Chapter 158 It turns out that other people's doctoral dissertations are like this

After Xu Yuan finished his entire report, he realized that he had exceeded the time originally stipulated by the conference. Although the conference did not remind him of this during his speech, he still politely apologized to the audience.

"Today's report is a bit long. I'm sorry to take up everyone's time."

He put a lot of effort into this report, mainly to prove the singularity of differential geometry.

Because of the particularity of the singularity, it is hailed by the entire academic community as the core problem of differential geometry.

He still used the method he had previously used to prove Qiu Chengtong's conjecture, combining methods from different branches of mathematics and innovating new formulas to finally successfully complete the proof.

So the process is relatively complicated.

Fortunately, today's report is just a report, and the core content is basically covered.

If I were to write a normal paper in detail, it would probably take more than a hundred pages.

However, what surprised him was that the lecture hall was extremely quiet and silent at this moment.

Everyone stared at the screen in a daze, their expressions seemed frozen on their faces.

Then, I don't know who took the lead and the others stood up and left through the back exit. Their speed was no slower than that of students leaving school.

Xu Yuan stood on the stage and watched this scene, and a question mark emerged in his mind.

"what's the situation?"

Based on past performance, shouldn't he be very excited at this time?

Even if you suspect the conclusion is not valid, you should at least raise your doubts on the spot.

Just as he was surprised, he soon noticed that Deligne and others who were sitting in the front row came up.

"I knew there would be a surprise when I came to listen to your report. Sure enough, my guess was right this time."

Deligne stopped in front of Xu Yuan and said with a smile: "Singularity is a core problem in differential geometry. You have proved it, which has taken the study of differential geometry a step further." It seemed that he didn't know how to praise Xu Yuan's contribution to mathematics.

At the same time, it was precisely because his guess was accurate that he became even more astonished at Xu Yuan's mathematical talent.

It has been less than a year since Xu Yuan proved Qiu Chengtong's conjecture.

Xu Yuan once again proved the singularity of differential geometry.

Every time he appears in the mathematics community, he brings surprises to everyone.

Although the study of singularities in differential geometry is not as well-known as twin primes and Yau's conjecture, it provides new mathematical tools for those who will study differential geometry in the future.

This situation contributes more to the development of the mathematical community.

However, he didn't know that Xu Yuan had actually been helping with projects at the Space Technology Research Institute for more than half a year.

Not totally absorbed in the singularities of differential geometry.

In other words, it didn't take Xu Yuan too long to prove the singularity.

It can only be said that as Xu Yuan accumulates his knowledge of mathematics and studies so many difficult problems in the branches of mathematics, his own mathematical level is constantly improving. With stronger abilities, it will be easier to study difficult problems with less effort.

For example, the new formula used in proving singularity was a combination of two formulas.

"Actually, I was planning to study singularities in differential geometry as the topic of my doctoral dissertation. But when I received the invitation from the conference committee, I just used it as the content of my one-hour report." Xu Yuan replied embarrassedly after hearing what Deligne said.

He was not talking nonsense at all. After discussing with the school, he would graduate in June next year if nothing unexpected happened.

According to the process, you must write a doctoral dissertation.

Because I had just started studying differential geometry with Tang Shihong, I chose this topic as my research topic.

When he received the invitation from the conference committee, he didn't want to use his previous paper to give a one-hour report, so he simply used the topic of his graduation thesis.

Of course, nowadays, giving a speech directly at a mathematicians' conference can be considered a special doctoral dissertation defense.

At that time, you can skip the defense phase and attend the graduation ceremony directly.

I believe the college would be happy to see this. After all, when I was defending my undergraduate thesis, the college had to find many well-known domestic professors to form the jury.

Now that Xu Yuan has even won the Gauss Prize, who else in the country is suitable to be a judge for the thesis defense?

It is better to graduate with a Ph.D. as soon as possible and work as a professor to do a better job.

Xu Yuan didn't take it too seriously, but he felt differently when Deligne and the other people around him heard it.

Naturally, they have all supervised graduate students and are very clear about the level of master's and doctoral dissertations, but they have never seen a paper that solved the core problems of differential geometry be used as a graduation thesis.

Any paper he writes is at this level. No wonder he won the Gauss Prize at the age of just over 20.

Just as everyone was secretly thinking about whether they should be more strict with their students when they returned, the atmosphere was suddenly interrupted by Wells.

"I have to go back and verify the conclusions, so I won't accompany you for now. We'll talk in detail in a couple of days."

The last sentence was obviously directed to Xu Yuan.

Almost as soon as he finished speaking, he walked through the middle and hurriedly left the lecture hall.

Deligne smiled and explained, "Wells must have become interested in your research on the singularities of differential geometry, so he wanted to go back and verify your conclusions. The same is true for the others who left."

