Chapter 716: Shining Like a Star in the River of Civilization!

In the auditorium, with the official start of the weak Riemann conjecture report, the audience, like a hundred birds and a phoenix, everyone's eyes fell on the figure on the report platform.

The figure is not very tall and majestic, but standing on the stage at this moment, it is like a phoenix perched on a building tree, stealing everyone's attention.

The calculations flowing on the screen and on the blackboard are like bright stars in the background of the building wood, shining with dazzling light, and like the Milky Way, flowing in this winding universe.

Standing on the lecture table, standing in front of the blackboard, Xu Chuan pinched the white chalk in his hand and wrote the formula in front of him one by one.

The pieces of the puzzle about the Riemann conjecture in my mind are once again clearly engraved in the neurons, like a long march of 100,000 miles, a deep and indelible memory.

Sitting in the crowd under the stage, Eduard Witten and Pierre Deligne, two former mentors in the front row, sat together, looking at the young people on the stage with praise in their eyes.

This is the Riemann conjecture, the top problem that has been chased by the mathematical community for a whole century and a half.

If there is such an opportunity, a mathematician can exchange his soul for the answer to a certain mathematical problem. It can be said that more than 90% of mathematicians will give the same answer to this question.

That's the 'Riemann conjecture'!

It reveals the deepest secrets of prime numbers in one fell swoop, elegantly giving precise expressions for the distribution of prime numbers.

For the first time, people can get a close look at the laws of primes dancing in nature, which is so bold and uninhibited, like gentle moonlight sprinkled on the waveless sea when calm, and like a monstrous wave pouring on a lonely boat when rushing, which makes people love and hate, and their eyes are wandering.

This puzzle, proposed by the mathematician Riemann in 1859, has puzzled the world for more than a century and a half.

At the same time, it is also the only major problem that is 'unsolved' among the mathematician Hilbert's 23 problems.

In 2000, it was listed by the Clay Institute of Mathematics as one of the Seven Millennium Problems, and is recognized as the first of the Seven Millennials.

In such a grand century, even a single cent of progress is a great achievement worthy of celebration by the entire mathematical community.

It's just a pity that for a century and a half, countless mathematicians who have tried to solve it, including Gauss, Riemann, Grothendieck, and Turing, who have stood at the pinnacle of the human mind, have all fallen in front of the dragon of Riemann's conjecture.....

To this day, this strange mountain, which stands at the pinnacle of human intelligence and is still like a majestic mountain, has finally been climbed halfway up and built a solid camp for those who come after it in a position that no one has ever reached.

At the same time, on the other side, Professor Tao Zhexuan, who was sitting with Faltings, touched his chin and stared at the blackboard and the lecture table with bright eyes.

"Interestingly, the continuity of the Riemann function is actually related to the eigenvalues of random Ermi matrices in physics, and a pure mathematical problem can be linked to the orthogonal eigenfunctions in the degenerate subspace?"

"It always feels like there's something hidden in there, don't you think?"

Sitting next to Tao Zhexuan, Professor Faltings, whose face was expressionless, glanced at him, paying no attention to his excitement and speculation.

Something other than pure mathematics may be wonderful enough for others, but for him, it is not enough.

Tao Zhexuan didn't care about Faltins' indifferent attitude, the question just now seemed to be asking, but it was more of his own talk.

Sometimes, reading a paper by yourself and listening to the author of a paper give a presentation are completely different concepts.

Now, for example, in this report, which was less than half an hour, he had found an area that he hadn't noticed before.

It's a great feeling for a mathematician!

.......

In the auditorium, time ticks

A: Minutes and seconds passed.

Half an hour is not a long time, and before you know it, it has already passed.

In front of the blackboard, Xu Chuan took a deep breath, and the chalk in his hand fell on the last two lines of calculations.

「..... When 0

"Going one step further and proving o(x^1?e), it is possible to reverse the Riemann ζ(s) letter that there are no non-zero triviality points in the region of 0≤Re(s)≥1-e!"

Looking at the blackboards that had already been replaced one after another, and looking at the mathematical formulas that densely occupied most of the page, Xu Chuan took a deep breath and threw the chalk in his hand into the basket.

The report of the brief dissertation has come to an end here.

For him, who had already accomplished this great feat a month ago, it was not difficult to recount the process to the audience again.

Even if there are dozens of Fields Medal winners sitting in the audience, and most of the top scholars in the mathematics field are seated, there is nothing difficult.

However, the really hard part is where it begins.

The Riemann conjecture, the ultimate mathematical problem involving more than 2,500 'theorems', the cornerstone of the mathematical edifice, must have countless questions in the entire mathematical community, right?

Thinking about it, Xu Chuan breathed a long sigh of relief, turned around and walked back to the report table from the blackboard.

No matter what the future holds, and whether the weak Riemann conjecture is correct or not, he needs to face it after all.

Taking a deep breath and scanning the auditorium, Xu Chuan said softly, "The proof paper report on the weak Riemann conjecture has been completed, and the next step will be the question session."

"If you have any doubts or questions about this certificate in your mind, you can raise your hand now, and I will do my best to answer them."

The voice fell, and the auditorium was silent, not a single raised arm.

Seeing the empty auditorium and the silent crowd, Xu Chuan was slightly stunned, and he didn't understand what the situation was for a while.

In the face of the weak Riemann conjecture, a proof that is related to the foundation of the entire mathematical community, there is not a single problem?

In the auditorium, everyone in the middle and back rows looked at each other, you look at me, I look at you.

There must be questions, but the bigwigs in the front row didn't ask questions, where did they dare to raise their hands?

And in the front row, those big bulls in the mathematical world also look at me, I look at you, not a single one raised their hands, and in the end, everyone's eyes fell on Faltins.

