From all-round academic master to chief scientist - Chapter 293 I already have a wonderful method, but I don’t have enough time

“Lin’s theorem draws an equal sign between the two forms of function and layer, so that in terms of mathematical form, the most basic concept of function in mathematics is linked to the layer in topological space.”

“The Hodge conjecture forms a channel between geometric topology and algebra, making it possible to directly express those geometric shapes that we thought were extremely abstract in the form of polynomials.”

“There are certain similarities between the two, as I also mentioned in my paper proving Lin’s theorem.”

“Then, I will start with Lin’s theorem, from functions to topological spaces, and then to polynomials, to introduce my report today.”

After Lin Xiao finished speaking, the following PPT also turned a page.

“We assume that X is a topological space, and C is a category. The pre-layer of an object in C on the space X is given by the following data:”

[For each open set in X, given an object F(U) in C]

[For each inclusion relation V U between open sets, given a morphism resU in category C, V : F(U)→ F(V)]

…

As Lin Xiao’s narration began, everyone present listened attentively, especially the mathematicians who wanted to see what medicine Lin Xiao was selling in the gourd.

Who knew that there was extremely important information hidden in one of Lin Xiao’s words?

The mathematicians present could not wait any longer, so that when Lin Xiao started to talk, no one discussed what Lin Xiao said, and they all listened attentively.

In this way, time passed quickly, and Lin Xiao’s report gradually entered the final part.

However, the previous parts were completely satisfactory, just as written in his report, and there was nothing out of line.

In a report like this, the speaker usually shows off his performance, such as talking about some off-topic topics. This is normal, but Lin Xiao changed his normal behavior, which made the mathematicians below come to see his report specially. The family was confused.

Does this guy really want to speak so honestly?

So, finally some mathematicians couldn’t help but start discussing it.

“Professor Lin is going to continue talking like this? No more unnecessary 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.”

When the mathematician who couldn’t wait any longer heard this, he had no choice but to be patient and continue listening.

However, Andrew Wiles, who was sitting not far away, had a smile on his face. This feeling that only he understood was not a good feeling.

Looking at the colleagues around him who still had solemn faces, or confused or confused expressions, he couldn’t help but smile in his heart.

Then, he raised his head and looked at the young figure on the stage, curiosity and expectation arose in his heart. He understood the arrangements of Lin Xiao’s previous two reports. Lin Xiao clearly intended to completely prove Hodge’s conjecture.

So, did Lin Xiao really prove the Hodge conjecture?

If this thing is true, then for the mathematical world, this is no less than setting off an 18-magnitude strong wind, an 18-magnitude earthquake and a tsunami.

The Millennium Problem has such qualifications. For example, the proof of Poincaré’s conjecture caused an unknown amount of enthusiasm in the mathematical community. It can be said that the entire mathematical community has focused on the man with a big beard and no trace of it. As for the slovenly Russian mathematician, the mathematics community in those years also became agitated. If Perelman had not refused various awards, otherwise, the related heat would have been 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, Ricci flow theory, so in just a dozen years Finally, in 2002, the Poincaré conjecture was completely solved.

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

Andrew Wiles showed a more curious expression. At the same time, he also felt his heart itching. He wanted to rush up and ask Lin Xiao directly if he had proved Hodge’s conjecture.

But as soon as he thought about it, he quickly shook his head. He couldn’t sit still like the other guys.

At this moment, he suddenly heard two more conversations coming from the side.

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

“Oh, he said that there will be another miracle in our mathematical world soon.”

“A miracle? What is that?”

“I don’t know either. Of course, since Professor Lin has said so, we can just look forward to it.”

“All right.”

“…”

When Andrew Wiles heard this conversation, he couldn’t help but raise his eyebrows.

“Miracle?”

It seems that his guess was probably right.

Feeling like a stone had fallen from his heart, he crossed his legs, changed to a comfortable sitting position, and continued to watch Lin Xiao’s performance quietly.

Lin Xiao, who was above, didn’t care at all what the audience was thinking. The old god talked about the contents of the report comfortably. It was so plain that only the wonderful discussion in the report could remind people that he was a man who had just He won the Fields Medal and was the youngest Fields Medalist in history.

He opened the PPT on the fifth to last page of his report and said: “So, finally we can get the correct statement about the integral Hodge conjecture.”

“That is: when The sum of classes and cohomology classes.”

“So far, we have obtained the correct integral Hodge conjecture. Now, we have completely pulled the geometry problem into the field of numbers, and even into the relatively simple field of differential calculus, instead of what it used to be.”