When Xu Yuan heard this, he immediately realized that everyone was eager to verify the conclusion.

Only then could I leave impatiently. But thinking about it, it was normal, after all, there were really no good verification conditions in the lecture hall.

Just as the thought stopped here, Deligne's words suddenly came to my ears again.

"Wells is quite knowledgeable in differential geometry. Are you worried that your conclusions will be overturned?"

Hearing this, Xu Yuan remained calm, and it was obvious that he was already accustomed to this.

Mathematics is a rigorous subject.

Whenever someone announces the proof of a difficult problem, countless mathematicians verify it, which also ensures that there are errors in the proof process.

Even when Perelman proved the Poincaré conjecture, it took two or three years for the Clay Mathematics Institute to officially announce to the academic community that the Poincaré conjecture had been successfully proved and solved.

On the contrary, if no one is interested in the published paper, it is truly worthless.

Therefore, in response to Deligne's question, he immediately uttered a few words in the affirmative answer with confidence.

“I am confident in my conclusion.”

"I believe that," said Deligne, nodding.

He had been reviewing Xu Yuan's paper from the very beginning, so he knew very well that if Xu Yuan was not confident, there would be no report today.

Kang Kebi, who was standing nearby, waited politely until the conversation between Xu Yuan and Deligne ended before he took the initiative to express his feelings at the moment.

"Thank you very much for letting me listen to such a wonderful lecture. It turns out that you are a well-deserved Gauss Prize winner."

There is no doubt that Kang Kebi was very excited at this moment. The Gauss Prize was awarded for the first time to such a mathematical genius, and he also proved the singularity of differential geometry at the conference.

This will naturally increase the value of the Gauss Prize.

To some extent, Xu Yuan and the Gauss Prize can be considered as mutual achievements.

"I would also like to thank you for giving me the award." Xu Yuan thanked Kang Kebi with a smile.

Even though the two of them were just chatting for a few simple sentences, they became much more familiar with each other, and the smiles on their faces never disappeared while they were talking.

Then Kang Kebi and Deligne did not stay for long. They said hello to Xu Yuan and left with the remaining small group of people.

At this moment, there were only three people including Terence Tao left on the stage.

"Your report today is much better than mine. If those scholars in the field of differential geometry knew about it, they would probably be so happy that they couldn't sleep at night."

Tao was speaking half-jokingly, but the first sentence was clearly a heartfelt sigh.

After all, who could have thought that Xu Yuan would have new results so soon and announced them directly at the Mathematicians' Conference? It is 100% certain that he cannot compare with him.

There are some things you have to admit.

Xu Yuan was humble when he heard this: "We are still verifying whether the conclusion is valid."

"I still have great confidence in you," Tao Terence continued.

As soon as he finished speaking, another overseas Fields winner next to him couldn't help but speak in English to add to his comments.

"You are the most gifted mathematician I have ever met, Xu. Although my main research area is not differential geometry, after listening to your report, I can feel the rigor of the entire proof process. I think no matter how much verification is done, it cannot change the fact that the singularity of differential geometry has been proved."

"Thank you." Xu Yuan expressed his gratitude to him.

"Your contribution to mathematics qualifies you for the Fields Medal." The remaining overseas scholar also echoed.

Soon when there was no one else left in the lecture hall, Xu Yuan turned around and left without wasting any more time.

However, he did not leave the venue, but walked towards the lecture hall where the group reports were held.

Prepare to see how Ma Zhiming and Zhang Yitang's 45-minute report goes.

It is worth mentioning that Xu Yuan made a big move at the report meeting.

He successfully proved the singularity of differential geometry, which attracted many mathematicians to verify it.

The content of the report has already been submitted to the conference and will be released to the outside world through special channels, so everyone attending the conference can see the paper and verify it at the first time.

The result is that everyone stays in their hotel rooms and does not go out to verify the conclusions.

As a result, no one attended the subsequent lectures, which suddenly seemed a bit deserted.

If the live scene were filmed and released, people would probably think that the International Congress of Mathematicians was no longer viable.

-

Wells locked himself up in the hotel for the past two days, and even had the waiters deliver his meals to his door. Because everyone knew how Wells was when he was immersed in a problem, no one, including Deligne, came to disturb him.

That morning, Wells was lying on the hotel table, with scattered handwritten draft papers under his feet.

But he didn't care at all. After writing the last formula, he stared at the result on the draft paper, and then he quickly fell into ecstasy.

"The conclusion is indeed valid. Under a certain geometric background, singularities have a specific structure."

After saying this, he didn't care about his own image and pretended to get up and leave. He couldn't wait to talk to Xu Yuan.

(End of this chapter)