"The current sieving method cannot truly prove Goldbach's conjecture, unless the sieving method continues to be optimized or another method is adopted." In the quieter seats in the ceremony hall of Jingzhou University, Xu Yun and Minter exchanged ideas about Goldbach's conjecture. After the question, I expressed my understanding: "If you break Goldbach's conjecture into two more basic conjectures by creating a number set, perhaps the difficulty of the proof will be reduced."
Mingte, who was opposite him, listened to all the words and was increasingly shocked.
So much so that even his expression was almost unbearable.
When he first heard that Xu Yun was also studying number theory, he only thought that his understanding was limited to the preliminary stage.
After all, as the prover of Hodge's conjecture, his areas of expertise should be algebraic geometry and topology.
It is impossible to still have the energy to study number theory in depth.
So thinking that discussing with Xu Yun would not put him under any pressure, he agreed wholeheartedly.
As a researcher at the Clay Mathematics Institute, he is considered a genius in internationally renowned universities such as Cambridge and Harvard, and his biggest goal in life is to prove the world's mathematical problems.
Perreman proved the Poincaré conjecture. He was sincerely impressed and admired his madness for mathematics.
He was ashamed of himself.
But Hodge's conjecture was proved by a young man who was still in the undergraduate stage, which made him a little unconvinced.
Even after reading the paper, you know the value inside.
For this reason, he took advantage of this report meeting and specifically asked his teacher Griffith to bring him along to participate.
I just want to see the prover of Hodge’s conjecture with my own eyes.
As a result, he didn't expect that Xu Yun would give him such an unexpected surprise when they first met.
Not only does he have a thorough understanding of number theory, he even provides a fifth method to prove Goldbach's conjecture.
Although this is just an idea, it is not yet certain whether it will be useful.
But it is enough to prove that Xu Yun's time studying number theory will definitely not be short, and his level may not be lower than his own.
Goldbach's conjecture is also a difficult problem in world mathematics, but unlike Hodge's conjecture, it belongs to the field of seemingly simple number theory.
This conjecture was originally proposed by Goldbach. Any integer greater than 2 can be written as the sum of three prime numbers. However, since modern mathematics no longer uses the convention that 1 is also a prime number, the modern statement of the conjecture has become Any integer greater than 5 can be written as the sum of three prime numbers.
Scholars who study Goldbach's conjecture know that there are currently several main ways to prove it.
They are idle prime numbers and exception sets, as well as the three-prime number theorem Goldbach's problem of small variables.
The creation of a number set mentioned by Xu Yun now splits Goldbach's conjecture into two more basic conjectures, which is undoubtedly a brand new method.
Even though he was very unconvinced with Xu Yun before, now he had to admit his talent in mathematics.
"I didn't expect that you have such a deep understanding of number theory. You should have started studying it very early, right?" Mingte asked a question with a complicated expression, and then sighed from the bottom of his heart: "Although it was only a short exchange, it also made me happy. I gained a lot.”
Since Xu Yun became interested in number theory, he spent time and energy studying and researching it.
It is impossible not to understand several conjectures in the field of number theory.
The most famous of them are Goldbach's conjecture and twin prime numbers, as well as the Riemann hypothesis that countless people want to prove.
To prove Goldbach's conjecture, the most studied method by mathematicians around the world is to use lazy prime numbers to prove it.
An idle prime number is a positive integer with a small number of prime factors.
If a+b is used to represent a proposition.
Every large even number N can be expressed as A+B, where the number of prime factors of A and B does not exceed a and b respectively.
In this way, Goldbach's conjecture can be written as 1+1.
Progress in this direction is promoted by the screening method.
Among them, the one closest to Goldbach's conjecture is 1+2 proved by domestic academician Chen Jingrun.
Unfortunately, there has been no progress since then.
The creation of several sets that Xu Yun talked about was just a proof idea that he accidentally thought of.
There is no specific calculation process, and I don’t know if it is feasible.
During the exchange with Mingte, I mentioned it casually, but I didn't expect that the other party suddenly seemed to be a different person.
Even my attitude is much better.
Faced with Mingte's question, he didn't think too much and was still used to telling the truth.
“It was after I proved the Hodge conjecture that I became interested in number theory and conducted in-depth research.”
"What?"
"After proving Hodge's conjecture?"
When Mingte heard this, the expression on his face could no longer be tense, and he lost his voice and said something in surprise, his mind was full of question marks.
Although he didn't know when Xu Yun proved the Hodge conjecture, judging from the time of submission to the Annual Journal of Mathematics, it was probably only two months at most.
But if you can understand it to this extent, your mathematical talent can no longer be described as a genius.
It can only be said that it is no wonder that others can prove the Hodge conjecture.
Taking a deep breath to temporarily suppress the huge waves in his heart, he asked the question he wanted to know most in English.
"Are you going to continue to prove difficult mathematical problems in other worlds?"
For mathematicians, being able to prove one of the world's most difficult mathematical problems is enough to go down in history.
If someone can really solve multiple world mathematical problems, he will definitely be the greatest being in the history of mathematics.
