Great Country Academician

Chapter 716: Shining like a star in the long river of civilization!

In the auditorium, as the report on the Weak Riemann Hypothesis officially began, everyone's eyes fell on the figure on the reporting stage like a hundred birds paying homage to the phoenix.

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

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

Standing on the reporting platform and in front of the blackboard, Xu Chuan held the white chalk in his hand and wrote down the familiar formula one by one in front of his eyes.

The pieces of the puzzle related to the Riemann Hypothesis in my mind are once again clearly engraved in the neurons, just like re-walking the Long March of 100,000 miles. It is a profound and indelible memory.

Among the people sitting in the audience, two former mentors, Edward Witten and Pierre Deligne, sat together in the front row, looking at the young people on the stage with praise in their eyes.

This is the Riemann Hypothesis, a top problem that has been pursued by the mathematical community for a full century and a half.

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

That is the ‘Riemann Hypothesis’!

It reveals the deepest secret of prime numbers in one fell swoop and elegantly gives the precise expression of prime number distribution.

For the first time, people can take a close look at the rhythm of prime numbers dancing in nature. It is so bold and uninhibited. When it is calm, it is like the gentle moonlight shining on the waveless sea, and when it is rushing, it is like huge waves pouring into a lonely boat. People are intertwined with love and hate, and their eyes are wandering.

This difficult problem raised by the mathematician Riemann in 1859 has troubled the world for more than a century and a half.

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

In 2000, it was listed among the seven millennium problems by the Clay Mathematics Institute, and is recognized as the first of the seven millennium problems.

On such a grand problem of the century, even a tiny bit 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 have tried to solve it, including Gauss, Riemann, Grothendieck, and Turing, who have stood at the pinnacle of human intelligence. Man guessed that the giant dragon was defeated in front of him.

To this day, this strange mountain that stands above the pinnacle of human intelligence is still like a majestic mountain. Someone has finally climbed up to half of it, and established a solid camp for those who came after it at a location that no one has ever reached before.

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

"Interestingly, the continuity of the Riemann function is actually related to the eigenvalues ​​of random Hermitian matrices in physics. A pure mathematical question is actually linked to the orthogonal eigenfunctions in degenerate subspaces?"

"It always feels like there's something hidden in the middle, what do you think?"

Sitting next to Terence Tao, the expressionless Professor Faltings glanced at him and paid no attention to his excitement and speculation.

Things other than pure mathematics may be exciting enough for other people, but for him, they are just mediocre.

Tao Zhexuan didn't care about Faltings' indifferent attitude. The question he just asked seemed like a question, but it was more like he was talking to himself.

Sometimes, reading a paper yourself and listening to the author of the paper give a report and explain are two completely different concepts.

Just like now, in this short report of less than half an hour, he has found an area that he had not noticed before.

This feeling is really great for a mathematician!

In the auditorium, time ticked by minute by minute.

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

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

".When 0\u003cRe(π)\u003c1, the Riemann ζ(s) function can return to the π(x) function, and π(x)=∫2x·dt/ln t+ O/ln^Ax). "

"Going one step further, we prove that when O(x^1ε), we can reversely deduce that there are no non-zero trivial points in the region of 0≤Re(s)≥1-ε for the Riemann ζ(s) function!"

Looking at the blackboard that had been replaced one after another and the dense mathematical formulas occupying most of the page, Xu Chuan took a deep breath and threw the chalk in his hand into the basket.

The report briefly describing the thesis is over here.

For him who had accomplished his great feat a month ago, it was not difficult to tell the audience about the process again.

Even if there are dozens of Fields Medal winners and most of the top scholars in the mathematics world sitting in the audience, it is not difficult.

However, the real difficulty begins.

The Riemann Hypothesis, the ultimate mathematical problem involving more than 2,500 'theorems', is the cornerstone of the mathematical building. The entire mathematical community must have countless questions, right?

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

No matter what the future holds, no matter whether the weak Riemann hypothesis is correct or not, he will eventually have to face what he should face.

After taking a deep breath and looking around the auditorium, Xu Chuan said softly: "The paper report on the proof of the weak Riemann hypothesis has been completed, and the next step will be the question-and-answer session."

"If everyone here has any doubts or questions about this proof, you can raise your hands and ask them now, and I will do my best to answer them."

After the words fell, there was silence in the auditorium, not a single raised arm.

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

Faced with a proof related to the foundation of the entire mathematical world such as the weak Riemann hypothesis, is there not a single problem?

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

There must be questions, but the big guys in the front row didn’t ask any questions. How could they dare to raise their hands?

In the front row, the big names in mathematics looked at each other, but no one raised their hands. In the end, everyone's eyes fell on Faltings.

