Chapter 1032 The Future of Number Theory

on stage.

The seventh whiteboard has been filled!

When the eighth whiteboard was dragged to the stage, there was basically no suspense about the outcome.

The fluent calculation and clear thinking, as well as the appalling use and understanding of mathematical tools, have conquered almost all the audience at the scene.

It turns out that the pure complex variable function proposition can be so twisted and bizarre.

It turns out that the complex plane and the differential manifold, which seem to be not in the same dimension at all, can achieve such a high degree of unity on the issue of the Riemann zeta function.

The pen hanging on the whiteboard is like Beethoven's baton. The chaotic prime numbers are on the tip of his pen, like notes endowed with meaning to life, hitting the heartstrings of everyone in the audience.

As Schultz said, it all seemed to come from the void, as if it didn't belong to the performance of this world.

The audience sitting in the audience wished that this report would never end, and that the heartbeat that washed their souls would never stop.

It's better to go on like this until the entire universe is ripped apart by that magical pen, revealing to them all the secrets of God's language...

Sitting under the stage and staring at the stage, Molina bit her lip lightly, her fists on her knees kept clenching and loosening, her stubborn eyes were full of unwillingness.

The layers of shackles that had trapped her for countless days and nights were cut off one by one under the brushstrokes of the flowing clouds and water, and he couldn't even make him stop for a second or even frown lightly. arrive.

This feeling of powerlessness filled her with frustration.

Even if she is not qualified to make a conclusion as to whether a proposition has been proved, but from the atmosphere that haunts the scene, she can clearly perceive that this is no suspense.

After all, that glimmer of suddenness won't lie.

Even she herself is one of the persuaded members...

Sitting next to Molina, her former tutor Sophie Morrell, a mathematics professor whose youth has long since disappeared and the corners of his eyes have begun to climb crow's feet, glanced at his former student and said in a soft voice .

"In my opinion, there is at least an 80% chance that he did it... What are you going to do?"

Molina was silent for a while, and lowered her eyes slightly.

"I don't know, maybe I'll go home for a vacation first..."

She spent ten years in pursuit of the answer to this proposition.

Although he is reluctant to admit such a result, the irreversible fact is so cruel.

It was she who lost.

Looking at the depressed Molina, Sophie sighed softly and said comfortingly.

"You shouldn't get into the horns. In addition to the Riemann conjecture, there are many propositions in this world that are worth your thinking."

Molina was silent for a while, then raised her head and said.

"Maybe."

...

Yes.

The proof has reached this point, and basically there is no suspense.

Especially when the eighth whiteboard was half-written, even Professor Faltings, who sat there without saying a word from the beginning, shrank his pupils instantly.

Just a moment ago.

A certain locked iron gate in his heart, together with the one-step-wide stone wall, collapsed in an instant. And after the collapsed ruins, he saw a brand new world he had never seen before...

When was the last time he felt this way, he couldn't remember clearly.

He only remembered that he seemed to be very young at that time, that Grothendieck had not retired at that time, and the young and vigorous self wrote a letter to the pope of algebraic geometry, which he now sees as " Childish" letter...

Sitting next to him, Professor Deligne, who was just as silent as him from beginning to end, just staring at the whiteboard meticulously, suddenly spoke up.

"Do you think he did it?"

Being a little caught off guard by this question, Professor Faltings was stunned for a moment, and after calming down, he gave a conservative answer.

"More than ninety percent."

Hearing this sentence, Professor Deligne, who is usually unsmiling, suddenly smiled, and paused for a while before speaking.

"When did you start jumping to conclusions in such ambiguous terms."

The expression on his face did not change because of the old friend's ridicule. Professor Faltings, who is keen on "Germanic humor", rarely returned with a poisonous tongue this time, but said calmly.

"...After all, it is Riemann's conjecture, and we have to be cautious. Besides, don't just ask my opinion, how do you feel about it yourself?"

In response to this sharp rhetorical question, Professor Deligne was silent for a while before speaking.

"I can't find a suitable counterexample to refute him for the time being, just like I can't find a non-trivial zero point beyond the critical line..."

After a pause, Professor Deligne continued to speak in a positive voice.

"All I can say is that his proof is logically self-consistent."

Professor Faltings gave him a slightly surprised look, but didn't say anything, just looked away from his face flatly.

Although he didn't say it clearly, he already understood what Deligne meant.

This kind of answer is almost the same as the proof of the person on the stage, and the difference is only one public statement...

At the same time, it was not just Deligne and Faltings who were discussing this issue. Sitting on the other side of the venue, almost the same discussion was also going on.

