After leaving the award ceremony of the Cole Prize in Number Theory, Zhao Xiancai returned to the hotel, packed his luggage and rushed back to Princeton.

Moreover, after returning to Princeton from Atlanta, Zhao Xiancai went out less often than before.

When time came to the first day of school at Princeton University, a long-lost knock on the door pulled Zhao Xiancai from the world of mathematics back to the real world.

"I don't know many people here in Princeton, so why would someone knock on the door? It couldn't be Senior Brother Zhang again, right?"

After hearing the knock on the door, Zhao Xiancai thought to himself as he walked to the door and opened it.

"Professor Deligne?"

After opening the door and seeing Deligne standing at the door, Zhao Xiancai said with some surprise.

"Yes, it's me. Are you surprised to see me?"

After seeing Zhao Xiancai, Professor Deligne also smiled at Zhao Xiancai.

"I'm a little surprised. I didn't expect you to come over. Please come in."

As Zhao Xiancai spoke, he invited Professor Deligne into the room.

Since Zhao Xiancai had been studying Polignac's general conjecture in seclusion since he came back from Atlanta last time, his beard and hair had grown a lot at this time.

Even Professor Deligne was a little surprised when he saw his unkempt appearance.

"I know you are currently studying Polignac's general conjecture. How is your research going?"

After being invited into the room by Zhao Xiancai and sitting down, Professor Deligne asked Zhao Xiancai.

"Fortunately, as I expected, it was solved before the holiday ended. It was solved last night. I was just verifying my proof process."

Although he didn't know why Professor Deligne came to see him, Zhao Xiancai truthfully told the truth about his research on Polignac's general conjecture.

"Solved? Do you mean that you solved all the general conjectures raised by Polignac? Did you prove his conjecture or disprove it?"

Although I feel in my heart that Polignac's general conjecture must be correct, it's just that people have never found the correct way to prove it.

But after Professor Deligne learned that Zhao Xiancai said that he had solved the general conjecture raised by Polignac, he was still very surprised and asked this question.

"Proved, but for the proof of Polignac's general conjecture, I modified the method that Zhang Yitang used to prove that there are infinite pairs of prime numbers with gaps less than 70 million. First, I proved that Polignac's general conjecture is

This is true when a relatively large number reaches infinity.

After that, I designed a program and used the program to prove numbers smaller than that amount, which proved the Polignac general conjecture."

Zhao Xiancai explained.

"However... when I was verifying it just now, I suddenly had inspiration and discovered a proof method that seemed to be more concise and convenient.

If this method is feasible, my proof process can be at least half as long as before."

Zhao Xiancai continued.

"I didn't expect you to prove Polignac's general conjecture so quickly.

Moreover, your experience in the proof process is somewhat similar to the proof of the weak Goldbach conjecture a few years ago.

It seems that I really came to the right place this time.

However, it seems that I didn’t come at the right time, because I seemed to have interrupted your thinking about a simpler and more convenient way to prove Polignac’s general conjecture.”

After listening to what Zhao Xiancai said, Professor Deligne said the same thing.

Deligne has experienced many things in his life and has seen many geniuses, but this is the first time he has seen someone like Zhao Xiancai solve various mathematical problems in units of months.

The proof of the weak Goldbach conjecture he refers to is Harold of Peru in 2013, who proved that any odd number greater than 10^30 can be written as the sum of three prime numbers.

As for those below 10^30, they were calculated one by one, verified in this way, and finally passed the verification. After all, computers today are very powerful.

In this way, part of the proof is derivation and part is verification, and the weak Goldbach conjecture is completely proved.

"Perhaps, in my lifetime, I can really see Goldbach's conjecture and Riemann hypothesis proven, and the hope lies in him.

Francis is indeed right, the 21st century may indeed be a legendary century, at least for the field of mathematics."

After finishing speaking, Professor Deligne looked at Zhao Xiancai, who was unshaven and had very fluffy hair, like a chicken coop, and thought to himself.

"That's okay. I already have a prototype in my mind about that method, and your arrival didn't affect anything.

But, Professor Deligne, what do you mean when you say you are at the right time?"

Zhao Xiancai finally asked Professor Deligne about his purpose of coming to see him this time.

"I came here mainly for two things. One thing is that before I came, the school was still discussing whether to let you graduate early now.

Their disagreement is not that they don't want you to graduate early. After all, as a winner of the Ramanujan Award and the Cole Number Theory Award, now all over the United States... No, it should be that major universities around the world want to attract you to become a professor in their schools.

Their disagreement is whether they want you to graduate now or wait until the next batch of graduates graduates to graduate with them.

However, it seems now that once I tell them that you have solved the general conjecture raised by Polignac, few people will stop you from graduating now.

What I want to ask you is whether you want to graduate now.

The second thing is about Alexander Grothendieck.

He was my supervisor when I was a doctoral student. I completed my doctoral thesis under his guidance. He is also the teacher who has had the greatest influence on me in my life.

Since 1970, he had been away from the scientific community, and in 1990, he left all his mathematical writing manuscripts and settled in the Pyrenees.

From then on, he lived a secluded life, completely cut off from the research community.

Even in 2010, he requested a ban on the dissemination of all his writings.

But although my teacher has been away from academia since 1970, he has never given up his research in the field of mathematics, but those research results and many of his subsequent manuscripts have not been published.

Before he passed away in 2014, I was always by his side. I have some of his original manuscripts here.

As for more manuscripts, you will need to go to Europe."

After Zhao Xiancai inquired, Professor Deligne finally explained his purpose to Zhao Xiancai.

And after he finished speaking, he took out several well-packaged manuscripts and handed them to Zhao Xiancai.

At this time, Zhao Xiancai did not know that his indirect contact with Grothendieck, the deceased emperor of modern algebraic geometry and a mathematical genius of the last century, would bring him something unexpected.

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