Ultimate Scholar

August 10th.

Li Mu, who had already boarded the plane, waited quietly for takeoff.

Suddenly, a message popped up on the phone.

It was sent by Yun Rongshang.

It's a picture of an airport.

Yun Rongshang: [I'm already on the plane, I'm leaving soon]

Li Mu also took a photo of the airport outside the window and sent it: [(photo.jpg) I am also on the plane. 】

Yun Rongshang: [Hey, where are you going? 】

Li Mu: [Go to Beijing to attend a mathematics conference]

Yun Rongshang: [It means you are coming to Beijing? Damn it, I'm at the Shanghai International Airport right now, but the plane is about to take off, otherwise I'll see you for the last time. 】

Li Mu: 【See you again next year. 】

Yun Rongshang: [That's right, after you come here next year, you must tell me, senior sister, I will explore the way here for you first. 】

Li Mu: [Uh... Is there a possibility that you will call me senior by then? 】

Yun Rongshang: [? ? ? Why? 】

Li Mu: [Because I'm a direct Ph.D. student, and you are a Master's student. In a sense, I am a Ph.D., so I am older than you in terms of degree, so you have to call me senior]

Yun Rongshang: [Student, Junior, Junior, Junior]

Li Mu: [vertical middle finger.jpg]

Yun Rongshang: [Stop talking, my plane is about to take off, see you in half a year]

Li Mu: 【See you in half a year】

Putting down the phone, the corners of Li Mu's mouth twitched slightly.

Thinking back to Yun Rongshang's reaction after telling Yun Rongshang that he was going to Oxford that day in the amusement park, he couldn't help laughing.

Of course, no matter what, in a foreign country, if you can have someone you know together, it is indeed a lucky thing.

Shaking his head, he didn't think about it anymore, and his thinking returned to the twin prime number conjecture.

Inspired by the pattern of a cup last night, he saw the dawn of proving the twin prime conjecture.

A finite field, also known as a Galois field, is a field that contains only a limited number of elements. For example, it can be simply understood that this field contains only five numbers, 1, 2, 3, 4, and 5, and in this In finite fields, 4+3=2.

It looks similar to hexadecimal, but the difference is quite big, because no matter how many times it loops, it will eventually loop through the elements contained in this field.

"The characteristic number of a finite field must be a certain prime number p, so the prime field it contains is isomorphic to Zp. If F is a finite field characterized by p, then the number of elements in F is p^n..."

Li Mu thought in his heart.

"In this way, prime numbers can be anchored..."

"By the way, prime polynomials!"

This term flashed through his mind, and Li Mu's eyes suddenly lit up.

With the flash of inspiration, he couldn't help but want to start writing.

As soon as he said it, he immediately took out the Parker 51 and the draft paper from his bag, opened the small table, and began to write according to the thoughts in his mind.

At such moments, his thoughts are like a spring of thousands of dendrobiums, which can come out of nowhere.

In an instant, a lot of ideas appeared in his mind, and under the ability of multitasking, he started to deduce from three angles at the same time, while his hands habitually deduced from the fourth angle.

When thinking about a problem, he always feels awkward if he doesn't write something on his hand.

In this way, after a while, the plane was about to take off, and the stewardess also came to his side and reminded: "Sir, please put away the small table, we are about to take off."

"Oh well."

Li Mu recovered quickly this time, nodded, and put away the pen.

It's just that the corners of his mouth are slightly raised.

After a while of derivation, he has once again found the right path.

"On the basis of finite fields and prime polynomials, it seems that the circular method has become difficult to incorporate, but if the combination of the circular method and the finite field is first realized, it will be relatively easier."

While putting away his own small table, Li Mu was also thinking in his heart.

The circle method is the most commonly used technique in modern number theory, and it is very good at dealing with prime numbers.

Just like its application in Goldbach's conjecture is very extensive.

Mathematicians are constantly changing the circle method to solve these problems related to prime numbers.

And now, he also has such an idea.

It's just that his idea is more difficult to realize.

Combining circle method and finite field has great technical requirements.

Of course, this is relative to others, but for Li Mu, it doesn't seem to be difficult.

Even in his mind, there are related derivations.

This idea of ​​combining the two methods also made him feel a little emotional.

Although the current mathematics has been refined into many parts, there are many related to algebra, such as algebraic geometry, algebraic topology, algebraic number theory and so on.

But there also seems to be an invisible line between these branches of mathematics, which connects them, and seems to have the possibility of moving towards unity.

It's like the grand unified theory in mathematics: the Langlands program, and its purpose is just like this.

The physics community seeks to unify the four fundamental forces, hoping to explain all physical phenomena in this way.

The Langlands Program attempts to link number theory, algebraic geometry, and group representation theory to achieve the unification of these three important branches of mathematics.

This problem is of great significance to the mathematics community, so since the Langlands Program was put forward, many mathematicians have gone on and made important contributions to it, and won the Fields Medal for it.

But how long until the realization of the Langlands program?

Li Mu didn't know.

But if his method can be successful, it can be regarded as a help in the realization of the Langlands program.

...

The plane flew across the sky and finally landed at Shangjing International Airport.

Dragging the suitcase, Li Mu walked out of the airport, and then saw Lin Yao standing at the pick-up gate, looking around, finally saw him, and waved to him with a smile.

"Professor Lin."

Li Mu walked up and greeted him.

Lin Yao was also invited to this Huaguo Mathematics Academic Summit, and he also had to give a report, so he also flew from Shanghai to Beijing today.

"Well, let's go, the Mathematics Association has contracted a pick-up vehicle, let's go to the car and wait."

Lin Yao didn't talk nonsense, and directly took Li Mu to the boarding point.

The contracted vehicle is a commercial van, and there are already many people sitting on it.

All are domestic mathematicians.

It's just that, after Li Mu got into the car, he felt a little awkward.

As for where the abruptness lies...

He felt it carefully.

Well……

As if he was a young man?