From all-round academic master to chief scientist

For Professor Sanak, reading papers is a very common thing. After all, as the editor-in-chief of the "Annals of Mathematics", he needs to review many papers.

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

So now he is looking for the right person to read Lin Xiao's report, especially for this kind of achievement in the field of number theory.

When he won the Wolf Prize in Mathematics, it was related to his contribution to the field of number theory.

Similarly, as Professor Pompieri said, no mathematician would not be interested in these prime number problems. After all, they seem so simple and clear. They are just positive integers. Although they are solving problems In the process, it is inevitable to use all kinds of strange and even complicated mathematical symbols. Sometimes you have to use the radical sign to make it no longer an integer, but it always looks very simple!

Otherwise, why are civil scientists keen on solving Goldbach's conjecture instead of Riemann's conjecture?

Because they could understand Goldbach's conjecture with the knowledge gained from their nine-year compulsory education, they rushed forward with courage.

As for the Riemann Hypothesis, they probably have to ask what the ζ function is, not to mention that it also involves the complex plane, complex analysis and the like. If they are left to do it, even if they want to find a place to start, I am afraid it will still be difficult. 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 previous ideas were.

All in all, the prime number problem seemed neat, and so did the Mersenne primes, so much so that Professor Sarnak had also studied these things.

However, in Lin Xiao's paper, the problem of Mersenne prime numbers is solved in the last ten pages. The first sixty or so pages mainly discuss the combination of modular formal theory and group theory to realize the transformation of polynomials.

So this is what Professor Sarnak is looking at now.

"Hmm... the previous transformation seems a bit 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 give a speech at the conference. This is what Professor Sanak originally thought Lin Xiao was going to do. .

However, we have only reached the thirteenth page now, and there are still a lot more to come.

What kind of tricks did this Lin Xiao pull out...

He finally understood why Professor Viana came to him to read Lin Xiao's report. Probably Professor Viana also felt that Lin Xiao did not play according to the routine, so he came to him, the initiator, to see how to deal with it.

Shaking his head gently, what else could he do? I could only continue watching.

But he still hopes that he can receive the last piece of 'joy'. No matter what, he is the young man he likes.

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 a bit interesting."

He looked down again.

[ρf, λ:=ρf, λ(mod λ):GF→GL2(Fλ)...]

The more he looked, the closer his eyes came to the screen, hoping to see more clearly.

Because, with the changes around here, his thinking followed suit, and it seemed as if there were two strings in his mind that suddenly connected together and started playing.

This step also made him feel amazed!

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

He recited silently, his head shaking as if with emotion.

"This young man's ideas are really different from those of an old guy like me."

Suddenly remembering something, he pulled the scratch paper from the side and started to calculate.

In this way, time passed slowly. In the office, Professor Sarnak's other students looked at Professor Sarnak, not knowing why he was so emotional.

Hasn't this happened to him before when reviewing manuscripts?

In the name of helping the professor make coffee, a graduate student walked up and picked up Sarnak's coffee cup, and then took a look at the computer. After looking at it for a while, he was at a loss. Whose thesis was this? ?

This seems to be number theory, but it doesn't look 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 some expert in the Langlands program?

This PhD student in mathematics at Princeton University gave up thinking and chose to make coffee for the professor honestly.

In this way, time passed slowly.

A paper of more than seventy pages is of course very long. Although the first ten pages are easier to understand and can be read quickly, the middle forty pages are not so easy because it involves a new kind of mathematics. method, so Professor Sarnak must also treat it rigorously.

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

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

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

All famous scientists in history made their most important achievements between the ages of 20 and 40, such as Einstein's theory of relativity, Newton's calculus, the law of universal gravitation, etc.

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 Mersenne's distribution law of prime numbers.

Since Euclid, the father of geometry, began to study this problem 2,300 years ago, up to now, countless great mathematicians have continued to try to realize it on the extremely simple form of 2^p-1. The breakthrough, until now, has finally been completed in the hands of this eighteen-year-old boy.

If you say that this is Lin Xiao's peak period, Professor Sarnak naturally doesn't believe it.

In terms of a normal distribution image, he believed that Lin Xiao's current state was somewhere on the left side of the image, still a long way from the highest position.

However, this is just what he thinks. It is unknown whether Lin Xiao really is a normal distribution image or y=x(x\u003e0).