Although he did not believe that such a genius could exist, as he came into contact with Xu Yun, this thought seemed to grow out of control.
Xu Yun naturally has no idea of continuing to prove the world's mathematical problems. After all, the random reward extraction cannot be related to the relevant process. He wants to rely on brain overclocking to solve the problem. He does not know how many points and energy capsules will be consumed.
At least what he has left now is far from enough.
Deep learning of number theory is a need for new knowledge, which can give him a sense of pleasure.
Not specifically to prove conjecture.
What's more, what he needs to do most now is to determine the direction of his thesis and successfully complete his graduation defense.
He had no intention of hiding anything on this issue and answered directly to Dr. Minter:
"I will be busy writing my graduation thesis to complete my undergraduate studies, but I don't have the time or energy to solve mathematical problems in other worlds."
"This difficult problem should be left to you, Dr. Minter."
To put it simply, I won’t compete with you for the proof of Goldbach’s conjecture.
However, there is another prerequisite that Xu Yun did not mention, that is, first of all, Minter really has the ability to prove Goldbach's conjecture.
After all, although he is not very interested in proving mathematical problems in other worlds, who can say for sure what will happen in the future? Maybe one day he will be inspired and prove Goldbach's conjecture.
After hearing Xu Yun's words, Mingte felt depressed and complicated at the moment.
Although he is a Ph.D. student in the Department of Mathematics at Harvard University, he is not as good as the undergraduate student in front of him who is busy with his defense, and he is still in the field of number theory, which he is best at.
If I had known earlier, I wouldn't have followed the teacher here.
He regretted it a bit.
Xu Yun didn't know what Dr. Mingte was thinking at this moment. Just when he was about to say something more, he suddenly noticed Wu Zhongping and Professor Griffith from the Clay Mathematics Institute approaching from the corner of his eye. Yuan Chengming, who was originally with them, became Qin Xiangxin and Tang Yanshan.
"headmaster."
"Professor Griffith."
He stood up quickly and greeted Qin Xiangxin and Tang Yanshan politely.
"How was your interaction with Dr. Minter?"
Wu Zhongping seemed to be asking casually, but in fact he was a little worried, afraid that Xu Yun would be made things difficult for Mingte.
Whether he, Qin Xiangxin or Tang Yanshan, they all knew that number theory was Xu Yun's weakness.
I have never studied in depth or consulted professors in this field. If Mingte really deliberately made things difficult for me, I would be somewhat embarrassed about my face.
That's why he brought people here specially, thinking that if something happened, he would find an excuse to send Xu Yun away.
Before Xu Yun could answer, Dr. Mingte, who also stood up next to him, spoke up first.
"Xu Yun has a deep understanding of number theory. Some of what he said made me enlightened. I hope we can continue to communicate if we have the opportunity in the future."
As the words fell, several people, including Wu Zhongping, had some doubts in their hearts.
Number theory is an elective course in the Mathematics Department of Peking University, and none of them knew that Xu Yun had studied it systematically.
How to teach an overseas Ph.D. studying number theory in this situation.
"Did the doctor say this on purpose?"
This guess came to mind, and I immediately felt more favorable towards this overseas doctor.
"You are really the most gifted mathematical genius I have ever seen." Griffith knew his student's character well, allowing him to take the initiative to praise others in the fields he was good at, which shows that Xu Yun is indeed very knowledgeable about number theory and loves talents. The heart sprouted and couldn't help but praise: "I didn't expect that in addition to algebraic geometry and topology, you also have a good understanding of the field of number theory."
"I also learned a lot from Dr. Minter. Number theory is far more profound than I imagined."
Xu Yun responded humbly to Griffith, and then watched him and Dr. Minter return to the room arranged by Beijing University to rest.
Among the hundreds of people who came to attend the report meeting, many of them were half-buried in age and basically went to bed very early.
Therefore, the party before the lecture did not last long, and the ceremony hall soon became quiet.
Everyone is looking forward to being in the best condition tomorrow to welcome this grand event that belongs to the entire mathematical community.
Originally, Wu Zhongping and the others wanted to ask Xu Yun about number theory, but in order to allow him to perform normally at the report meeting tomorrow, they finally suppressed the question temporarily.
…
The next day.
Around nine o'clock in the morning.
The largest academic lecture hall at Jingzhou University is already full of people, and anyone you can find is a well-known scholar in the field of mathematics.
Under the lecture hall, a large number of cameras were set up to ensure the simultaneous progress of the online live broadcast.
In addition to being open on major website video platforms, the live broadcast entrance will also be broadcast in real time on TV stations.
It is even reported globally on international channels.
It can be said that this is the first time such a large-scale report meeting has been held since the establishment of the domestic mathematics community.
Before the report meeting officially started, there was already a heated discussion on the Internet.
Although most people couldn't understand it at all, thinking that it was a world-wide mathematical problem proven by Chinese people, their enthusiasm for watching the live broadcast, driven by the pride derived from blood, did not diminish at all.
(End of chapter)