This former first person in the field of mathematics, known as the scholar closest to Grothendieck, and also became the first scholar under the Pope, in the study of the Riemann conjecture, the understanding of the Riemann conjecture is probably the first in the world today.

Even if the one standing on the report stage now solves the weak Riemann conjecture, it may be really difficult to say who is strong and who is weak in the research and understanding of the Riemann conjecture between the two people.

Sitting in the red seat in the front row, Faltins looked expressionless, as if he didn't feel the gaze of everyone.

Seehathedoes？

He doesn't have any questions, just ask them if you have any questions.

Sitting next to Faltins, Tao Zhexuan glanced at him with some surprise, a little surprised.

If Professor Faltings doesn't have any problems, then the weak Riemann conjecture is eighty percent, no, ninety percent or more wrong.

Thinking about it drifted in his mind for a moment, Tao Zhexuan coughed lightly and raised his right hand.

In that case, he should be the first to ask questions.

It just so happened that he didn't understand that the continuity of the Riemannian function is related to the eigenvalues of random Ermi matrices in physics.

On the report platform, looking at Tao Zhexuan, who was the first to raise his hand, Xu Chuan also breathed a sigh of relief, and nodded with a suggestive look.

In the auditorium, it has long been done

The protocol clerk who had prepared for the work trotted over briskly and handed the microphone to Professor Tao Zhexuan.

After taking the black microphone, coughing lightly and trying the microphone, after confirming that there was no problem, Tao Zhexuan spoke: "On page 42 of the report paper, I noticed that when the reporter completed the continuity processing of the Riemannian function, the extraordinary zero point of the Riemannian function corresponded to the eigenvalue of the Hermitian operator. Could the reporter please provide a detailed explanation of this part?"

In front of the reporting desk, Xu Chuan was a little surprised after hearing the question.

For the weak Riemann conjecture, this correspondence is not really an important step in the core proof process.

The correspondence between the continuity and nontrivial zero points of the Riemann function and the eigenvalues of random Ermi matrices in physics is not strictly his work. Rather, it was the discovery of the American mathematician Montgomery in the last century, and he just expanded on this foundation and closely related it to the weak Riemannian function.

After thinking for a while, Xu Chuan walked back to the blackboard, turned over the blackboard full of formulas, revealing a neat back, and while picking up a piece of chalk from the chalk basket, he explained:

"The eigenstates corresponding to the different eigenvalues corresponding to the Hermitian operator are orthogonal and are simply expressed as: ∫μ*μndt=δn....."

"And the set of all eigenfunctions is a complete base, which can be proved by Sturmlyauer's theorem, that all eigenstates of the Hermitian operator constitute an orthogonally normalized complete base. Similar to the ax, y, and z base vectors of the Cartesian coordinate system form any vector, all the base sums can form a state ......"

After succinctly explaining the problem, Xu Chuan pinched the chalk and turned to look at Tao Zhexuan in the front row again

, smiled and said, "The more complex the system, the larger the corresponding random matrix (the higher the order)."

"When the world is continuous, it corresponds to the semi-classical model in quantum theory (Planck's constant tends to 0) and when the order tends to ∞, it corresponds to geometric optics. And when the order is finite, the world is discrete, corresponding to quantum theory (Planck's constant is finite), corresponding to wave optics."

"If a system is universal and extensive, it's like labeling yourself as 'I'm a complex coupled system,' telling people that they can model it with random matrices. The inside of such a system is like a "conductor", constantly transferring electrons, heat, water, energy, and so on."

"Mapping the zero point of the Riemann Zeta function to this matrix is the answer I gave."

"Perhaps this will be a major hint to the Riemann hypothesis, but I haven't found a way to do it yet."

After a slight pause, Xu Chuan seemed to remember something again, and then added, "Oh, that's right. If you want to fully understand this line of thinking, perhaps it will require you to have a little bit of knowledge of the physical system."

Under the stage, after listening to Xu Chuan's answer, Tao Zhexuan's eyes had a thoughtful look, and he casually said 'thank you' and sat down.

With Tao Zhexuan taking the lead, the question session was officially on the right track.

For the mathematical community, at least in this century, there is probably no more important problem than the Riemann conjecture.

Although it is only a phased achievement, there are countless scholars who are crazy about it.

Even if Xu Chuan tried his best to answer every questioner's question in the fastest and most concise words, the four hours in the afternoon were still far from satisfying everyone.

Of course, Xu Chuan didn't expect a single presentation meeting to make everyone in the auditorium understand the proof of the weak Riemann conjecture.

In fact, he estimates that even more than a month has passed since the proof of the weak Riemann conjecture was published, less than one-fifth, or even one-tenth, of all of you in the room can fully understand the mathematical paper today.

But it doesn't matter.

As long as the top group of people can understand this proof paper smoothly, then today's presentation will be a success.

After all, top-notch math is never available to everyone

Something that can be played.

......

It started at half past two and continued until half past six in the afternoon, a full four hours, and the question session officially ended.

When standing on the stage, the moment Xu Chuan announced the official end of the question session, thunderous applause rose like a tide, resounding throughout the entire auditorium, and it lasted for a long time.

The proof of the weak Riemann conjecture undoubtedly means that the mathematical community is one step closer to the summit of this majestic peak.

It also means that there are more than 2,500 'theorems' based on the confirmation of the 'Riemann hypothesis', and they will be one step closer to being sublimated into real 'theorems'.

It also means that from now on, another legend will be added to the monument of mathematics, and it will be passed down in history forever with the name of the person who has left the stage.

Like the shining star in the sky, it shines on the entire academic community and the direction of civilization!

.......

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