Time passed quietly, and what everyone probably didn't expect was that the influence of this major event in the mathematics world continued to expand.
It has even surpassed Academic Circle and affected the international political circles.
Even politicians from various countries have expressed great concern about this matter.
For example, in the United States, their president personally came to the Mathematics Department in Princeton University and met with many scholars in Prime Pioneer Program. He also expressed condolences to them and proposed that the U. S. government is willing to provide them with considerable conveniences to help them conduct mathematical research without any worries in the process of trying to challenge Riemann Hypothesis.
Of course, the president has made no secret of his purpose.
In his impromptu speech at Princeton, he directly stated. "I have always insisted on a view that our United States is the country with the most geniuses in the world, and it is also the country with the greatest scientific research potential in the world. No country, no one, or anyone can match our scientists!"
"Especially when our scientists come together, no one in the world has more potential than us!"
"This reminds me of the great scientists who secretly conducted atomic bomb research at Los Alamos, Oppenheimer, Fermi, etc., as well as the scientists who are now trying to build our own nuclear fusion reactor at Utah. Undoubtedly, they are all so great that I cry every time I think of these things."
When he said this, the president acted as if he was in tears, wiped his eyes, and looked very moved.
However, he then cheered up and said very impassionedly, "So, now, I also believe that the mathematicians of Prime Pioneer Program can successfully complete their ultimate goal and completely solve the problem of Riemann Hypothesis."
"As for that Xiao Yi, after all, he is just one person, and he will definitely lose!"
"We not only have the smartest people, but also the most talented team. Any mathematical problem is just a simple small problem."
"So, let us fight! fight! fight!"
After all, he was like the world-famous painting that was photographed after the failed assassination attempt, waving his fist and expressing his belief to the people present.
Mr. President's words are indeed quite inspiring. When relevant news broke, they still attracted praise from quite a few "Wolf Warriors" in the United States.
After all, during this period of time, because of things related to nuclear fusion, there has been a saying in their country that their scientific potential is not as good as before, and they are even facing the possibility of being surpassed by China.
Therefore, the president is probably doing this to boost the scientific research atmosphere in their country, hoping to strengthen people's confidence in this aspect.
However, as the president is a comedian, he still has a lot of fun. For example, when the president was delivering a speech on video, the expressions of the many mathematicians below almost seemed as if they were being penetrated by magic sounds and could not hear a bit. Probably in their eyes, this was a group of top mathematicians, listening to a "monkey" who did not understand mathematics at all, encouraging them to solve Riemann Hypothesis.
Especially the expression of Terence Tao, which was completely disgusting, made many netizens burst into laughter.
Terence Tao himself has no dealings with this Mr. President, and now being forced to listen to his speech is already a very uncomfortable thing, let alone listening to this kind of thing.
Netizens directly added emoticons to him: Stop talking, stop talking.
And Terence Tao turned around and started complaining directly on the Internet.
[I really don't understand why this guy insists on paying attention to such a thing. This is our own business in the mathematics community, but he wants to elevate this matter to a political level. This is simply an insult to our mathematics!
Now I even kind of expect Xiao Yi to succeed in advance and then slap this guy in the face!
Of course, considering this is Riemann Hypothesis, I won't let it go, nor will any of us, come on! Xiao Yi, now we know that your paper is your response, so we will do our best to make this challenge more epic!]
"Well... this guy still has a young mentality."
Xiao Yi naturally saw Terence Tao's remarks and couldn't help but sigh.
As of this year, Terence Tao is already 52 years old. He is already an old man, but his mentality has always been young.
Looking back at himself, it may be because as the level of Ruthless Continuous Study BUFF gets higher and higher, his mentality becomes more and more rational, which makes him feel more and more like an older person.
"Perhaps sometimes, I should also find some young people's things to do?"
Xiao Yi laughed at himself.
At this time, Wang Hao, who was next to him, said, "Perhaps, you can try to fall in love? Isn't falling in love just what young people do."
Xiao Yi's brows suddenly raised, he turned to look at Wang Hao, and asked, "If that's not the case for young people falling in love, wouldn't it be called falling in love?"
Wang Hao said with a smile, "If it's not a young person's love affair... I think it's probably a love affair for the purpose of carrying on the family line."
Xiao Yi smiled and said, "If I were in love, then I would most likely be in love just to carry on the family line. Otherwise, in my current situation, do you think I really have time to enjoy the experience of young people falling in love?"
Wang Hao spread his hands and said, "If you want to take time off to fall in love, I think the leaders will agree."
Xiao Yi immediately narrowed his eyes and looked at Wang Hao, and said, "Don't tell me, which leaders have you also received tasks from, to persuade me to get married or something?"
Wang Hao immediately waved his hands and said, "No, absolutely not! I am really just thinking about you."
"What's your relationship with Wang Li?"
Xiao Yi asked again.
"Uh..." Wang Hao couldn't laugh or cry, "Brother Li and I really have nothing to do with each other. As you know, Brother Li's hometown is from Qinxi, and I am from Hui Province."
"Brother Li has been called." Xiao Yi waved his hand directly. "Then don't say anything. Even if you two didn't have a relationship before, you have a relationship now."
Wang Hao shrugged helplessly.
Just kidding, one is Xiao Yi's guard and the other is his assistant, it's hard not to recognize them!
Xiao Yi didn't say anything more, lowered his head, looked at the pile of draft paper on the desk again, and continued his research on Riemann Hypothesis.
But for now, his main research focus is on the development of the Elliptic Inverse Analytic Continuation method.
The more he researched, the more he discovered that this method he accidentally created had many possibilities.
