From Almighty Scholar to Chief Scientist

Chapter 95 What kind of image is Lin Xiao?
For Professor Sarnak, reading papers is a very common thing. After all, as the editor-in-chief of "Annual Mathematics", there are many papers that need to be reviewed by him.

Especially those submissions that have the potential to be published in the "Annual Journal of Mathematics", whether they are in line with his research field or not, he has read many of them.

So now let him read Lin Xiao's report, and he found the right person, especially the results in the field of number theory.

He won the Wolf Prize in Mathematics in the first place because of his contributions in the field of number theory.

Similarly, as Professor Pompieri said, there is no mathematician who will not be interested in these prime number problems. After all, they seem so simple and clear, aren’t they just positive integers one by one, although they are solving problems In the process of , it is indispensable to use all kinds of strange shapes and even complicated mathematical symbols, and sometimes you have to use the root sign to make it no longer an integer, but it looks very simple anyway!

Otherwise, why are minkes keen to solve Goldbach's conjecture instead of Riemann's conjecture?
Because they can understand Goldbach's conjecture with the knowledge they have acquired in their nine-year compulsory education, so they rushed forward with courage.

As for the Riemann conjecture, they probably still have to ask what the ζ function is, not to mention that it also involves the complex plane, complex analysis, etc., which makes them do it, even if they want to find a place to start, I am afraid they still have to do it. They have to learn complex analysis, and before learning complex analysis, they have to learn mathematical analysis, but after learning this, they probably know how ignorant their thoughts are.

All in all, the prime number problem looks neat, and so do the Mersenne prime numbers, so much so that Professor Sarnak once worked on these things.

However, in Lin Xiao’s paper, the problem of Mersenne primes is solved in the last ten pages, and the first 60 pages mainly discuss the combination of modular form theory and group theory to realize the transformation of polynomials.

So Professor Sanak is looking at this part now.

"Hmm... the previous transformation seems interesting. It seems to be the method in his paper? Well, it has been sorted out."

Seeing this, he shook his head helplessly. In fact, this is enough. Lin Xiao can already use the previous part as a report, and then he will give a speech at the conference. This is what Professor Sanak thought Lin Xiao would do at the beginning. .

However, we have only reached page No.13 now, and there are still a lot of them behind.

This Lin Xiao, what kind of showmanship did he do...

He finally knew why Professor Viana asked him to read Lin Xiao's report. Probably, Professor Viana also felt that Lin Xiao didn't follow the routine, so he asked him, the instigator, to see how to deal with it.

Shaking his head slightly, what else can I do, I can only continue to watch.

But he still hopes that he can receive the last 'happy', no matter what, it is also the young man he fancy.

Then, he continued to look down.

Soon, he saw a line of formula.

【tr(ρf, λ(Frobp))=C(p, f)...det(ρf, λ(Frobp))=Ψ(p)N(p)^k01...】

"This step... is interesting."

He looked down again.

【ρf, λ:=ρf, λ(mod λ):GF→GL2(Fλ)...】

The more he looked, the closer his eyes moved to the screen, trying to see himself more clearly.

Because, with the transformation around here, his thinking also followed up, and it seemed that there were two strings in his mind, which were suddenly connected together, and then played.

This step made him also feel amazed!

"It's really unbelievable that this method can still be used, or...too bold!"

As he read silently, his head shook with emotion.

"This young man's thinking is really different from that of an old guy like me."

Suddenly remembered something, he pulled the draft paper from the side and started to calculate.

In this way, time passed slowly. In the office, Professor Sanak's other students looked at Professor Sanak's appearance, and they didn't know why he was so emotional.

Didn't he have this kind of situation when he was reviewing manuscripts before?

In the name of helping the professor make coffee, a graduate student went up to pick up Sanak's coffee cup, and then glanced at the computer. After looking at it for a while, he was also at a loss. Which big guy's paper is this? ?

This seems to be number theory, but it's not like number theory. There are some homomorphic group structures in it, and there seems to be a bit of modular form theory in it. Could it be someone who studies the Langlands program?
The Princeton University mathematics doctoral student gave up thinking and chose to make coffee for the professor honestly.

In this way, time passed slowly.

The paper of more than 70 pages is of course very long. Although the first dozen pages are relatively easy to understand and can be read quickly, the middle 40 pages are not so easy, because a new mathematical method has been involved. So Professor Sanak has to be serious about it.

The east coast wind blew from daytime to evening, until the sun disappeared west of Princeton, a city full of rural scenery, in the office, Professor Sarnak finally raised his head.

"Probably, Gauss was also so amazing at the beginning..."

He sighed slightly. From this paper, he saw the thoughts of great mathematicians burst out in it, as if the truth was conceived in it.

For all famous scientists in history, the most important achievements in their lives were made between the ages of 20 and 40, such as Einstein's theory of relativity, Newton's calculus, the law of universal gravitation and so on.

And this Lin Xiao, who is only 18 years old now, has already created such an excellent mathematical theory and put an end to the problem of the distribution of Mersenne prime numbers.

Since Euclid, the father of geometry, began to study this problem two thousand and three hundred years ago, until now I don’t know how many great mathematicians have continued to try to achieve breakthroughs in the extremely simple form of 300^p-2. , until now, the final result has finally been completed in the hands of this young man.

If it is said that this is Lin Xiao's peak period, Professor Sanak naturally does not believe it.

If he used the normal distribution image as an example, he believed that Lin Xiao's state at this time was somewhere on the left side of the image, and there was still a long distance from the highest position.

However, this is just what he thinks. As for whether Lin Xiao is really a normal distribution image, or y=x (x>0), it is unknown.

(End of this chapter)