When he saw that Lu Zhou wrote down the key formula, Fefferman looked at Tao Zhexuan, who was sitting next to him, and asked.

"You are more authoritative than me in the field of analytic number theory... What is your opinion?"

There was a look of excitement in his eyes, but before Professor Tao, who knew everything, had time to speak, the sloppy man sitting not far from him clenched his fists excitedly and almost stood up.

"This is it!"

He roared in a low voice, hammering his fist on his thigh excitedly, turning a blind eye to the slightly sullen gaze from the scholar next to him, venting his excitement in his own way.

It was as if he was not watching a briefing, but a hot-blooded game.

He glanced in that direction dumbfounded. Tao Zhexuan, who was interrupted by the conversation, withdrew his gaze and looked at Professor Fefferman, who had the same satisfied expression on his face, and said with a shrug.

"It seems... this question has already been answered for me."

"As for my opinion, the same as his."

...

Write it down with the last line of the equation.

With the pen tip hanging on the whiteboard finally gently put down.

At this moment, everything is quiet.

Not a single sound could be heard in the entire venue.

Taking two steps back, looking at the neatly handwritten formula on the whiteboard, Lu Zhou spent about half a minute to reminisce about the hearty feeling and the hardships he had traveled on this pilgrimage over the past few years. every step……

At the same time, he also gave the audience half a minute to sort out what he just said.

After clearing his hoarse voice, Lu Zhou turned back to the silent venue and said slowly.

"Here, we can already answer the question of the distribution of the non-trivial zeros of the Riemann zeta function with a positive statement. That is, all the non-trivial zeros of the Riemann zeta function are located on the complex plane Re(s)=1 /2 on a straight line."

"The proof is over here, and the unfinished exploration has finally come to an end here. However, the exploration of the future has just begun, and there are still many questions in this world that we don't know how to answer."

"For example, as an analytic continuation of the Dirichlet L series, are all the non-trivial zeros of the Dirichlet L function also located on the straight line of the complex plane Re(s)=1/2? And what about the self-defeating L function? We still cannot give a definite answer to these profound questions."

"Historical experience tells us that whenever we solve a problem, there must be more problems waiting for us. But I think it must be a happy trouble, and our academics are prosperous because of this. "

Having said that, Lu Zhou paused and continued.

"Some words I originally planned to wait until the academic community gave a clear characterization of my thesis, but... In my opinion, there is no difference."

The silent venue was silent.

Feeling the heavy recognition from the silent silence, Lu Zhou nodded lightly, responded to all the expectant eyes, and raised the volume to continue.

"Answering the previous friend's question, after the completion of the Riemann conjecture, where will the analytic number theory go?"

"My answer is that this ancient discipline must be rejuvenated and more prosperous than ever."

"As for myself, maybe I will study the Dirichlet L function and the generalization of the Riemann conjecture...that is, the generalized Riemann conjecture, and maybe I and my friends will study the Riemann zeta function behind the non-trivial zero-pair correlation function. The physical meaning of that sounds equally exciting enough."

"Of course, in fact, in my opinion, I prefer a more grand proposition."

After a pause for about three seconds, he looked around at the pair of eyes in the venue that were focused on him. Lu Zhou, who had already unloaded all his burdens, took a deep breath and said the sentence in a relaxed tone. He had long wanted to the words said.

"...that is, unifying algebra and geometry!"

Almost as soon as Lu Zhou said these words, the entire venue was like a pot of boiling water, boiling in an instant!

Unify Algebra and Geometry!

Shocked, suspicious, curious, confused, sneered, or expressionless…

"Unification...algebra and geometry? Omg!"

"This, this is too exaggerated."

"I don't know how high the sky is! The solution of Riemann's conjecture depends on how the academic circles define it, and it is already so inflated!"

"But if it's him, maybe it's really possible..."

All kinds of clamorous sounds formed a rushing torrent under the stage, impacting everyone's eardrums and nerves.

Academician Wang widened his eyes in surprise, unable to believe that Lu Zhou would suddenly say such a crazy idea.

Molina's face was full of shock. There is no doubt that this is a larger and unattainable mountain than Riemann's conjecture. She doesn't understand that he has already accomplished such a great cause, why should he stand at this time? such a flag.

Similarly, Faltings' pupils were slightly enlarged in shock.

It's just that his shock was a little different from that of most of the people present.

Staring at the young man standing on the stage, the old man whispered something to himself.

"...It was actually preempted."

Unified Algebra and Geometry...

That's exactly the last thing he intends to do before retiring.

Unexpectedly, there is such a coincidence. This plan has just begun, and someone and him have thought of it.