No matter how detailed Lin Xiao's report is, it is obvious that there are still some things that are incomprehensible to the people present.
At the same time, incomprehensible problems are just ordinary problems. The more fatal problems are those that arise after each step of the paper has been understood to a deep level.
These questions are what can break the logical line of this paper.
The academic world has always been cruel, and it is difficult for even some geniuses to develop stably in it.
Unless you are like Lin Xiao, a genius who has reached an extreme level, you will not encounter any of the cruel things that happen to young scholars in the beginning of your academic career, such as being squeezed by your mentor, having your papers robbed, etc.
.
And the same is true even in top academic circles.
It can be said that 99% of the people present were looking forward to Lin Xiao's ultimate failure in their hearts.
After all, there is only one Riemann Hypothesis. If it is proved by Lin Xiao, then among their seven major mathematical problems of the millennium, wouldn't there be only one BSD conjecture left?
Moreover, the Riemann Hypothesis is so famous that as long as you complete the proof, you will immediately become one of the most famous mathematicians in the world, leave your name in history, and become a person on par with those mathematicians in history.
Of course, although these people are not sure that they will be the ones to win the crown in the future, but what if?
And even if Lin Xiao's proof fails, it is undeniable that the method used in the paper that Lin Xiao has published is indeed very sophisticated. Maybe they can find the correct answer from the mistakes in it.
What about the road?
There are not a few people who hold this idea.
After all, who made academia a vanity fair?
Of course, only those scholars who have already achieved great heights and have won all the honors they can get can be gratified by Lin Xiao's proof.
"Hello Dr. Lin, I am Cornel Beetz, professor of the Department of Mathematics at Imperial College. What I want to ask about is page 32. What you describe here, in the Hermitian matrix, what we have
What is the logical connection between the N points of the joint probability density function on the real line that need attention and the original formula of the random Hermitian matrix with given symmetry?"
After hearing this question, people present turned over the papers in their hands, looked at page 32, and found the question of the first questioner.
Then people nodded involuntarily. Yes, this question was a good one and hit one of the key points.
After Lin Xiao heard this question, he just smiled slightly. Without picking up the paper and finding page 32, he walked directly to the small blackboard he had just used when reporting, picked up the blackboard pen, and
Started writing.
【Γ(1 +β/2)^N/(2π)^N/2∏……】
People present were stunned when they saw Lin Xiao's actions. But after seeing what Lin Xiao wrote, they couldn't help but feel surprised and admired in their hearts.
They all saw very clearly that Lin Xiao started writing directly after listening to the questions. He did not need to review the questions at all like them.
How strong a memory and deep familiarity with the paper do you need to be able to achieve this level?
And to this extent, will Lin Xiao's paper really have fatal problems?
People who had previously been expecting Lin Xiao to finally prove his failure suddenly woke up.
They were facing the smartest people in the world, and who had ever heard of Lin Xiao's proof being wrong?
Perhaps Lin Xiao has not appeared in the world of mathematics for a long time, which has caused some of the rising stars to become mentally unstable.
After all, after so many years, perhaps since Lin Xiao returned to China in 2023, Lin Xiao has not appeared much in the mathematics world, and almost eight years have passed, which is enough for a ten-year-old primary school student to enter university.
Graduate students have officially entered the workforce, which is enough for some talented scholars to be promoted from ordinary lecturers to professors.
[…|λj?λk|^β]
On the rostrum, Lin Xiao finished writing the final formula on the blackboard, then turned to look at the professor of mathematics at Imperial College, and asked with a smile: "Mr. Beetz, do you need me to explain further?"
?"
"Ah..." After hearing what Lin Xiao said, Professor Cornel Beetz reacted quickly, and then said in amazement: "I don't have a problem anymore, so this is how it was solved."
He was actually obsessed with the answers given by Lin Xiao just now, because the formulas Lin Xiao wrote on the blackboard undoubtedly answered his questions perfectly.
And among the people at the scene, as long as they had some research in this direction, they could easily understand Lin Xiao's answer, so everyone else basically turned the page and looked at other parts of the paper.
Then Cornel Beetz said no more and bowed slightly to Lin Xiao, "Thank you Dr. Lin for your answer. I have no questions."
