From Almighty Scholar to Chief Scientist

However, someone soon said: "Don't worry, the title does not state that it is a proof of Hodge's conjecture!"

Hearing this, they reacted.

The above only mentioned the integral Hodge conjecture, and did not show that it was really proved.

However, at this time, a staff member who studied algebraic topology and algebraic geometry said: "But, this is the integral Hodge conjecture! Previous research on the integral Hodge conjecture has basically failed. The integral Hodge conjecture , which is of great significance for truly solving the Hodge conjecture!"

"There is also a new kind of motivational coherence in front of the title. It is very likely that Professor Lin Xiao is mainly talking about it in this report, and this is motivational coherence! There are quite few people studying this thing now."

Hearing what this colleague said, everyone else couldn't help but feel confused.

The Hodge conjecture alone is enough to make young people in their 20s or even graduate students in mathematics feel very powerful.

And for these mathematics students living in St. Petersburg, it can be said that it is a very glorious thing to prove the Millennium Puzzle Prize, because Perelman, who proved the Poincaré conjecture, is also a life in St. Petersburg.

It's just that Perelman obviously also brought his hermit style to the extreme. After he proved the Poincaré conjecture, he received worldwide attention, and he was so troubled that he resigned from all the jobs in the research institute. They parted ways almost completely, so that there is not much news about Perelman now.

Of course, no matter what, Perelman, as a Russian, solved one of the most famous mathematics problems in the world, which is still admired and spread by Russian mathematics students.

"Then let's take a look! I can't wait to know to what extent Professor Lin Xiao has achieved Hodge's conjecture."

Then, they began to read this article.

But after reading two pages just now, someone said: "Forget it, you can read it, I won't read it."

As soon as he finished speaking, another person also said: "I don't watch it either."

Then came the third person: "I was wrong. I couldn't even understand the proof of the Poincaré conjecture 20 years ago, let alone the current Hodge conjecture."

"Wooooow, it's too difficult!"

……

So just like that, only the previous person who studied algebraic geometry and algebraic topology, and Alexander were left.

"Can you do it!" Alexander said helplessly, "I still need to see the format."

"Then you two take your time, let's slip away first."

With that said, those people all ran away.

Alexander rolled his eyes, then looked at the only colleague left behind, and said, "Belic, fortunately there is still you, let's watch with me."

Bellich said, "Are they all gone?"

"Huh? They're all gone."

"Then it's my turn to go." Bellich said and turned away.

Alexander: "...then why do you stay for a while?"

Bellich: "I can't show that I, a student of algebraic topology and algebraic geometry, can only understand a little more than them? Let's wait for the evaluation of other professors later!"

Alexander: "...but now I know."

"So you have to keep this secret for me, and treat you to dinner later!"

Alexander: "...deal!"

Until Bellich also left, Alexander changed the format of this report that he could not understand at all, and then sent the report to the chairman of their conference organizing committee.

The organizing committee of the conference is a researcher at the Institute of Mathematics of the Russian Academy of Sciences, called Oleyevich. When he received the report from Alexander, he became interested.

"Oh? Has Professor Lin Xiao finally sent the report?"

"Let me be healthy..."

When he opened the report, he was also stunned.

"Hodge...guess?"

"And it's still... the integral Hodge conjecture?"

Oleyevich also studies algebraic topology and algebraic geometry, so he is very aware of the importance of the integral Hodge conjecture.

"Could it be that Professor Lin Xiao has found out the correct integral Hodge conjecture?"

With such interest, he downloaded the paper and started to read it.

Compared with those young mathematics students, his experience is obviously richer, so he can still understand this paper.

In this way, until the end, there was a look of wonder on his face.

"It has to be this Professor Lin Xiao..."

He could already predict how many surprises Lin Xiao's report would cause.

However, he has not realized that Lin Xiao is more than just this report.

Chapter 2 Ninety

For Oleyevich, he knew that Lin Xiao's report was of great importance to the study of Hodge's conjecture.

Both forms of integral Hodge conjecture in the past have certain errors, that is to say, mathematicians have found counterexamples, so mathematicians are still pursuing a new integral Hodge conjecture, which can perfectly combine Hodge Conjectures are summarized.

Now, in Lin Xiao's report, a very rigorous discussion process was used to propose this brand-new motivational cohomology person, and then he came up with this new integral Hodge conjecture. In this regard, it is enough to make Ole Jevic believed it very much, and Lin Xiao later used a counter-evidence method to prove that his integral Hodge conjecture was completely correct, and it carried all the information of the original Hodge conjecture.

"Loss of information" is a common situation that hinders the development of mathematics, and generally occurs in changes of form.

For example, Lin Xiao’s Lin’s Theorem solves the change from function to layer. In the past, not all functions could be transformed into layers, because some information would be lost during the transformation process, that is to say, some Information will be lost after transformation.

The form of incomplete information will naturally affect the process of solving mathematical problems, so how to solve this problem requires the development of new tools.

For Lin's theorem, it is a tool to achieve lossless transformation between functions and layers.

In the process of transforming Hodge's conjecture into integral Hodge's conjecture, it is necessary to use the function that cohomology can be converted into differential form. However, due to the limitation of tools, this conversion process will lead to the loss of some information, so it is also As a result, the errors of the past two integral Hodge conjectures appeared.

But now, Lin Xiao's brand-new motivational co-homology once again solves such a fatal problem, allowing the original "information" to be transformed without loss in two forms.

Therefore, for this, Oleyevich was very amazed by Lin Xiao's report. Undoubtedly, this is a very remarkable achievement.

The importance of this report cannot be overstated.

"It makes me look forward to Professor Lin's report."

Shaking his head, Oleyevich looked at the end of the report again, and suddenly he was taken aback.

