From Almighty Scholar to Chief Scientist

It's just that the previous part is quite satisfactory, that is, according to the content written in his report, there is nothing beyond the outline.

In this kind of report, the speaker will usually play a little bit, such as talking about some off-topic things, which is very normal, but Lin Xiao changed his normal routine, which made those who came to see the mathematics of his report Everyone is confused.

This guy, do you really want to speak so honestly?

So, finally some mathematicians couldn't help discussing it.

"Professor Lin is going to continue talking like this? Don't talk about any extra topics?"

Other mathematicians who still maintained such patience said: "Don't worry, isn't it the end yet? The last disconnected part of his report is the most critical."

The mathematician who couldn't wait heard this, so he had to be patient and continued to listen.

However, Andrew Wiles, who was sitting not far away, showed a smile on his face. This kind of feeling that only he understands is not very good.

Seeing that the colleagues around him still looked solemn, bewildered, or puzzled, he couldn't help smiling.

Then, he raised his head and looked at the young figure on the stage. Curiosity and anticipation arose in his heart. He understood the arrangement of Lin Xiao's previous two reports. Lin Xiao clearly intended to thoroughly prove Hodge's conjecture.

So, did Lin Xiao really prove Hodge's conjecture?

If this is also true, then for the mathematics community, this is no less than setting off a strong wind of magnitude [-] plus an earthquake and tsunami of magnitude [-].

The Millennium Problem has such qualifications. Like the proof of the Poincaré conjecture at the beginning, it set off a lot of heat in the mathematics world. It can be said that the entire mathematics community has focused on the bearded man with the slightest As for the slovenly Russian mathematicians, the mathematics world in those years also boiled up. If it wasn't for that Perelman who rejected various awards, otherwise, the related enthusiasm would be even greater.

However, the difficulty of Hodge's conjecture is probably not lower than that of Poincaré's conjecture, because the tool to solve Poincaré's conjecture has appeared between 1990 and 2000, that is, the Ricci flow theory, so in only a dozen years Finally, in 2002, the Poincaré conjecture was completely solved.

However, the tools that can be used to solve Hodge's conjecture have not yet appeared. It means that if you want to solve Hodge's conjecture, you must first find a tool that can be used to solve him. So, has Lin Xiao found it?

Andrew Wiles showed a more curious expression. At the same time, he himself felt itchy. He wanted to rush forward and asked Lin Xiao directly if he had proved Hodge's conjecture.

But just thinking about it, he quickly shook his head again, he couldn't sit still like those other guys.

And at this moment, he suddenly heard two conversations coming from the side.

"Kenig, I remember that after Professor Lin came to the stage to receive the Fields Medal yesterday, he seemed to have whispered to you, right? What did he say?"

"Oh, he said we're going to have another miracle in mathematics soon."

"A miracle? What's that?"

"I don't know either. Of course, since Professor Lin has said so, let's just look forward to it."

"Ok."

"..."

When Andrew Wiles heard this conversation, he couldn't help raising his eyebrows.

"Miracle?"

It seemed that he was probably right.

Feeling like a boulder fell to the ground, he raised his legs, changed to a comfortable sitting position, and continued to watch Lin Xiao's performance quietly.

As for Lin Xiao above, he didn't care what the audience in the audience were thinking at all. He won the Fields Medal and is the youngest Fields Medal winner in history.

He turned to the fifth-to-last PPT of his report and said: "So, finally we can get the correct statement about the integral Hodge conjecture."

"That is: when X is a projective complex manifold, each cohomology class H^(2k)(X,Z)∩H(k,k)(X) is the reverse of the algebraic period with integral coefficients on X class and the sum of cohomology classes."

"So far, we have obtained the correct integral Hodge conjecture. Now, the problem of geometry has been completely pulled into the field of numbers, and even the relatively simple field of differentiation, not the past."

Hearing what Lin Xiao said, the mathematicians off the court still couldn't help but nod. No matter what, the gold content of this report is high enough, at least it can be ranked in the forefront of all reports this time.

Once this integral Hodge conjecture is proposed, it is enough to set off a frenzy of research on Hodge's conjecture again in the mathematical community.

Of course, the premise is that the report ends here, and Lin Xiao didn't add those few lines of formulas behind.

Of course, Lin Xiao should talk about the formulas in the next few lines that made more than half of the mathematicians present itch.

So these mathematicians sat up straight and waited seriously for Lin Xiao's next words.

However, Lin Xiao walked to the side without haste, first picked up the water glass placed on the podium, took a sip, and moistened his throat.

It wasn't until the mathematicians below were a little anxious that he put down the water glass, then stood in front of the stage again, and said with a smile: "Originally, my normal report was successfully concluded by proposing the integral Hodge conjecture."

nonsense!

Every mathematician who wanted to send blades to Lin Xiao rolled his eyes.

"But..." However, Lin Xiao changed the subject at this time, and said with a smile: "Since I have figured out the integral Hodge conjecture, I will naturally want to prove it. For this, I have paid a lot. Much work with little effort."

"And finally..."

Speaking of this, Lin Xiao stopped abruptly, making all the mathematicians who had pricked up their ears puzzled, and then reacted.

Lin Xiao is trying to whet their appetite again!

However, just when they were in a hurry, Lin Xiao took out another thing from his bosom.

A colorful thing.

The people below looked at this scene and couldn't help but be taken aback.

This is?

a toy?

And it is a toy that is popular all over the world. Many people recognize it. Those who don't know the name will call it a colorful spring, and those who know the name will also say the official name "Slinky".

However, why is Lin Xiao taking this thing out now?

Of course, the mathematicians below finally showed expressions of "it's finally here". Lin Xiao, as expected, came up with something different in the end.

So, what did Lin Xiao want to say when he took out this spring toy?