Lin Xiao nodded, then looked elsewhere.
"Next person."
Then many hands were raised, waiting for Lin Xiao's roll call.
Lin Xiao didn't hesitate and started ordering it casually.
"Hello, Mr. Lin, I am from the Max Planck Institute..."
"Dr. Lin, I am Princeton University..."
"Professor Lin, I am from Beijing University..."
After hearing a question from Beijing University in their native language, Lin Xiao naturally answered more patiently.
When everyone present saw this, they couldn't help but feel a little envious, and they also thought, if they also joined Beijing University, would they also be able to get such special treatment?
Moreover, China is developing quite well now. Maybe we can give it a try?
This kind of idea took root in the minds of many people, and then it became somewhat out of control.
And Lin Xiao probably didn't expect that he would have such an influence just by taking care of his compatriots.
Of course, he wouldn't care too much if he found out. After all, if you really want to adapt to life in China, you have to learn Chinese first.
I’m afraid that in the future, language will be the thing that stops foreigners from entering China, right?
In this way, each question passed, and time passed slowly for an hour.
There seems to be a tacit understanding among the people asking questions, and the difficulty of the questions is constantly increasing from simple to difficult.
The knowledge and reputation of the person who asked the question are also constantly deepening.
In the end, even Deligne asked a question from a rather tricky angle, which made everyone present feel shocked when they heard the question and didn't know how to answer it.
What surprised the people present even more was that when faced with such a question, Lin Xiao still did not read his paper, but directly answered the question after getting it.
This also made the people present sincerely admire Lin Xiao again.
And the time is almost half past twelve, so it should be time for dinner.
Many people present already felt a little hungry in their stomachs.
Of course, with Deligne's question over, no one in the audience seemed to have any more questions.
People present couldn't help but feel a sense of relief, it was finally over.
Undoubtedly, this will be an academic report of the century, and the entire report process is also very smooth. Whether it is Lin Xiao's previous report statement or the subsequent question-answering session, he has shown what is known as the history of mankind.
The most intelligent person ever.
It is truly a worthwhile trip.
For those students who did not understand anything in the entire report, whether they understood it or not was secondary. The most important thing was that they participated in this grand event.
Even when you chat with others in the future, you will have something to brag about.
In the auditorium, among the rows of seats belonging to Chinese participants, many mathematics undergraduates or graduate students present could not help but show admiration on their faces when they saw Lin Xiao's performance.
"Lin Shen is so handsome!"
"It's so cool. Those questions are so difficult. Lin Shen actually answered them without even thinking or reading the paper. He's so powerful."
"Senior brother, do you still understand the questions asked by the other elders? How difficult are Professor Deligne's questions just now?"
Facing the junior sister's admiring question, the senior brother's face immediately turned red, then he scratched his head, waved his hands and explained: "That's not true, I don't understand it either, but... as long as it's something we don't understand, then...
It just means it’s difficult.”
Upon hearing this explanation, the junior sister, who still looked very admiring, rolled her eyes.
Doesn’t everyone know this?
When the senior brother saw this, in order to maintain his face in front of his junior sister, he immediately said: "Oh, don't worry, my intuition must be correct. How about we ask the professor?"
As he said this, the senior brother asked the leading professor sitting next to them: "Professor Wang, do you think so?"
Professor Wang, who was suddenly cueed, immediately glared at the senior brother angrily, then coughed twice and said to these students: "Well, sometimes what your senior brother said is right, as long as you don't listen.
You know, the difficulty level must be very high."
"So don't think too much about it. After you go back, continue to study hard and strengthen yourself."
Suddenly, the professor gave another lecture, and these students suddenly lost interest in talking.
They all had a feeling that Professor Wang himself must not understand Professor Deligne's question.
Of course, none of them guessed wrong, and if they could understand the question Deligne asked, it would be enough for them to write a paper on District One.
On the other side, the chairman of the Chinese Mathematical Society and another domestic mathematics academician were also sighing at this time.
"As expected of Chief Lin, he first spoke for two hours and then answered questions for an hour. His thinking was still so clear."
"It's terrible, if it were me, I would be annoyed even in two classes."
"After all, Chief Lin is still young."
