I just want to be a quiet scholar

Chapter 48
Time is not sympathetic, it flies slowly when waiting for a salary, and it flies very fast during exams.

Shen Qi did not make any effective action within an hour, leaving him not much time.

Is it over, is it all over?

Is this my limit?

No, this should not be the fate of a scholar.

I have failed many subjects.

I also played games all night.

I used to have the king rank.

In a blink of an eye, he became a scumbag.

I have been disappointed, lost all direction.

Until you see math, that's the only answer.

Shen Qi thought a lot in this hour, and when he was thinking about the past, it showed that he really had nothing to do.

What is the source of this array of numbers?Looking at the form, it looks like a group, but I have never seen such a strange group, full of magic.Could it be a fake group?It seems that it is not a group at all?

After racking my brains to search in the brain knowledge base, the only response to Shen Qi... The knowledge point you called is not in the service area.

There is no way to do this. No matter how strong the brain is, if there is a blind spot in knowledge, it will give up treatment.

Unless you create a whole new set of theory yourself, this is the only way.

But Shen Qi currently does not have the level of a master of his own kind.

"Perhaps I have scored full marks in the previous exams, and the journey has been too smooth. How do you say that, when the heavens will entrust the people with great responsibility, they must first suffer their will and win their sisters."

Shen Qi, who was in the predicament, was thinking wildly, thinking about it, he laughed himself, I am so talented, is this a level 1 language proficiency?
"Mr. Tian, ​​you can't save me this time. The sexage system is useless here."

"Mr. Liu, the algebraic knowledge you talked about is too exaggerated. This time IMO, I didn't use it at all. I can get to this point by my own exploration."

"Mr. Zhang, I haven't seen you for a long time. When I was in the fourth grade of mathematics, you stopped giving me a small stove, saying that there was nothing to teach me."

Scenes from the past are played in Shen Qi's mind in a fragmented way. The experience in the past few months is like a dream. If you can get the IMO world number one, it will be the most beautiful dream.

"Mr. Zhang, I went to your office a few months ago, and you asked me where I learned from myself."

"I said, I learned about the Cayley transition matrix and the Weierstrass quadratic form, and it was a bit of a pretense at the time, and I didn't know much at that time."

"Then you're instantly stunned."

"I can't forget this scene. From now on, I will start the road of being a scholar."

"Haha, time flies so fast, it's the third year of high school in a blink of an eye."

"Hehe...Fuck!"

Shen Qi was shocked, and he suddenly caught a glimpse of inspiration, which was fleeting and elusive.

This kind of feeling seems familiar. The finale of the National Digital Federation of China at the beginning of this month was the inspiration that saved Shen Qi. Teacher Tian saved Shen Qi. Irrational number, show to the national final champion.

"Go back, go back."

Shen Qi replayed the random thoughts just now in his mind.

"Mr. Zhang, I went to your office a few months ago, and you asked me where I learned from myself."

"I said, I learned about the Cayley transition matrix and the Weierstrass quadratic."

……

"Although mathematics may appear to be nothing more than a language or tool, most of its vivid concepts can provide keys to new areas of thought."

"Determinants and matrices are completely reforms in mathematical language. Shen Qi, you must deeply understand this before you can make a difference in algebra."

……

Shen Qi smiled, very happy, there is no way out of the sky.

Last time Teacher Tian saved him, this time Teacher Zhang saved him.

In fact, what Shen Qi should thank the most is himself. He never chose to give up in difficult situations. Mathematics often requires persistence and even madness. He and his final stubbornness saved him.

The Kayleigh transition matrix and matrix theory, which were used for coercion, finally came into play at the most critical moment.

No matter what kind of monster, monster, or group this digital array is, it can't escape the mirror in my hand, the Matrix.

The tool for comprehending or translating group theory is the matrix.

Array of numbers according to the title:

1 1 =
196884 = 196883 + 1
21493760 = 21296876 + 196883 + 1
864299970=842609326+21296876+2*196883+2*1
……

Shen Qi wrote a matrix homomorphism:
A(gi*gj)=A(gi)*A(gj)

Expand it into a matrix representation:
|Ag-0|
|Ai-0|
|0-Aj|
……

This matrix language looks complicated, but its meaning is very simple and straightforward, that is, a matrix representation of a group G is a homomorphic mapping of an element g of G to a set of fixed-order nonsingular square matrices A(g).

