Everyone at the scene was shocked that Xiao Yi was able to start proving it so quickly.
It even seems that all the connected steps have a basic idea.
This is simply...
A little outrageous to the point of going too far.
Especially the difficulty of this problem, in their opinion, it is completely impossible to start.
Maybe this question is not as difficult as Riemann Hypothesis, or some other conjecture.
But this is by no means a simple question, especially since it now involves the new theory Generalized Modular Curve, which is from a high position.
The complexity has increased even more.
Although Generalized Modular Curve is quite important, its complexity can be seen by everyone present.
To prove a more troublesome conclusion on such a complex new theory...
Anyway, they felt that if they were allowed to go up, they would have to think about it for a few days first... right?
Well, it could be a week, or even a month.
Especially since this is just preliminary thinking.
After all, in the beginning, they didn't even know where to start.
Only now, after seeing Xiao Yi's method, did they understand a little bit.
But the key is, how did Xiao Yi figure it out so quickly?
They are puzzled now.
In the end, it can only be attributed to one reason.
Because he is Xiao Yi.
Just such a reason.
"... Now we consider Hecke feature H(M(E), s) of M(E). From the construction of M(E), H(M(E), s) should contain L(E, s) as one of its factors. At the same time, the action of σ on M(E) should induce some kind of automorphism of H(M(E), s)——"
[H(M(E), s)=ε(M)* p^(-s/2)* H(σ(M(E)), 1-s)]
"Then, combining the first step and the third step, we can get-"
[L(E, s)| H(M(E), s)]
"This means that the automorphism of L(E, s) can be promoted to the automorphism of H(M(E), s). In other words, the modular properties of E can be "embedded" into the modular properties of M(E)."
After writing this, Xiao Yi turned his head, smiled and said to the mathematicians present, "At this point, I think the next steps will become very clear."
"So, we can deduce the embedding of curves from the matching of L-functions. Specifically, if L(E, s) can be embedded in H(M(E), s), then there should be an isomorphism."
[φ: E→ M(E)]
"... such that φ induces an embedding from L(E, s) to H(M(E), s)."
Finally, it took about half an hour, and the entire blackboard was filled with the steps written by Xiao Yi, and it was just right, with no extra white space.
Coupled with the excellent blackboard writing of Xiao Yi, this blackboard is full of a kind of beauty unique to mathematics.
Xiao Yi put down the blackboard pen, clapped his hands, turned around, went to a small podium set up in front, picked up his water glass, took a sip, drank the last sip of water in it, then put it back steadily, and then looked at the people present again.
At this moment, the entire venue was still silent.
Everyone is still immersed in the rigorous and unmistakable proof on that blackboard.
Although for most viewers, the contents of this blackboard are as incomprehensible as a bible.
But it doesn't stop them from now finally understanding the feeling of "artwork" that Terence Tao and the others mentioned at the beginning.
This is indeed a true work of art!
As for the mathematical masters in the front row, they were completely immersed in the proof process of Xiao Yi just now and the current result.
Other ordinary viewers can now understand the feeling of the artwork they are talking about, let alone them?
Many friends of mathematicians feel that the real partner of a mathematician is mathematics, not themselves.
This is especially true for top mathematicians.
Therefore, when facing the derivation process of such a blackboard, they truly felt the wonderful beauty.
The beauty unique to mathematics.
And now, such beauty is once again brought to them by Xiao Yi.
It's like the feeling I had when I first started reading the paper.
Their hearts were filled with such joy.
"It's so beautiful..."
They lamented.
Of course, in addition to its beauty, they were also deeply amazed by the correctness of this proof.
The last question asked by Schultz, most of them may still be a little confused about Xiao Yi's answer.
But with this problem and such a complete proof, they could easily understand it.
After all, the proof of Xiao Yi is really quite easy to understand, and they can easily understand it.
Of course, understanding the answer does not mean that I can have sex with you.
It can only be said that the proof process of Xiao Yi can be regarded as taking "smartness" to the extreme.
As long as you figure out where this coincidence is, the whole process will become clear.
But if you want to find this lucky place from the very beginning, it will be as difficult as climbing to the sky.
Perhaps, only Xiao Yi in the world can discover such a coincidence.
As for other people who want to solve this problem, they may only use other methods to prove it.
The whole place was so quiet that the photographer did not dare to press the shutter at this moment, for fear of disturbing the moment when the truth was revealed.