After hearing what Lin Xiao said, the mathematicians in the audience couldn’t help but nod. No matter what, the gold content of this report is high enough, and it can at least be ranked at the top of all reports this time.

Once the integral Hodge conjecture was proposed, it was enough to once again set off a frenzy of research on the Hodge conjecture in the mathematical community.

Of course, the premise is that the report ends here and Lin Xiao does not add those few lines at the end.

Of course, Lin Xiao’s next step was to talk about the next few lines that made most of the mathematicians present itchy.

So these mathematicians all sat upright and waited seriously for Lin Xiao’s next words.

However, Lin Xiao walked to the side unhurriedly, first picked up the water glass placed on the podium, took a sip, and moistened his throat.

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

nonsense!

Every mathematician who wanted to send Lin Xiao a blade rolled their eyes.

“But…” However, Lin Xiao changed the topic at this time and said with a smile: “Now that I have figured out the integral Hodge conjecture, I will naturally want to prove it. For this, I have paid a lot of money. A lot of work for a little effort.”

“And eventually…”

At this point, Lin Xiao stopped abruptly, making all the mathematicians in the audience who had pricked up their ears puzzled, and then they came to their senses.

Lin Xiao is deliberately tempting them again!

However, just when they were in a hurry, Lin Xiao took out something from his arms.

A colorful thing.

The people below looked at this scene and couldn’t help but be stunned.

This is?

A toy?

It is also 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. Those who know the name also say the official name “Slinky”.

But, why would Lin Xiao take this thing out now?

Of course, the mathematicians below finally showed expressions of “finally done.” Lin Xiao, as expected, came up with something a little different in the end.

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

Everyone present was waiting and watching.

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

He raised his head again and said with a smile: “This is a very interesting toy.”

As he said that, he also played with the toy. Of course, because he was not very skilled, he accidentally took off his hand while swinging it, and then the toy fell to the ground, causing a burst of laughter from the audience.

“Sorry, it seems 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 a toy. Just a toy.”

“However, in my eyes, or in the eyes of friends who study topology, this is a very classic one-dimensional topological homeomorphism.”

“Now, let’s try to describe it in numbers.”

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

Then he said: “Hodge’s conjecture studies the polynomial solution set of topological homeomorphisms in various dimensions.”

“The Hodge conjecture of the (1,1) class was proved by Lefschetz in 1924, which means that the Hodge conjecture is true for H^2. Hodge proposed this conjecture based on Lefschetz’s proof.”

“Then, the toy in my hand, as a one-dimensional manifold, is obviously able to hold Hodge’s conjecture.”

“But how do we extend this to higher dimensions?”

The question raised by Lin Xiao aroused the thinking of everyone below.

Yes, how to expand to higher dimensions?

At this time, Lin Xiao smiled and turned the PPT 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, please look at these lines.”

The mathematicians below suddenly showed a look of surprise.

These lines…

Didn’t the discussion start from the case of H^2?

If you say so…

All the mathematicians were suddenly shocked and looked at Lin Xiao excitedly. Does this mean that the proof of Hodge’s conjecture is no longer far away?

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

They all immediately looked at Lin Xiao, looking forward to his next words.

But at this moment, the PPT turned another page.

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

In addition, below this real-time time, there is a line of text.

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

“Thank you all, that’s the end of my story.” Lin Xiao said with a smile.

Everyone: “????”

Now that we’ve talked about it, are you still playing Fermat’s game?

Do you know that Fermat would have been beaten if it weren’t for the inconvenience of transportation?

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

Good guy, this kid is better at playing than him.

Even Fermat’s tricks were used!

However, didn’t Lin Xiao say that he would give everyone an answer at this conference, but now that your report is over, this is your answer?

This is even more exciting than the original report!

However, just before the crowd got excited, Lin Xiao smiled calmly and said: “If you are still interested in the next process, you are welcome to listen to my Fields Lecture the day after tomorrow, and I will continue to tell you the next content. .”

Fields Lecture the day after tomorrow?

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

However, if you put it this way, wouldn’t Lin Xiao have already reached the stage of Fields Lecture?

Everyone couldn’t help but marvel, perhaps only Lin Xiao could prepare the content of the Fields Lecture so confidently in advance, right?

“Okay, now everyone can ask questions, but time is limited, so I will only answer one question. Please understand.”

Lin Xiao said with a smile.

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

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

Then, he slowly said his question: “Lin, since you said that you have found a wonderful method that can extend the low-dimensional situation to high-dimensional, is it high-dimensional in a broad sense?”

Lin Xiao looked at Deligne, and then nodded seriously.

Deligne smiled happily: “Then I’ll look forward to the answer you will give us the day after tomorrow.”