This man who was once the first person in mathematics is known as the scholar closest to Grothendieck, and has also become the first scholar under the Pope. His research on the Riemann Hypothesis and his understanding of the Riemann Hypothesis are probably the best today. First in the world.

Even if the person standing on the reporting stage has solved the weak Riemann Hypothesis, it is hard to say who is stronger and who is weaker based on their research and understanding of the Riemann Hypothesis.

Sitting on the red seat in the front row, Faltings had an expressionless face, as if he didn't feel the gazes on him.

See what he does?

He doesn't have any problems. If you have any questions, just ask them directly.

Sitting next to Faltings, Terence Tao glanced at him in surprise, a little surprised.

If Professor Faltings does not have any problems, then the weak Riemann hypothesis is 80%, no, more than 90% correct.

After thinking about it, Tao Zhexuan coughed lightly and raised his right hand.

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

It just so happened that he didn't understand something about the fact that the continuity of the Riemann function was actually related to the eigenvalues ​​of the random Hermitian matrix in physics.

On the reporting table, looking at Terence Tao who was the first to raise his hand, Xu Chuan also breathed a sigh of relief and nodded with a hint of his eyes.

In the auditorium, the concierge who had already made preparations trotted over quickly and handed the microphone to Professor Terence Tao.

Taking the black microphone, he coughed slightly and tried the microphone. After confirming that there was no problem, Tao Zhexuan said: "On page 42 of the report paper, I noticed that the reporter was completing the continuity of the Riemann function When processing, there are extraordinary zero points corresponding to the eigenvalues ​​of the Hermitian operator through the Riemann function. Regarding this part, can the reporter please give a detailed explanation?”

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

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

The continuity of the Riemannian function and the correspondence between non-trivial zero points and eigenvalues ​​of stochastic Hermitian matrices in physics are not strictly speaking the results of his research. It is the discovery of the American mathematician Montgomery in the last century. He just further expanded on this basis and closely related it to the weak Riemann function.

After thinking for a while, Xu Chuan walked back to the blackboard, turned over the blackboard full of calculations, revealing the clean back, picked up a piece of chalk from the chalk basket, and explained:

"The eigenstates corresponding to different eigenvalues ​​corresponding to the Hermitian operator are orthogonal, and are simply expressed as: ∫μ*mμndτ=δmn"

"And the set of all eigenfunctions is a complete basis. It can be proved by Sturm Liouville's theorem, that is, all the eigenstates of the Hermitian operator constitute an orthogonal normalized complete basis. With the rectangular coordinate system Similar to how the basis vectors x, y, and z form any vector, the sum of all basis vectors can form a state."

After briefly explaining the problem, Xu Chuan held the chalk and turned to look at Terence Tao 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). 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 a finite value), corresponding to wave optics."

"If a system shows universality and extensiveness, it is like labeling itself "I am a complex coupled system" and telling people that it can be modeled with random matrices. The inside of such a system is like a "conductor" "Similarly, electrons, heat, water flow, energy, etc. will be continuously transferred."

"Corresponding the zero points of the Riemann Zeta function to this matrix is ​​the answer I gave."

"Perhaps this will play a significant role in solving the Riemann hypothesis, but I have not yet found a corresponding method."

After a slight pause, Xu Chuan seemed to remember something again, and then added: "Oh, by the way. If you want to fully understand this idea, maybe you need to have a little knowledge of the physical system."

At the reporting table, after listening to Xu Chuan's answer, Tao Zhexuan's eyes had a thoughtful look in his eyes, and he casually said "thank you" and sat down.

With Terence Tao taking the lead, the question-and-answer session was officially on track.

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

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 each questioner's question in the fastest and most concise way, the four hours in the afternoon were still far from enough to satisfy everyone.

Of course, Xu Chuan did not expect that everyone in the auditorium could understand the proof of the weak Riemann hypothesis in just one lecture.

In fact, he estimated that among all the people here, even though it has been more than a month since the proof of the weak Riemann hypothesis was released, less than one-fifth of the people can fully understand this mathematical paper today. One, or even one tenth.

But that doesn't make any difference.

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

After all, top mathematics is never something that everyone can master.

Starting at 2:30 p.m. and lasting four hours until 6:30 p.m., the question-and-answer session officially ended.

When Xu Chuan stood on the stage and announced that the question-and-answer session was officially over, thunderous applause rose like a tide and resounded throughout the entire auditorium, lasting for a long time.

The proof of the weak Riemann hypothesis undoubtedly means that the mathematical world is a big step closer to the top of this towering peak.

It also means that there are more than 2,500 'theorems' based on the verification 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 the name of the person who has left the stage will be passed down in history forever.

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