Zhao Xiancai knew what Professor Deligne's next plan was. He was not asking him what he wanted to do after becoming a professor, but asking him. Now that he had solved Polignac's general conjecture, he was ready to study

What is the mathematical problem of .

So after Professor Deligne asked, Zhao Xiancai also replied: "Next, I am going to study Goldbach's conjecture, but I will definitely not spend too much time on it in the short term."

"Do you want to go back to your country?

I know that it was the Spring Festival in your country a few days ago. This Spring Festival is the most important festival of the year for you Chinese people. During the Spring Festival, no matter where people are, they all have to go back and reunite together.

You didn't go back during the Spring Festival this year. Now that you've graduated, it's really time to go back and see your parents.

And after you finish your studies here and get your degree certificate and graduation certificate, you have to go back to your previous university to attend the graduation ceremony, right?"

It seems that Professor Deligne is quite familiar with some Chinese festivals and corresponding customs.

"Yes, the thread is in the hands of a loving mother, and the clothes are on the body of a wanderer.

When I was in college in China, I actually didn’t have much experience in this aspect. It wasn’t until I came here that I had more experience in this aspect.”

When he said this, Zhao Xiancai discovered that the poem "I am a stranger in a foreign land, I miss my family even more during the holidays" seemed more appropriate.

After all, the reason why he is more likely to feel homesick in the United States than in the capital is probably because many of the habits here are quite different from those in China, which makes him feel like "being a stranger in a foreign land".

a feeling of.

In the capital, because they were all in China, everyone around him spoke Mandarin, and the styles and customs were not much different, so Zhao Xiancai didn't have much of a feeling of being a "foreigner in a foreign land".

However, as for the things about his hometown, he has pretty much talked about them up to this point, and Zhao Xiancai did not mention the poem "I am a stranger in a foreign land alone, and I miss my family even more during the holidays."

And if you want to fully express the artistic conception of this poem in English, for Zhao Xiancai, who has not studied English very much, and who has no problem with daily communication and reading literature at Princeton, it is very difficult.

It's still a bit troublesome.

"The dean of our School of Mathematics at Beijing University contacted me a few days ago, about letting me go back to attend the graduation ceremony and degree awarding ceremony."

Zhao Xiancai once again talked about returning to Peking University to participate in the degree conferment. Although Yang Gang is no longer the dean of the School of Mathematical Sciences at Peking University, Zhao Xiancai still habitually calls him "his school" when talking to Professor Deligne.

long.

Zhao Xiancai only realized this problem when he said the word "dean", but he did not change his words and continued on.

"You want to go back, after all, it is also your alma mater.

As for Goldbach's conjecture, this is not urgent.

Goldbach guessed that even if you look at so many people doing research, there are still many people who have made some research results.

But its properties are completely different from those you have studied before, whether it is Erdez's arithmetic sequence conjecture, the later twin prime number conjecture, or the just-solved Polignac's general conjecture.

I'm not saying that the difficulty between them is different. After all, different mathematical problems have their own mathematical difficulty. I am not proficient in them all, and it is not easy to compare the difficulty between them.

I’m talking about their impact on the entire mathematical community, and even on society as a whole.”

Professor Deligne said to Zhao Xiancai.

Professor Deligne is indeed right. If Goldbach's conjecture and the twin prime conjecture are proved by different people at the same time, then under normal circumstances, the popularity of the person who proved Goldbach's conjecture will definitely be higher than that of the person who proved the twin prime conjecture.

High.

Goldbach's conjecture is called a bright pearl in the crown of the queen of mathematics, number theory. The title of the most solved conjecture is not obtained out of thin air.

"Professor, the weak Goldbach conjecture was proved in 2013 through part of the verification and part of the derivation.

The strong Goldbach conjecture was also proved to be ‘1 2’ as early as the last century.

What do you think is the reason why Goldbach’s conjecture has still not been solved until now?”

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Since Professor Deligne also mentioned Goldbach's conjecture, Zhao Xiancai also asked about it.

After all, Professor Deligne is already seventy-three years old this year. For Zhao Xiancai, a young man who is only twenty years old, he has really crossed more bridges than Zhao Xiancai has walked.

Therefore, when Zhao Xiancai asked him this, he really wanted to hear his opinion on Goldbach's conjecture.

As for the weak Goldbach conjecture and the strong Goldbach conjecture mentioned by Zhao Xiancai, the weak Goldbach conjecture refers to "any odd number greater than 5 can be written as the sum of three prime numbers", while the strong Goldbach conjecture refers to

The answer is "Any even number greater than 2 can be written as the sum of two prime numbers."

Among them, the Strong Goldbach Conjecture is the Goldbach Conjecture that people often mention. This conjecture is also called the Goldbach Conjecture about even numbers.

The weak Goldbach's conjecture is called the Goldbach's conjecture about odd numbers.

The reason why Goldbach's conjecture about odd numbers is called weak Goldbach's conjecture is because if you can prove the Goldbach's conjecture about even numbers, you will naturally prove the Goldbach's conjecture about odd numbers.

But proving Goldbach's conjecture about odd numbers does not prove Goldbach's conjecture about even numbers.

"Actually, if the person who is going to prove Goldbach's conjecture is not you but anyone else, I would be pessimistic about his ability to solve the problem of Goldbach's conjecture.

Because whether it is the circle method or the sieve method, they seem to be somewhat inadequate for studying Goldbach's conjecture.

At least as far as the current situation is concerned, when Chen Jingrun proved ‘1 2’ through the sieve method, the sieve method had already reached the end of Goldbach’s conjecture.

So I think that to truly prove Goldbach's conjecture, we can only make some improvements based on existing mathematical methods.

Otherwise, a completely new mathematical method would have to be created.

However, you can be said to be the smartest, most genius, and most mathematically gifted person I have ever met.

So you said that what you are going to study next is Goldbach's conjecture, which I am really looking forward to. And didn't you also say that you were going to study a brand new mathematical method before?

No matter whether it is the Erdős arithmetic sequence conjecture, the construction problem of Abelian expansion in the whole real field, or the twin prime conjecture and Polignac's general conjecture, they have not allowed you to explain what you are saying.

A complete set of mathematical methods was developed.

This Goldbach conjecture should be possible, right?"

Professor Deligne said that it seemed that through his contact with Zhao Xiancai, he was quite confident in Zhao Xiancai's research on Goldbach's conjecture.

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