At the end, there are several lines of mathematical formulas.

"Huh? Why is there still at the end...Professor Lin hasn't finished yet?"

With some doubts, he took a few more glances.

After a while, a serious color appeared in his eyes.

"This is...Professor Lin is actually going to start proving this conjecture?"

The few steps at the end are the proof that the integral Hodge conjecture begins to unfold.

But although it is only a few simple steps, it is enough to arouse the imagination of mathematicians like Olejevic.

According to the steps given by Lin Xiao, if we continue to work on it, maybe we can produce some important phased results?

At least for now, Lin Xiao's last few lines already have such potential.

Not to mention the real proof, but the staged results are also very important in mathematics, just like Perelman was able to prove the Poincaré conjecture because there is a mathematical tool called Ricci flow, which plays a very important role in it. Importantly, this also made Perelman publicly stated that the mathematician named Richard Hamilton who came up with the Ricci flow had made a greater contribution than him.

But even so, but——

"Why are there only so few steps!"

For the first time, Oleyevich felt the abhorrence of broken dogs, and even felt like sending Lin Xiao a blade.

This can obviously be written in the future, at least with Lin Xiao's ability, it is definitely possible to write in the future.

But he got stuck at such a critical step and stopped writing.

Oleyevich scratched his hair, feeling itchy.

I believe that no mathematician can resist the temptation to prove Hodge's conjecture, or any of the seven millennium problems. The $100 million award from the Clay Institute alone is enough to make many mathematicians Hungry.

Mathematicians are often not that rich, so they were surprised to learn that Perelman didn't even accept the $100 million.

And that’s not to mention the fame that comes with it, and the need for self-actualization, which is the Millennium Dilemma after all.

So Olejevic really wanted to know how to write after this crucial step.

"Professor Lin, what the hell is he going to do!"

But no matter how confused he was at this moment, even if he thought about it, he probably never thought that Lin Xiao wanted to reproduce the process of Andrew Wiles proving Fermat's last theorem.

If you can't figure it out, then don't think about it.

So Olejevic stopped meddling and put the report into the archives. After it was reviewed and it was completely confirmed that there was no problem with the content of the report, it could be uploaded to their 2022ICM official website.

Oleyevich could even imagine that when other mathematicians downloaded Lin Xiao's report and read it, they would, like him, hate Lin Xiao's step stuck in a critical point.

Maybe, after Lin Xiao finished his report in his speech, the audience would still make a fuss.

Oleyevich was already looking forward to that time.

Shaking his head and putting this matter behind him, he was about to start other work, but at this moment, someone suddenly called him.

He saw that it was his friend Zorelovsky, who was a professor of mathematics at St. Petersburg State University.

St. Petersburg State University is second only to Moscow State University in Russia, and its status is equivalent to Qingbei in China.

Although in the so-called international university rankings, the ranking of St. Petersburg State University can only compete with the 985 schools outside Huaguo and Qingbei, but in fact its own strength cannot be objectively expressed by those international rankings, because these international rankings are all Paying attention to an internationalization, in layman's terms, is the requirement for English, so in the QS university rankings, for example, universities in the English-speaking area are basically ranked in the forefront.

It is precisely because of this that the strength of St. Petersburg State University is actually very strong.

At the same time, Russia's basic mathematics education is also very strong, and St. Petersburg State University has naturally inherited this strength. Even Perelman graduated from St. Petersburg State University.

It is precisely because of this that Zorelovsky is quite famous in the world of mathematics.

After answering the phone, he smiled and said, "Dude, why are you in the mood to call me?"

Zorelovsky on the opposite side did not greet him, and said directly: "Did you know? Lin Xiao from Huaguo has decided to hold a report on the proof of Lin's conjecture at their Shangjing University. Are you planning to go?"

Oleyevich was taken aback, "Proof of Lin's conjecture?"

Of course, he is also very interested in this matter. As a researcher of algebraic geometry, he is certainly not unfamiliar with Lin's theorem. For example, in some of his recent research, he has used the research on Lin's theorem.

But then he said helplessly: "I'm in charge of the International Congress of Mathematicians now, so I probably don't have time to go."

"That's right, that's true." Zorelovsky said: "The report will be held until June [-]th. I guess you really don't have time."

"Hmm... wait, you said June [-]th?"

Suddenly, Oleyevich sat up directly, and when Zorelovsky said that Lin Xiao planned to give a report on June [-], he suddenly felt something was wrong.

One week after June [-]th, it will be the International Congress of Mathematicians, and there will be a one-hour report by Lin Xiao at that time.

So what is Lin Xiao planning to do?

Two reports in ten days?

No, there are Fields Lectures.

Although he, the chairman of the organizing committee, cannot comment on the Fields Medal, which is determined by the International Mathematical Union, but he can still get some news. The probability of this Lin Xiao winning the Fields Medal is [-]%. big.

This made him fantasize even more.

Lin's guess?Integral Hodge Conjecture?

There are also several steps that Lin Xiao will try to prove Hodge's conjecture at the end of the report.

Oleyevich always felt that Lin Xiao wanted to make a big deal.

"It's June [-]th, what's the matter?"

On the other end of the phone, a friend's inquiry came.

Oleyevich came back to his senses, then smiled and said, "It's nothing, I just think that this year's mathematics world may not be ordinary."

Zorelovsky said with a smile: "Professor Lin proved his own Lin's conjecture in January. This alone is enough to make this year's mathematics world extraordinary."

Olijevic shrugged: "Well, what I want to say is that this year's conference should not be too ordinary."

"Really? Then I can look forward to it."

"Well, look forward to it." Olejevic said: "I am looking forward to it too."

……

Time is fleeting.