Everyone present waited and watched.

At this time, Lin Xiao on the stage looked at the Slinky in his hand, and smiled on his face. Who would have thought that it was this toy that looked a little magical and was fun to play, which inspired him to conjecture about Hodge. What about the proof?

Looking up again, he smiled and said, "This is a very interesting toy."

As he spoke, he also played with the toy. Of course, because he was not very proficient, he accidentally dropped his hand while shaking it, and then the toy fell to the ground, which caused a burst of laughter from the audience.

"Sorry, it seems that I still can't play with this kind of toy." Lin Xiao quickly picked it up again and said with a smile, but then he said: "Of course, in the eyes of most people, this is just Just a toy."

"However, in my eyes, or in the eyes of friends who study topology, this is a very classic one-dimensional topomorphism."

"Now, let's try to describe it numerically."

As Lin Xiao spoke, the PPT also turned the page, and a mathematical description of the geometric figure slinky appeared.

Then he said: "The Hodge conjecture studies the polynomial solution sets of topological homeomorphisms in various dimensions."

"As for the Hodge conjecture of the (1) class, it was proved by Lefschetz in 1, which means that the Hodge conjecture is true for H^1924. Hodge proposed this conjecture based on Lefschetz's proof."

"Then, the toy in my hand, as a one-dimensional manifold, can obviously hold Hodge's conjecture."

"But how do we extend this to higher dimensions?"

Lin Xiao's question aroused the thinking of everyone below.

Yes, how to expand to higher dimensions?

At this time, Lin Xiao smiled, and the PPT turned the page again, returning to the last few lines of his report.

【H^2（S2，Z/2（1））≌H^2 et（S2，C，Z/2（1））……】

"Now, everyone, please look at these few lines."

The mathematicians below suddenly showed a sudden look.

These few lines...

Isn't the discussion started from the case of H^2?

If so...

All the mathematicians were shocked and looked at Lin Xiao excitedly. Does this mean that the proof of Hodge's conjecture will not be far away?

So, is Lin Xiao going to break through this miracle next?

They all looked at Lin Xiao immediately, expecting what he would say next.

But at this moment, the PPT turned a page again.

But on this page, there is a huge real-time time. It is now 12:25:21, and there are less than 5 minutes before the end of this report.

In addition, under this real time, there is another line of words.

Everyone squinted their eyes and looked at this line: I now have a wonderful method to expand the low-dimensional situation to high-dimensional, but due to lack of time, so...

"Then thank you all, this is the end of my narration." Lin Xiao said with a smile.

Everyone: "????"

So much for this, are you still playing Fermat?

Did you know that Fermat would have been beaten if he hadn't had a bad commute back then?

And Andrew Wiles at the bottom was also stunned, and then gave Lin Xiao a thumbs up.

Good guy, this kid is better than him.

Even Fermat's tricks were used!

However, didn't Lin Xiao say at the beginning that he wanted to give everyone an answer at this conference, but now that your report is over, this is your answer?

This is even more appetizing than the original report, okay?

However, just before the excitement of the crowd, Lin Xiao smiled lightly and said: "If you are still interested in the next process, you are welcome to listen to my Fields lecture the day after tomorrow. At that time, I will continue to tell you about the next content .”

The Fields lecture the day after tomorrow?

Everyone was stunned again, and then suddenly realized that Lin Xiao had also taken this matter into consideration.

However, in that case, wouldn't Lin Xiao have already reached the stage of Fields Lecture?

Everyone couldn't help but wonder, probably only Lin Xiao can prepare the content of Fields lecture in advance with such confidence?

"Okay, everyone can ask questions next, but time is limited, so I will only answer one question, please forgive me."

Lin Xiao said with a smile.

Soon, rows of hands were raised below, and in the end, Lin Xiao chose Pierre Deligne who sat at the front.

In the eyes of everyone, Deligne stood up and looked at Lin Xiao.

Afterwards, he slowly articulated his question: "Lin, since you said that you have found a wonderful method that can extend low-dimensional situations to high-dimensional ones, may I ask if it is high-dimensional in a broad sense?"

Lin Xiao looked at Deligne, then nodded seriously.

Deligne smiled gratifiedly: "Then I look forward to the answer you will give us the day after tomorrow."

Chapter 295 He Wants to Prove the Hodge Conjecture? !

After Deligne's voice fell, he sat back safely.

Lin Xiaoze also said with a smile: "Then, this is the end of this report, thank you all, and see you the day after tomorrow."

Afterwards, he packed up his things and left the stage.

In the auditorium, the faces of those who failed to ask the question showed regret. Of course, it was impossible for them to compete with Deligne, so they could only temporarily put aside the questions in their hearts.

However, when they recalled the question Deligne asked just now and Lin Xiao's answer, they were all stunned.

Is Lin Xiao going to extend the Hodge conjecture established in low dimensions to high-dimensional situations in a broad sense?

At present, regarding how many dimensions the Hodge conjecture holds, mathematicians in the past have only studied the fifth dimension, and the establishment of these dimensions mostly requires a lot of assumptions, that is, the so-called preconditions, and even Even the Hodge conjecture in the four-dimensional case is true, and current mathematicians have not yet solved it.

Then, what Lin Xiao wants to solve now is the high-dimensional situation in a broad sense?

Wouldn't that be the same as saying...

Is Lin Xiao going to completely solve Hodge's conjecture?

The mathematicians who came back to their senses all showed shock on their faces.

"Oh! Buy! Karma! He wants to prove Hodge's conjecture?!"

"This... is too unbelievable, right?!"

"I thought he was talking about expanding to high dimensions to solve the problem of Hodge's conjecture in four dimensions. Now tell me, what he is going to solve is the complete Hodge conjecture?"

"Is this...Professor Lin?"