At this time, both of them began to feel like they had to accept their old age.
"It seems that this report ends here. After all, even Deligne has asked questions."
"probably."
The other person nodded.
At this moment, Lin Xiao also spoke up: "So, does anyone else have questions?"
Just when everyone thought there was no problem, three more hands suddenly rose up in the audience.
After seeing these three hands, everyone present was stunned. Do you still have three questions?
Everyone looked at them and couldn't help but gasp, good guys, there were two heavyweights among them.
One is the famous Faltings, a master of mathematics who once served as the director of the Max Planck Institute of Mathematics. His status in the world goes without saying.
And another heavyweight was Perelman, who proved Poincare's conjecture. He was sitting in a corner of the audience. It is estimated that no one next to him recognized him, and no one present expected that.
This great man would actually leave his hut in Russia and come to Paris.
Of course, if you think about it, it is no exception. After all, no mathematician can refuse to participate in the proof report of the Riemann Hypothesis.
Obviously, this mathematician is no exception.
However, the third person is relatively less well-known, because he is a young man who looks younger than Lin Xiao. He is probably just studying for graduate school now.
This young man is raising his hand now. Does he have any important questions?
Or are you just trying to please others?
But Lin Xiao on the stage didn't think too much. When he saw the three raised hands, he smiled slightly.
It seems that this is the final test.
Three people, three problems, how difficult will these problems be?
He smiled and said, "It seems that we have to wait a little longer before it's time for us to eat."
Everyone present smiled, and Lin Xiao also said: "Okay, I need to think about who to choose."
However, at this time, Perelman and Faltings put down their hands in a tacit understanding, and it seemed that they both planned to let the young man ask questions.
Next to Faltings, Wiles said with a smile: "Tsk, tell me, what kind of question will that young man ask?"
Faltins shook his head, "I don't know, but I'm more curious about what Perelman's problem is."
"Then let's listen to this young man's problem first."
Wiles looked at the young man and suddenly said: "Hey, the person sitting next to this young man is Peter Schulz. Could it be that he is a student of Schulz?"
When he was confused, the young man was also pointed out by Lin Xiao, and then he said: "Dr. Lin, hello, I am Shuke Black, a doctoral candidate in the Department of Mathematics at the University of Bonn."
"My question is: Your entire paper first connects the Lindelof conjecture and the problem of large prime number gaps, so that they form a whole, thus forming a stronger conjecture and proving it."
"Then we expanded the results of this proof and discussed its value range on the complex plane."
"And in this process, you used a method that can be used to analyze the density gap of prime numbers more deeply..."
After hearing what Shuke Black said, most of the people present felt impatient.
This one-step method is the core and key point of Lin Xiao's entire paper. Everyone in the room didn't know how many times they had studied it.
What questions can be asked now?
Coupled with the fact that this was a young man, many people immediately began to conclude that this was a person who was trying to please others.
However, not everyone thinks so.
Wiles sat up straight, with some interest in his eyes.
"Oh? This question... seems interesting, Gould, what do you think?"
He turned to look at Faltings beside him.
However, what surprised him was that Faltings' eyes were very serious at this time, he looked down at the paper, and at the same time made a "shush" gesture, apparently telling Wiles to stop talking.
Seeing this, Wiles couldn't help but be stunned. Could it be that the question this young man asked was actually the question Faltings planned to ask?
And if he looked towards the back corner, he would also find that Perelman also lowered his head, looking at the paper with a serious face.
"...then, at this time, if I set n equal to p, the function value will expand infinitely under any circumstances, and then the point with a value of half will obviously not fall on the same straight line.
."
"This will falsify the Riemann Hypothesis."
"That's my problem, thank you."
As Shuke finished his story, the entire audience fell silent.
Because at first he looked down upon Shuke, but now he realized that he didn't even understand the young man's question.
And those who understood it had the same serious expressions on their faces as Faltings and Perelman.
Obviously, they are all aware of how serious this problem is.
Just like on the Go field, one side seems to be winning steadily, but the other side's layout looks very messy at first glance. However, unexpectedly, a sudden chess piece can shake up the entire situation and kill the dragon.
This is a fatal problem.
