked at the question.
"Huh? It's actually a limit question related to prime numbers? It looks like something."
Chen Beihua rubbed his chin.
He paused the video, thought for a moment, then took out his pen and started writing.
After a while, he completed the first solution.
"Well, the most important thing is the transformation at the beginning. This is the key point."
"The next step is to use Prime Number Theorem and Stolz's theorem. This question is quite interesting."
"However, the second method..."
Chen Beihua is in trouble.
It is more difficult to break through previous thinking and find a second solution to a problem.
The inherent inertia of the human brain makes it always difficult to break through this inertial thinking and find a second way to solve a problem after completing it.
Probably if the brain cells have their own ideas, they will probably think: Is there something wrong with this person? The problem has been solved, why should we think about the second solution?
Therefore, if you want to come up with the second solution, you must first overcome this inertia of the brain.
However, as a PhD in mathematics, Chen Beihua's thinking ability is relatively stronger than ordinary people, so after spending almost ten minutes, he thought of the second method.
"Finally done!"
He breathed a long sigh of relief, and a smile appeared on Chen Beihua's face again.
It seems that I am still pretty good, being able to come up with such a brilliant second method.
But then, his expression became sad.
This third method... how to do it?
He racked his brains just now to come up with the second method, the third method... God knows how much time it will take him.
After thinking about it tentatively, he finally gave up.
"Forget it, don't think so much. 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 was 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 Scholar Xiao to solve this problem!"
Chen Beihua had a feeling of comparison in his heart. It took him about three minutes to figure out the first method. How long would it take Xiao Yi to use it?
However, the next moment, he found that he was defeated.
Xiao Yi After getting up, he seemed to start writing without even thinking.
Chen Beihua is stunned, is this written down??
Watching Xiao Yi complete the first method, he began to comfort himself, "It must be because I have already studied for a Ph. D. and haven't been exposed to this type of problem for a long time, so it took me three minutes to complete it."
"The second method, Xiao Yi, you have to think about it for a while, right?"
As a result, the next moment, he saw Xiao Yi start a new line and start writing the second method, and it looked like... 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 contains some more advanced things, which are definitely not something that can be learned in freshman Mathematical Analysis anyway.
However, the second method of Xiao Yi only used the most basic methods learned by freshman students, used them to the extreme, and finally completed this question.
"This is really awesome..." After looking at it for a moment, Chen Beihua 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. As far as he knows, some mathematics professors may have even forgotten the formula for finding the root of a quadratic equation.
After all, people are not computers. It is difficult to remember things from many years ago unless they are used frequently.
"So, how will Xiao Yi solve the third method?"
He gave up the comparison and started watching the video with the heart of an apprentice.
After a while, Xiao Yi in the video also started writing the third method on the other side of the blackboard.
As Xiao Yi first wrote the definition, Chen Beihua immediately showed surprise. "This is... the sieving method? I can actually think of using the sieving method to solve this problem..."
"Yes, it's no problem at all. w(n) itself represents the number of prime factors of a positive integer... Holy shit, that's great!"
Chen Beihua patted his thigh and was completely impressed.
He studies Functional Analysis. This direction can be applied in many places, whether it is number theory, or 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 stepped forward and asked.
"Oh, Lao Liu, I came across a video related to Xiao Yi, take a look, it feels so awesome!"
Chen Beihua replied.
As soon as Liu Dongchen heard this, he immediately came up to him, and at the same time he shouted, "Old Chen, you are not funny. I don't know that Scholar Xiao is my idol now, but you didn't send his video to me when you saw it?"
Chen Beihua rolled his eyes. "I just came across this video, okay?"
This Liu Dongchen is also one of the beneficiaries of etale's automorphic theory of algebraic varieties. Then some time ago, he began to claim to be a super fan of Xiao Yi. He looked like a licking dog, which made everyone in their laboratory dislike him.
snort!
Isn't it just by relying on this theory that a paper that can be published in the first section is so great?
It's not top.
Chen Beihua said that he was definitely not being bitter.
"Let me be healthy..."
Liu Dongchen came up and took a look.
"Hmm... this is a question about finding the limit? It should be Mathematical Analysis, who is a freshman. I remember that Scholar Xiao has just entered school this year."
"Hey, go ahead, you actually brought prime numbers in. Have you started doing this kind of problem in your freshman year? Do you need to use Prime Number Theorem to solve it?"
At first, he was a little surprised by the difficulty of this question. Then Liu Dongchen saw the first solution of Xiao Yi. He clapped his hands and said cheerfully, "By the way, Prime Number Theorem is indeed needed. 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 almost used to the limit. "I'm sorry! Can the pinch theorem still be used in this way? If I had known this skill during the entrance exam, I wouldn't have lost points on the final question."
"And this, Wo Ri, you can actually use Cauchy's Convergence Criterion here? This is equivalent to a substitute... Isn't it too dazzling? You are indeed my idol!"
"Scholar Xiao, I am Superman!"
Finally Liu Dongchen's attention turned to the third method in the video that Xiao Yi was writing at this time.
"Walter? There is actually a third method. This, this, this... this is the sifting method? It's so awesome..."
Just when Liu Dongchen was still expressing his admiration for his idol, suddenly Chen Beihua said, "Wait, stop talking!"
Liu Dongchen was stunned, "What's wrong?"
Chen Beihua pointed at what Xiao Yi was writing in the video, squinted his eyes slightly and said, "Look, what is he writing now...?"
Liu Dongchen was confused, but then he looked over.
"Hey... wait! This is... this is..."
His expression gradually changed from doubt to thinking, and finally he was stunned.
"Holy crap, is he planning to conduct a classification study on the parity issues in the sieve method?"
"What did you say? What is this?"
Chen Beihua asked hurriedly without responding.
At first, he just felt that there seemed to be something about the few lines of formulas written by Xiao Yi, which seemed to be related to the sieving method, but he could not tell the specifics.
However, Liu Dongchen's own research is in this direction, and it is normal for him to see it.
But Liu Dongchen shook his head, then took out his mobile phone and said, "I can only see a little bit for the time being, please wait first, I will ask."