It seemed that even they could feel the feeling of being wrapped in truth.
Of course, such tranquility will eventually need to be broken.
And the breaker didn't get an angry look.
"Okay, that's my answer to this question."
Xiao Yi said.
"Professor Wiles, do you still have any questions?"
Andrew Wiles stood up again.
At this moment, all that was left on his face was wonder and admiration.
"No, your answer... is much better than I imagined."
"If I were you back then, I probably wouldn't have been lingering in despair for so long..."
he sighed.
He has already assumed the role of Xiao Yi.
Today's Xiao Yi is like a cool version of his experience back then.
And Xiao Yi just smiled and said, "But doesn't your wandering experience also add a bit more storytelling to your life?"
"Failure always runs through life, but after experiencing a short-term failure, it is even sweeter to regain the joy of success."
Wiles was silent for a moment, then smiled, "Thank you for your guidance, God of Mathematics!"
As soon as he finished speaking, he sat back upright in his seat.
Xiao Yi nodded slightly.
The next moment, the audience burst into applause.
Not for anything else, but for this question and this answer.
Perhaps, it was also for what Xiao Yi said.
"It wasn't until this moment that I realized that the gap between him and me was not something that could be explained with just a few simple words."
Terence Tao said while clapping his hands.
"If I am Mathematical Mozart, then who is he?"
Feierman said with a smile, "Mathematical Jesus."
Terence Tao compared the title of God of Mathematics and couldn't help but said, "Well... doesn't this lower my status?"
Several people nearby laughed.
"It seems that Riemann Hypothesis's crown is finally going to be taken away by him."
Deligne sighed, and then added, "There can't be any more tricky questions, right? That shouldn't be the case, right?"
Bombieri also smiled and said, "I don't think it will happen."
"However, after questioning these two questions, I fully agree to take this crown away, even if it is Riemann Hypothesis."
Deligne nodded. "Yes, I completely agree."
"What's more, this also proves that we humans still have the ability to conquer mathematics."
"Although we organized Prime Pioneer Program and it was considered that we bowed our heads to mathematics, in the end, Xiao Yi made us raise our heads again."
More spectators applauded.
Maybe he is the top mathematician, or maybe he is a student.
Or, a woman.
Luo Mingya was sitting in a corner, looking at Xiao Yi on the stage and applauding gently.
Originally, Xiao Yi wanted to place her in a higher position, but in the end she said that she was not a mathematician and knew nothing about mathematics, so she had better give up those good positions to mathematicians who really looked forward to this lecture, and in the end, she chose this position.
Although it is located in the corner, you can still see the various postures of Xiao Yi in the report meeting.
Of course, this was also the first time she attended Xiao Yi's academic seminar, and it was also the first time she saw with her own eyes his true elegance in mathematics and how high his attainments in mathematics were.
That was something that captivated the entire mathematical community. No one had ever done it before, and probably no one would be able to achieve it since.
And for this, besides cheering for it in her heart, she was also deeply proud of it.
This was what attracted her most to him.
The applause lasted for a long time. After a while, Xiao Yi waved his hand to indicate that everyone could stop.
"Okay everyone, please stop for a moment, please stop for a moment."
After hearing his words, the audience gradually stopped applauding.
"So, are there any other questions to ask?"
Xiao Yi asked again.
The whole place fell silent again.
Will there still be one?
If there is still a problem now, what kind of problem is it?
However, this time, after waiting for a full minute, no one finally raised their hands.
And this also means that the mathematical community has completely recognized the proof of Xiao Yi.
Riemann Hypothesis has truly become history!
And Xiao Yi no longer waited, picked up the microphone, and said with a smile, "In that case, then I think... Riemann Hypothesis will stop here and become a monument in the history of mathematics."
"From now on, the mathematical world will also have one more Riemann theorem, and many propositions that are established because of it."
Applause once again sounded like thunder, filling the entire lecture hall. Everyone began to cheer for this incident and celebrate today's historic moment.
In the future, in the history of mathematics, it will also be recorded that Riemann Hypothesis completed the proof on November 1, 2028, and the prover: Xiao Yi.
This time the applause lasted longer than before.
The applause just now was because of the wonderful questions and answers, and the applause now is really celebrating today's results.
The mathematicians in the front row all showed sentimental expressions.
This problem they have been chasing for who knows how long is finally solved now.
It's a pity that the person who solves it is not myself.