Because according to Shuke Black, the non-trivial zero point that should fall on Re(s)=1/2 will directly become chaotic. However, according to the points that have been verified by the computer, it is obviously inconsistent with this point.
Does not match.
This also means that Lin Xiao’s proof is wrong!
Everyone was surprised. This young man seemed to be ordinary, but the questions he raised turned out to be so direct to the essence.
Being able to ask such a question is enough to show that this young man is not simple.
"Hey, Gould, isn't this young man's question exactly what you want to ask?"
On the other side, Wiles couldn't help but ask.
At this time, Faltings' originally serious expression suddenly showed a smile.
He nodded, acknowledged Wiles' question, and then said with emotion: "It seems that we will still have enough outstanding young people to appear."
"Perhaps, I should also imitate you and become a little more relaxed in my final old age."
"Haha, you should have been like this a long time ago." Wilhelm suddenly laughed.
Faltings nodded slightly and looked at Lin Xiao on the stage, "I just don't know if Lin can answer this question."
Wiles also nodded and looked at Lin Xiao.
If you want to win the crown of Riemann Hypothesis, you have to go through such difficulties to be able to see that the crown is hard-won.
But at this moment, people present suddenly discovered that even with such a question, Lin Xiao seemed to have still not read the paper to deepen their impression?
At this time, Lin Xiao finally spoke.
"Your name is Shuke Black? Are you Peter's student?"
"Yes." Shuke Black looked at the teacher beside him and nodded.
Lin Xiao smiled: "Yes, I have heard Peter tell me a long time ago that he has a very talented student, and it seems that he is you."
"And your question is also very good and valuable."
Hearing Lin Xiao's praise, everyone in the audience looked at Shuke Black. He was able to get Lin Xiao's praise, and he was another Fields Medal winner's student. He turned out to be a great boss.
ah!
Lin Xiao also continued: "As for this problem, if you want to solve it, it is actually very simple."
See, Lin Xiaodu admitted that it was difficult...wait, "it's also very simple"?
Lin Xiao's words once again surprised thousands of viewers.
Even those who don't understand can tell from the discussion that the question Shuke asked is very difficult.
As a result, Lin Xiao actually said that the solution to this problem was very simple.
Lin Xiao turned around, came to the blackboard, erased the writing on it first, and said at the same time: "I hope you can still remember the sieve circle method, Lin's group transformation method, and the mathematical vaccine-the root inspection method."
These methods are all mathematical methods he has developed to solve other problems.
At this time, under his interpretation, the ideas of these methods were gradually integrated and changed into a more harmonious method.
And Faltings, Perelman, and other top mathematicians, at this moment, their eyes became serious again because of Lin Xiao's story, until they were amazed.
They understand.
"Finally, substitute the limiting conditions here into the formula you just mentioned. I believe you will be pleasantly surprised to find that the situation you just raised is perfectly reconciled."
"All non-trivial zero points once again fall on the straight line whose real part is one-half."
"At this point, we can prove without a doubt that the Riemann Hypothesis is correct."
"Mr. Black, do you have any questions?"
"I..." Shuke Black followed the thoughts that Lin Xiao just described in his mind, and finally understood.
"I understand!" He said in an excited tone: "I have no problem! Thank you, Dr. Lin."
"You're welcome, continue to deepen your academic research, I believe in your future." Lin Xiao said with a smile, like a senior.
Although he is only a few years older than this Shuke Black.
But Shuke Black didn't feel anything. After being encouraged by Lin Xiao, he felt even more excited and thanked him again and again.
After the question was over, Lin Xiao faced the audience again and asked: "Are there any more questions?"
Everyone looked at Faltings and Perelman.
However, neither of these two people raised their hands to ask questions.
At this time, people also realized that the problem of Shuke Black was also the problem of these two!
Just when everyone was amazed, Faltings suddenly stood up and said to Lin Xiao: "Lin, thank you for solving the Riemann Hypothesis and helping me realize a dream."
Then, he bowed deeply.
The audience was stunned for half a second, and the next moment, they burst into applause.
Yes, the mathematics community would like to thank Lin Xiao!
Lin Xiao also smiled indifferently, bowed slightly to the applause of the audience, and left the scene gracefully without saying anything else.