Starting from the elliptical angle, it radiates out and gradually covers quite a lot of areas.
Whether it is number theory, Algebraic Geometry, Representation Theory, modular form, or further refinement to various Automorphic Forms, Dirichlet L-functions, etc., you can find the corresponding place.
So much so that the direction he is really exploring now is no longer Riemann Hypothesis, but Langlands Program.
Langlands Program, not geometry Langlands Program.
Moreover, what he is involved in now is not the superficial level of Langlands Program, but directly related to the most important conjecture of Langlands Program, the functority conjecture.
The functority conjecture is an important prerequisite for the realization of Langlands Program. The main reason is that it has played a huge role in the field of Representation Theory, as well as in number theory and geometry.
In Representation Theory, it provides a unified framework to understand the relationship between the representations of different groups; in number theory, it links automorphic representations with many important number theory objects, such as L-functions, Galois representation, etc.; in geometry, it inspires many profound thoughts and ideas, such as the development of geometry Langlands Program, thanks to the inspiration brought by the functority conjecture.
Once the functority conjecture can be proven, it will be of great help to the realization of Langlands Program.
However, judging from the current research status, it is still far away to prove the functority conjecture. Judging from the current results of Xiao Yi, what he is most likely to complete is Artin Conjecture.
Artin Conjecture is a typical example of the functority conjecture.
If Artin Conjecture can be proved, it will bring great help to the proof of functority conjecture.
However, now Xiao Yi is more concerned about the role of proving Artin Conjecture in proving Riemann Hypothesis.
Xiao Yi A simple derivation on the scratch paper, and finally it is easy to get a relationship.
"Well... to put it simply, before, because the classic Riemann Hypothesis does not correspond to any kind of Galois representation, even if Artin Conjecture is proved, it will not be of much help in proving the classic Riemann Hypothesis. Instead, it will be very helpful in proving the Generalized Riemann Hypothesis of the Artin L-function."
"But just hearing the name is helpful."
Xiao Yi smiled.
Generalized Riemann Hypothesis refers to various promotion forms of Riemann Hypothesis. There are many types, and Riemann Hypothesis of Artin L-function is just one of them.
For the most classic Riemann Hypothesis, the result of Artin Conjecture is completely unhelpful.
But now, with Elliptic Inverse Analytic Continuation, even if the classic Riemann Hypothesis does not have a corresponding Galois representation, Xiao Yi can form a connection between the two from another elliptical form.
And this way...
If Artin Conjecture can be proven, it will be of great help to prove Riemann Hypothesis!
In fact, it is equivalent to coming directly to a place that is extremely close to Riemann Hypothesis.
It's like a shortcut.
Of course, this shortcut is not that easy. After all, its premise still needs to be proven Artin Conjecture.
After all, the difficulty of Artin Conjecture is also placed there.
Although Artin Conjecture is not listed as one of Millennium Prize Problems, the difficulty of proving it is no less difficult than Millennium Prize Problems.
However, it is not that he has never solved Millennium Prize Problems. Since he dares to have such an idea, it means that he already has the idea to prove Artin Conjecture.
Still the same.
Elliptic Inverse Analytic Continuation!
Elliptic Inverse Analytic Continuation has endless possibilities.
Even on Artin Conjecture, it can play an extremely huge role!
Xiao Yi's brows raised slightly.
Now, many ideas have emerged in his mind, each of which can become a way of proving Artin Conjecture.
Therefore, one thing that he did not agree with in Liang Qiushi's reply to Zhihu was that among his many papers, Elliptic Inverse Analytic Continuation was really not a very ordinary paper, but a very important paper.
That is to say, there is still not much research on Elliptic Inverse Analytic Continuation in the mathematics community. If it were not for the paper he published, it would probably take some time before people truly realize that Elliptic Inverse Analytic Continuation has more clever applications.
Without further ado, he began to conduct in-depth research.
"First, give the Galois representation of the elliptic curve."
"Given an elliptic curve E on the field Q of rational numbers, consider its Tate module T(E), which is the Z-module generated by all the bisection points of E. Galois group Gal(Q/Q) naturally acts on T(E), which gives a Galois representation."
[ρ: Gal(Q/Q)→GL(2, Z)]
"Then you need to use L-function."
Associated with the above Galois representation ρ is the L-function L(s, E) of the elliptic curve E. This L-function can be defined by Euler product.
[L(s, E)=∏(p) 1/(1-a_p p^(-s)+p^(1-2s)), where p takes all the prime numbers (E is easy to restore), a_p is the trace of E in the reduction modulo p]
There are more and more derivations on the draft paper, and the elliptic curve itself can play a very important role in proving Artin Conjecture.
For example, Taniyama-Shimura theorem itself can be regarded as Artin Conjecture in the context of an ellipse, and the Artin Conjecture that Xiao Yi wants to prove now can be called a more general form of Artin Conjecture.
Therefore, the proof process of Taniyama-Shimura theorem can also become a reference in the process of proving Artin Conjecture.
"Then, using Langlands' corresponding method to study it is the best angle."
Xiao Yi raised his eyebrows and chose such an angle from the various ideas that emerged in his mind.
Since it involves the problem of Langlands Program, it must be very appropriate to use the method of Langlands Program to solve it.
Just like that, time passed quietly.
Whether you want to conquer Riemann Hypothesis or Artin Conjecture, it is destined to be a task that requires a long time of energy.
This is a long march of mathematics, and there are only a few, or maybe a dozen, people who can participate in such a long march.
There will even be some people among them who will only make up the numbers in the end.
Just like in the past, the one who finally solves a certain problem will be the only one.