From Almighty Scholar to Chief Scientist

Although they had expected this result, they couldn't help being surprised to hear that a 17-year-old high school student's thesis had passed the review of the Annals of Mathematics and would be published in it.

What a blessing.

With this thesis, it would be no problem for Lin Xiao to stay as a teacher at Shangjing University after graduation, and it might not be long before he can be rated as a full professor.

It is not enough to write a paper for a lifetime, and there is every chance to apply for Qianqing or something, and Qianqing has a starting fund of 300 million.

This young man doesn't have to worry about anything in his life.

Of course, they also sincerely hope that Lin Xiao can continue to develop his talent and become a pillar of Huaguo's mathematics community in the future.

……

Time passes quickly.

2018年的春节在2月16日，也就是2月15日是除夕。

As for the third year of Jincheng High School, the holiday will start on February 2th for ten days, and school will start after ten days.

Jincheng High School is also considered kind, and did not engage in any early start of school operations. Of course, Jincheng High School did it before, but it was reported by students, and then it disappeared.

Therefore, the senior high school students who are about to usher in the college entrance examination in less than four months finally ushered in their first long vacation after studying hard for so long.

However, for Lin Xiao, he didn't feel anything at all, because the school felt that he was going to prepare for the second stage of selection in late March, so he was specially approved not to use it for class.

Lin Xiao was not hypocritical either. He had classes six days a week, went to school two days, and stayed at home for the remaining five days.

While at home, he continued to read the math books sent to him by Beijing University.

Now another month has passed, he has read the previous abstract algebra, including geometry, ordinary differential equations and mathematical models, and has also studied the textbooks, and now he has begun to look at Ahlfors' complex analysis, that is, complex variable functions Argument.

Reading a book can't be fast, it's basically impossible to finish a book in a day and understand all the contents inside, especially these are all new knowledge.

For Lin Xiao, he has to read a book for at least seven days before he can fully understand it. For the slightly more troublesome ones, such as the complex analysis textbook, he has read it for eight days now, but there are still some contents left, and he still needs two more. It takes days to see it.

But, anyway, there is enough time, so he is not in a hurry.

Of course, after reading so many books, he also gained experience and truth points again. Today, the personal panel has become:

[Host: Lin Xiao]

[Truth points: 10.7]

【Universal truth branch level】

【Mathematics: Level 2 (91/250)】

[Chemistry: Level 0 (2/10)]

[Physics: Level 0 (2/10)]

[Biology: Level 0 (2/10)]

[Materials: Level 0 (0/10)]

[Informatics: Level 0 (0/10)]

Because I haven’t started studying other subjects yet, other subjects are still at level 0. However, Lin Xiao decided to start expanding other subjects after returning from IMO. For example, start with physics first, and focus on other subjects. Books are fine, anyway, reading books can add 5 experience points.

Of course, this will have to wait until after July this year.

……

The long holiday has begun, and New Year's Eve, February 2th, also quietly falls.

In Jincheng City in 2018, fireworks and firecrackers have not been banned. Listening to the continuous sound of firecrackers outside the window, as well as the occasional fireworks explosion from the distant sky, even Lin Xiao, who is immersed in learning, can hardly Maintain that state.

He put down his pen, opened the curtains, and looked out at the darkened sky, which was still sparkling from time to time because of the fireworks. Lin Xiao watched quietly, and his heart crossed the dark sky, constructing the scene of the universe, So, what is the truth of the universe?

"Lin Xiao, it's time to eat!"

Mom's voice sounded.

Lin Xiao responded, and went to dinner with his family.

And after the first day of the new year, it is natural to go to various relatives' homes to pay New Year's greetings. In the second year of junior high school, he and his family visited a certain relative's house.

When he arrived at the relative's house, he was naturally praised by the elders. After that, he was called by his relatives to help one of his little brothers with homework.

The younger brother is in the first grade of junior high school this year, and his grades are usually quite good, and he has been ranked among the top five in his class.

But, he is also only 12 years old and under 13 years old, and he is in the stage of rebellion.

Lin Xiao sat next to him and said with a smile: "Your mother asked me to teach you, is there anything you don't know?"

"No, you don't need to teach."

The little brother curled his lips, looking a little dissatisfied with Lin Xiao.

Since October last year, he has often heard his parents say, 'You learn from your cousin', 'Look at your cousin', 'Contact your cousin when you have time'...

In the past, he was the top five in the class and the top [-] in the grade. He was always called "other people's child" by other parents, but now he was bombarded by "other people's children". Of course, he was not convinced in the rebellious period.

Lin Xiao raised his eyebrows and continued to say with a smile, "That's fine."

Chapter 58 The little brother who was crushed by the show

The little brother refused, Lin Xiao didn't say much, and took out the "Real Variable Function and Functional Analysis" he was reading now from the satchel he brought.

Real variable functions and functional analysis are as difficult as complex variable functions, and Lin Xiao has to be serious enough to learn them.

Now that he has finished reading the previous part on real variable functions, he also came to the part of functional analysis. Functional analysis is even more heavyweight. It has already involved the analytical problems in infinite-dimensional vector spaces. The difficulty is difficult, so it is naturally unnecessary. Say more.

So after a while, he fell into the state of immersion again.

But when the little brother next to him saw that the big brother next to him had turned out a book and read it, he couldn't help but become curious.

What book did he read?