However, if you really let yourself go, can you really solve it?
This question is destined to be a question that can never be answered - of course, this is not necessarily the case. They can also try hard to use other methods in the future to see if they can prove Riemann Hypothesis.
But it is a pity that even if they prove it in the future, they will not be the first prover.
After the applause lasted for several minutes, it stopped again. Next, it was probably time for Xiao Yi to announce the end of this report meeting.
Everyone is also looking forward to the final conclusion of this report meeting and the subsequent reaction of the world.
"Okay, then, I would also like to thank you all for coming and participating in this report meeting for the last time. I hope this report meeting can leave a deep enough impression on you, and I hope you will not be disappointed."
"Of course, before the end, I have another discovery that I want to share with you."
Everyone was stunned for a moment, and then the scene, which was still slightly rusty, immediately became quiet. I want to know what Xiao Yi discovered?
"I believe everyone can see that a key idea in my proof is to connect different types of mathematical objects, such as elliptic curves, Riemann Zeta function, Galois representation, etc., and use the interactions between them to gain new insights."
"Of course, this kind of thinking also exists in all aspects of mathematics, including the process of proving Fermat's Last Theorem by Professor Wiles."
"So, after I completed the proof, through reviewing the entire proof process, I realized that there seems to be such a formula that can connect three mathematical objects."
When he said this, Xiao Yi dragged a small blackboard next to him and wiped the content on it while saying, "These three mathematical objects are automorphic representations, L-functions in number theory, and some natural objects in geometry."
"Now, we can give such a relationship. For each automorphic representation ρ, we can construct an L-function L(s, ρ) and a geometric natural object X(ρ), so that they satisfy the following relationship——"
[L(s,ρ)= L(s, X(ρ))]
"That is, the L-function of ρ is equal to some natural L-function of X(ρ)."
When the top mathematicians in the front row saw this relationship, they immediately narrowed their eyes and started thinking carefully.
And soon, they realized how significant this relationship was to the mathematical world.
"If this relationship can be established, it will also become a very powerful promotion for Langlands Program."
"Langlands Program foresees that every automorphic representation should correspond to a geometric object and a number theory L-function. As for this relationship, it can be further foreseen that there should be a direct equality relationship between this geometric object and the L-function."
"In other words, it can provide a unified perspective that connects the three branches of mathematics, algebra, geometry, and analysis. Through this relationship, we can transform problems in algebra into problems in geometry, such as the study of converting Representation Theory into clusters, or problems in analysis, such as the properties of L-functions, etc."
"I believe this will be more of a relation that promotes the unification of mathematics."
"And I already have a certain degree of confidence that this relationship can be established."
Later, Xiao Yi showed some simple derivation to the mathematicians present on whether this relationship could be established.
Mainly giving some specific examples.
And those mathematicians who could understand fell into further deep thought.
If you look at the examples given by Xiao Yi, it seems that this new relationship is indeed a question worthy of further consideration.
If it can really be proven...
This may not be another Riemann Hypothesis.
Therefore, Xiao Yi proved a Riemann Hypothesis and brought a new Riemann Hypothesis to the mathematical world.
"In short, that's it. We can see that after some detailed derivation, we can connect some of the objects. However, how to extend this connection to the entire field still needs some specific research in the future. At present, it is still a bit complicated to truly prove this problem."
Xiao Yi continued.
"So, I will announce it to the mathematical community as a new conjecture for the time being. I hope that the mathematical community can achieve a breakthrough on this issue in the future."
Then, he opened his hand and said, "Okay, now, that's all I want to share."
"Mathematics is a completely different direction from other subjects. I hope that every friend here can enjoy such differences in their future research and study of mathematics, and then bring more wonderful results to mathematics."
"This concludes my report, thank you all."
He opened his hands, bowed deeply, and turned to leave.
Those in the audience who did not understand his new conjecture immediately applauded.
Those audience members who understood were awakened by the deafening applause after a moment, and then they also applauded again.
Everyone also stood up and watched Xiao Yi leave. Even though his figure had disappeared behind the door into the backstage, the applause still did not stop, as if it was a concert, looking forward to his return and then proving a guess for everyone.
Of course, such a thing is naturally impossible to happen.
But no matter what, Riemann Hypothesis, which is engraved on the top of the mathematical crown, finally became a mark in history amidst such applause.
Mathematics, on the other hand, is still moving forward until the distant future.