To put it more simply, a group is a set of complex ciphers that are very difficult to understand, and a matrix is ​​one of the mothers of deciphering ciphers.

The only requirement is that you must be proficient in various decoding methods, the more the better.

If the array of numbers can be described by a matrix, then it is some kind of group, otherwise it is not.

When Shen Qi expressed this array of numbers in a regular permutation method, he was very surprised: "MMP...Monster-Group...It's really a monster, a monster group!"

What are the monsters?

That is, the largest scattered simple group.

Compared with other groups, the demon group is very young, about 40 years old.

This group is quite scary, so it was named Monster-Group by mathematicians.

It is difficult for ordinary people to play with the demon group, and when they play, they drive themselves crazy and break it.

The British mathematician Borchels made a significant contribution to the theory of demons. He proved the "moonlight conjecture of demons", an existence that is very magical and powerful just by its name.Bochelds won the Fields Medal for this great achievement.

Demon group, if you want to play it, you need at least a Ph.D. in mathematics at the entry level.

Why does this kind of question appear on the IMO test paper?
Are there any middle school students in the world who can handle it?
of course not.

No need to get it done either.

Shen Qi's understanding is that for this demon group, it is OK to give two different mathematical explanations.

Deciphering the swarm and describing the swarm are two different things.

No one can break Goldbach's conjecture, but many people can describe it: any even number greater than 2 can be written as the sum of two prime numbers.

Similarly, what Shen Qi wants to do is the latter, but not in words, but in pure mathematical language.

He used two matrix languages ​​to

1 1 =
196884 = 196883 + 1
21493760 = 21296876 + 196883 + 1
864299970=842609326+21296876+2*196883+2*1
……

It's enough to express clearly what it is, no need to crack it.

This question examines the knowledge and the skillful use of matrices.

We all know that a group can be represented by many matrices because the order of the matrix can be changed.

"First, let's send the Gloria Transformation Matrix." Shen Qi took out Gloria, the founder of the matrix theory, and used the Gloria Turning Matrix to express the first explanation of the demon group.

"One more round of Jordan Standard Matrix."

Soon, Shen Qi wrote two different matrix expressions.

Seeing that there was still time, he made another serve, the third one being the Hermite Matrix.

"If three rounds are not enough, then three more rounds!"

Shen Qisha's personality started to click, and he successively wrote the Klein abstract group matrix, the Weber prime field matrix, and the Henzel invertible element matrix.

Six out!
Made six rounds in more than an hour!

"My body is not hollowed out. If six rounds are not enough, then six more rounds!"

Shen Qi had never been so happy before, a kind of happy after a catastrophe.

Jingle Bell.

Then the bell rang.

The 4.5-hour exam time has come.

"Six rounds, only six rounds... It's a pity." Shen Qi ran out of time, he only wrote six matrix languages, a little annoyed.

After handing in the papers, Shen Qi seemed to be full of confidence when he saw the Russian players and the Indian-American players walking away happily together.

"There are many masters in the world, and I'm not the only one who can do this." Shen Qi devoted his life to learning in this IMO. What kind of results can be achieved depends on fate.

The marking work started in the afternoon of the same day and continued until the early morning of the next day.

Professor Wiles, the leader of the judging panel, is 60 years old and still insists on working.

Unable to remember how many cups of coffee were refilled, Professor Wiles was drowsy.

There are four exam papers in front of him, all with a perfect score of 42, from four different countries, Russia, the United States, South Korea, and China.

After hesitating for a long time, Professor Wiles finally made up his mind. He approved a "+42" after 1 in one of the full-mark exam papers.

For the last question, the other three full scorers all used two methods to give mathematical explanations.

And the player of "42+1" used six kinds, which is exactly equal to the sum of the other three players.

The "42+1" player is from China, and the English spelling of his name is Shen-Qi.

The first player with 42+1 points in IMO history was born, his name is Shen Qi.

(End of this chapter)