The little brother glanced at it from the corner of his eye, real variable function and functional analysis?

Immediately I didn't know what was going on.

It looks like it's awesome.

Also, functions?

Is this a math book?

Seeing that Lin Xiao didn't notice his appearance, he quietly turned his head and glanced at it, feeling dazzled immediately. Is this counted as mathematics?

There are so many strange symbols in mathematics?

But the little brother was only surprised for a while, and then he thought that it was just that he hadn't learned those things. If he had learned Lin Xiao's level, he would definitely be able to understand this book, just like he didn't study in high school now. Mathematics knowledge, but as long as I have learned mathematics in high school, I will definitely understand it.

So the little brother stopped reading more and continued to work on his own questions.

After doing one problem after another, my little brother finally encountered something that he couldn't think of when he was doing a big geometry problem.

"This question is a bit difficult."

He wrinkled his face and thought about it, but he couldn't figure out how to prove that this triangle is an isosceles triangle.

However, at this time, he remembered that there was a god-level person beside him who was praised by his parents every day. He couldn't help but turned his head to look at Lin Xiao. Turning around, the idea of ​​trying Lin Xiao came up.

So he said, "Hey, help me see this question and how to write it."

However, Lin Xiao did not respond.

The little brother couldn't help but wonder if Lin Xiao was stupid from reading.

"Hello? Hello?!"

He stretched out his hand and shook it in front of Lin Xiao. At this moment, Lin Xiao finally came back to his senses, looked at him suspiciously, and asked, "What's the matter?"

Although he was talking with his younger brother, Lin Xiao still recalled the Hahn-Banach theorem in the book in his mind.

"I've come across a question, see if you can write it down." The little brother pointed to the question he was writing.

"Oh, have you encountered a problem? Let me take a look."

Lin Xiao turned his head and glanced at the question. A triangle plus a circumscribed circle, and some line segments inside the triangle, and gave the corresponding conditions, and then asked whether the triangle AHD is an isosceles triangle.

But Lin Xiao, whose mind is full of the Hahn-Banach theorem, can't help but start thinking from the Hahn-Banach theorem.

At this time, the little brother next to him added another sentence: "If you can write it in 3 minutes, I will count you as good."

He wanted to see how good at mathematics this person his parents talked about every day was.

If he can't write his junior high school question in 3 minutes, then he will never agree.

However, Lin Xiao didn't listen to what he said at all. At this time, he had completely transformed this problem into the vector space in functional analysis.

He took out the draft paper next to him and started writing directly.

At the same time, he was talking about the process while writing, because he still remembered that he was tutoring others.

"We first convert the Euclidean space where the plane is located into Banach space, and set it as X, because Banach space is a fully normed vector space, that is, its existence 'length'."

The little brother was stunned when he heard Lin Xiao's words, you Sousa?

What Euclidean space, what Banach space?

What is a fully normed vector space?

But it’s not over yet, Lin Xiao continued: “According to Banach’s theorem, if X0 is a subspace of X, then f0 is a bounded linear functional defined on X0, then there must be a bounded linear functional on X. The function f satisfies the following conditions..."

As he spoke, Lin Xiao also wrote on the paper:

[(1) f(x)=f0(x) (for any x∈X0);

(2) ||f||=||f0|| (Table 0 below).

Then ||f0|| (Table 0 below) represents the norm of f0 on X0. 】

"Then convert point A, point B, point C... into points in this space, and construct function f(x)=..."

……

Looking at what Lin Xiao wrote, the little brother was even more confused.

are you kidding me

What the hell are these?

This is just a junior high school question, okay? !

In this way, he watched Lin Xiao's writing become more and more 'scary', he could understand every word, but when they were linked together, he was at a loss besides at a loss?

But this person thought he could keep up with the rhythm, and wrote while talking, without caring about his feelings at all.

till the end--

"So we can know that the function X of the triangle is a linear functional on Y, then all operators are equal, so we can easily know the norm ||T||1=||T||2."

"Because it is a linear operator, it returns to the Euclidean space, that is, AH=HD, that is, the triangle AHD is an isosceles triangle."

【Certificate completed】.

After writing the last two words stroke by stroke, Lin Xiao nodded in satisfaction. As expected of him, the knowledge he just learned can be used to solve problems.

"Do you understand?"

At this time, Lin Xiao remembered that he seemed to be tutoring others, so he couldn't help asking, and then looked at the little brother.

In the end, I saw my little brother staring blankly at himself, thinking about the three ultimate questions of philosophy.

Lin Xiao suddenly came to his senses, why did he use functional analysis to solve this problem?

This is a junior high school geometry problem!

"Uh, sorry about that, I made a mistake, try again."

Lin Xiao hurriedly looked back at the question again, and immediately said: "This question is very simple, first make an auxiliary line, connect BH, BD, DC, and then connect A, B, C, D to point O Get up, and then you..."

Once the auxiliary line is made, it will be easier to solve it.

"Look, didn't we prove that the two sides are equal, the problem is solved, it's quite simple."

After Lin Xiao finished writing, he turned his head to look at the little brother, but he still looked dumbfounded.

He stretched out his hand and shook it in front of his little brother, and shouted, "Zhou Mingyu?"

"Wow!"

As a result, the next moment, the little brother burst into tears because of Lin Xiaoxiu's collapse, which shocked Lin Xiao.