Section 364

Obviously, this question does directly hit the key weakness of the entire paper.

And this time, it was probably the first time that Xiao Yi showed his thinking appearance to so many people.

They couldn't help but observe Xiao Yi carefully, wanting to see what the mathematical god looked like when he was thinking about problems.

But now it looks no different from how they usually think.

That is to say, when they are thinking, they may frown, while Xiao Yi's eyebrows relax.

This meditation can probably be regarded as the most critical meditation in the history of mathematics, and it is also a meditation that everyone is looking forward to the result.

No matter what the result is, it can bring different interpretations.

In this way, a long time passed.

It took about two or three minutes.

As a report meeting, two or three minutes is undoubtedly a long time.

Especially now, there are thousands of people in the audience waiting for the results.

Until finally, Xiao Yi raised his head and finally spoke.

"First of all, I have to say that this is a sharp enough and hidden enough problem that I thought about it for a while before I remembered how I considered this problem when I originally proved it."

When everyone heard what he said, they all sat up straight.

Remember how you considered this issue in the first place?

Could it mean that Xiao Yi was already aware of this problem at the beginning?

So now, he thought about how to answer this question?

But then, Xiao Yi's words made them all stunned.

"Well, what I have to admit is that I did implicitly assume what you said, that all elliptic curves can be embedded in a generalized modular curve."

ah?

This statement...

Does Xiao Yi want to admit that he failed?

Everyone present seemed to be about to see a myth shattered.

After all, they had never seen Xiao Yi fail.

However, Xiao Yi's next words came immediately.

"Actually, when I first researched this point, my mathematical intuition told me that this hypothesis was completely correct, so I did not discuss this situation during the proof process. Therefore, I probably made a mistake. My fault is..."

Xiao Yi paused, then spread his hands and said, "This question is 'obvious' to me."

Everyone was stunned as they listened to his story.

What does this mean?

So, did Xiao Yi admit that he was wrong, or did he admit that this issue was actually an obvious theorem in his eyes, so much so that he felt there was no need to prove it in the paper?

Wiles was also stunned, not understanding the meaning of Xiao Yi's words.

After all, when he made this implicit assumption, it was basically because he subconsciously acquiesced to this in his mind, so it became a key flaw in the entire proof, so that he was confused in it for almost a year. It took years to succeed.

Now, what Xiao Yi said seems to be the same as the reason why he made the mistake in the first place.

But...

The information revealed in Xiao Yi's other words was slightly different.

For a moment, he was a little confused.

But then, Xiao Yi's words completely stunned all of them.

Xiao Yi turned his head, walked back to the blackboard, and said: "Well, in that case, I will prove it on the spot, proving that all elliptic curves can be embedded into a generalized modular curve."

Then he began to wipe the blackboard that had been wiped countless times in the previous report meeting, and also said: "Of course, the process of this proof may be a little long, so please continue to listen patiently for a while. ”

Everyone present was stunned for a moment.

Wha...what?

Live proof?

Where should they even start to solve this problem? Xiao Yi is going to prove it to them on the spot?

How long has passed since this question was raised?

For a moment, people couldn't help but start to wonder, what on earth was Xiao Yi thinking about during those few minutes of thinking just now?

Or, as he said just now, was he just recalling how he thought about this matter when he first proved it?

They were all a little stunned at this point.

Including the top mathematicians sitting in the front row, they all had the same reaction.

They all looked at Xiao Yi who was wiping the blackboard in disbelief, their faces full of disbelief.

"He wants to prove it on the spot? Can this kind of problem...such a complicated problem...can really be proved on the spot?"

Schultz said with some disbelief.

"Maybe ordinary people can't do it, but he is Xiao Yi, he might really be able to do it."

Faltings next to him smiled and acted very indifferently to this.

"I..." Schulz didn't know what to say.

On the other side, Deligne smiled and said, "It's starting to get interesting."

Bombieri said: "Isn't it getting more and more interesting?"

Deligne was startled, then laughed and said: "Okay, if you say it more accurately, it will indeed become more and more interesting."

Terence Tao seemed a little excited at this time.

"So, this kind of question is basically impossible to stump him. In his opinion, such questions are actually obvious. He is the real god of mathematics! Wow!"

As for Feferman and Qiu Chengtong next to him, they were a little silent, because in fact, they were also shocked by Xiao Yi's behavior of proving it on the spot.

Is this really still within the scope of human beings?

They really want to ask such a question.

But before they can think about it.

Xiao Yi on the stage has wiped the blackboard, then picked up the blackboard pen and walked to the blank space on the left.

"Well, my proof begins now."

"First of all, the reason why I felt that this was obvious when I proved it, or that I had such an intuition, was mainly due to my understanding of the L-function of elliptic curves."

"For any elliptic curve, its L-function should have some form of automorphism, which reflects some kind of intrinsic symmetry of the elliptic curve, and this automorphism, in my proof, is realized through the Hecke characteristics of the generalized modular curve."

"But now, if we need to prove this process strictly, then we need a series of logical inferences."

"Then, let's first give the proposition: for any elliptic curve E, there is always a generalized modular curve M, so that E can be equivariantly embedded in M."

"The first step is to consider the L-function L(E, s) of the elliptic curve E. According to the modular properties of the elliptic curve, L(E, s) should satisfy some form of functional equation and automorphism. Specifically, there should be a prime number p and an automorphism σ:E→E, so that——"

[L(E, s)=ε(E)* p^(-s/2)* L(σ(E), 1-s)】

"where ε(E) is a constant that depends on E."

"Next, we consider a formalized generalized modular curve M(E) generated by E. As an intuition, we can understand M(E) as a larger object generated by E through some product and quotient operations, similar to a group ring generated by a group."

"In this construction, the automorphism σ on E can be naturally extended to M(E), denoted as σ:M(E)→M(E)."

"Then the third step..."

While Xiao Yi was talking, he wrote down his proof process on the blackboard.

The people in the audience were completely stunned.

No, buddy, can you really prove it?

Chapter 294 Riemann Hypothesis Report (VI)

The people at the scene were shocked that Xiao Yi was able to start the proof so quickly.

It even seemed that he had a basic idea for all the next steps.

This is simply...

It's a bit outrageous.

Especially the difficulty of this problem, in their opinion, it is completely impossible to start.

Perhaps this problem is not as difficult as the Riemann hypothesis or any other hypothesis.

But this is by no means a simple problem, especially since it now involves the new theory of generalized modular curves.

The complexity is much higher.

Although the generalized modular curve is very important, its complexity can be seen by everyone present.

To prove a more troublesome conclusion on such a complex new theory...