August 10th.
Li Mu, who had already boarded the plane, was quietly waiting to take off.
Suddenly, a message popped up on the phone.
Sent by Yun Rongshang.
It's a picture of an airport.
Yun Rongshang: [I have already boarded the plane and will leave soon]
Li Mu also took a photo of the airport outside the window and sent it: [(photo.jpg) I was also on the plane. 】
Yun Rongshang: [Hey, where are you going? 】
Li Mu: [Going to Beijing to attend a mathematics conference]
Yun Rongshang: [You are coming to Beijing? Damn it, I'm at Beijing International Airport right now, but the plane is about to take off, otherwise I'd still be able to see him for the last time. 】
Li Mu: [See you again next year. 】
Yun Rongshang: [That's right. You must tell me when you come here next year. Senior sister, I will explore the way here for you first. 】
Li Mu: [Um... Is there a possibility that you will call me senior by then? 】
Yun Rongshang: [? ? ? Why? 】
Li Mu: [Because I studied for a direct Ph.D. and you studied for a master's degree. In a sense, I am a doctor. So I am older than you in terms of degree, so you have to call me senior]
Yun Rongshang: [Junior, Junior, Junior, Junior]
Li Mu: [Middle finger.jpg]
Yun Rongshang: [No more 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, Li Mu's lips curled up slightly.
Recalling Yun Rongshang's reaction when he told Yun Rongshang that he was going to Oxford that day at the amusement park, he couldn't help but laugh.
Of course, no matter what, if you can be with someone you know in a foreign country, it is indeed a lucky thing.
Shaking his head and thinking no more, his mind returned to the twin prime conjecture.
The inspiration he got from the pattern of a cup last night gave him a glimpse of the possibility 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 only contains five numbers 1, 2, 3, 4, and 5, and in this In finite fields, 4+3=2.
It looks similar to base, but the difference is still 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 with the characteristic p, then the number of elements in F is p^n..."
Li Mu thought in his mind.
"In this way, the prime numbers can be anchored..."
"That's right, a prime polynomial!"
This term flashed through his mind, and Li Mu's eyes suddenly lit up.
The flash of inspiration made him unable to help but write.
He immediately took out the Parker 51 and scratch paper from his bag, opened the small table, and began to write according to the ideas in his mind.
At such moments, his thoughts are like a spring of water, and he can escape from any place.
There were a lot of ideas in his mind in an instant, and with the ability to multi-task, he started to deduce from three angles at the same time, and his hands were habitually deriving from the fourth angle.
When thinking about a problem, he always feels awkward if he doesn't write something on his hand.
Just like that, after a while, the plane was about to take off, and the flight attendant came to his side and reminded: "Sir, please put away the tray table, we are about to take off."
"Oh well."
Li Mu came to his senses quickly this time, nodded and put away the pen.
But the corners of his mouth were slightly raised.
Just a while of derivation has once again allowed him to find the right path.
"On the basis of finite fields and prime polynomials, it seems that the circle method has become difficult to integrate, but if the circle method and finite fields are combined first, it will become relatively easier."
Li Mu was thinking in his heart as he put away his own small table.
The circle method is the most commonly used technique in modern number theory and 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 is holding such an idea.
It's just that his idea is more difficult to realize.
Combining the circle method with finite fields has great technical requirements.
Of course, this is relative to others, but for Li Mu, it doesn't seem to be difficult.
He even had relevant deductions in his mind.
This idea of combining the two methods also made him feel a little emotional.
Although mathematics now has been refined into many parts, there are many related to algebra alone, such as algebraic geometry, algebraic topology, algebraic number theory, etc.
But there seems to be an invisible line between these branches of mathematics that connects them, and there seems to be the possibility of unification.
Just like the grand unified theory in mathematics: the Langlands Programme, this is its purpose.
The world of physics seeks to unify the four fundamental forces in the hope of explaining all physical phenomena.
The Langlands Program attempted to connect number theory, algebraic geometry, and group representation theory to unify these three important branches of mathematics.
This issue is of great significance to the mathematical community, so since the Langlands Program was proposed, many mathematicians have stepped forward and made important contributions to this issue, and have won the Fields Medal for this.
But how long will it take before the Langlands Program is realized?
Li Mu didn't know.
But if his method can be successful, it can be regarded as a help in the realization of Langlands Program.
…
The plane flew across the sky and finally landed at Shangjing International Airport.
Dragging his suitcase, Li Mu walked out of the airport, and then saw Lin Yao standing at the pick-up gate, looking around. After finally seeing him, he smiled and waved to him.
"Professor Lin."
Li Mu walked up and said hello.
Lin Yao was also invited to this Chinese mathematics academic summit and had to give a report, so he also flew from Shanghai to Beijing today.
"Well, let's go. The Mathematical Society has contracted a pick-up and drop-off vehicle. Let's just wait in the car."
Lin Yao didn't waste any time and took Li Mu directly to the pick-up point.
The contracted vehicle was a commercial van, with many people already sitting on it.
All are domestic mathematics scholars.
It's just that after Li Mu got in the car, he felt a little strange.
As for where the ambiguity lies...
He felt it carefully.
Well……
It seems like he is just a young man?
(End of chapter)
