"Sure." Zhao Xiancai replied to Deligne.

"Oh? What is it?" After hearing Zhao Xiancai's answer, Deligne asked with interest.

"As for number theory, I actually want to develop a new set of mathematical methods of my own.

However, in the previous research problems, although I have used some new and slightly breakthrough methods, these methods are not systematic, and they are not as complete as the methods established by Peter Scholze.

So I want to study some more difficult number theory problems and take this opportunity to develop a new mathematical method of my own."

Zhao Xiancai told Deligne that things like mathematical methods and mathematical theories need to be studied when solving mathematical problems. After all, these things only appear to solve mathematical problems.

If a new mathematical method or new mathematical theory cannot solve any mathematical problem, then it will be useless no matter how new the method is.

Just like Fermat's Last Theorem, why has it always been so popular? Even though it has been solved now, many people are still studying it.

This is because many mathematicians were able to create some new mathematical methods when studying Fermat's Last Theorem, and the new mathematical methods they created can be used to solve other mathematical problems.

The so-called p-adic perfect space theory established by Peter Scholze is actually somewhat related to Fermat's last theorem.

Fermat's Last Theorem is like a chicken that lays golden eggs. Even though this problem has been solved, many people still try their luck to see if they can encounter their own golden eggs.

"About number theory? Riemann Hypothesis?"

After hearing Zhao Xiancai say that the problem he planned to study next was number theory, Deligne's first thought was the Riemann Hypothesis.

Because the "standard conjecture" that Deligne is currently studying is actually related to the Riemann Hypothesis.

If the "standard conjecture" can be proved, then one can extend Weil's proof of Weil's conjecture about the curve case to the case of algebraic varieties of arbitrary dimensions by replacing the Jacobian of the curve with the motive theory of the cluster, and it can be deduced that

Riemann hypothesis.

"I haven't thought about solving the Riemann hypothesis yet. I am going to solve the twin prime conjecture. If this conjecture is not enough for me to perfect the new mathematical method I created, there is also the general method proposed by Alphonse de Polignac.

Guess." Zhao Xiancai said.

[Recommended, the Huanyuan app is really useful for chasing books. Download it here. huanyuanapp. You can try it soon. 】

“The twin prime conjecture?

I remember that the last person who made a breakthrough in the twin prime conjecture was also a Chinese. He seemed to be teaching in the Department of Mathematics at the University of New Hampshire.

But now he has been invited by the president of the University of California, Santa Barbara to teach in the mathematics department there.

It seems that you Chinese people all have a unique hobby for the twin prime number conjecture?"

After hearing Zhao Xiancai say that what he planned to study next was the twin prime number conjecture, Deligne also smiled and said.

"No, I just feel that the problem of number theory can be solved by almost all branches of mathematics, so I chose this." Zhao Xiancai explained.

"In this case, I won't force you to join my research project.

However, if your research on the twin prime conjecture has not made any progress within a year, then I suggest you change your direction."

Deligne then told Zhao Xiancai that he was actually not very worried that Zhao Xiancai could not solve the twin prime conjecture, but being able to solve it and how long it would take to solve it were completely different things.

Although Zhao Xiancai spent a very short time solving the Erdős arithmetic sequence conjecture and the construction problem of Abelian expansion in the whole real field, the field of difference between the twin prime number conjecture and the first two problems is still quite large after all, and

The solution to the twin prime conjecture problem is also more difficult.

Therefore, it is best to explain some things clearly in advance.

"Professor, don't worry, one year is enough." Zhao Xiancai said.

With the system in place, if he still couldn't solve the twin prime number conjecture problem in one year, wouldn't all his points have been in vain?

"I don't have much research on the twin prime conjecture, but... the mathematical method used by the Chinese who proved the existence of infinite pairs of prime numbers with gaps less than 70 million last time may not be used to prove the existence of infinite prime numbers p

, so that p 2 is prime, you have to find another way."

Although Deligne did not do much research on the twin prime conjecture, he still tried his best to give Zhao Xiancai some suggestions.

"Professor, I know this. The Chinese who published the title "Bounded Intervals between Prime Numbers" in the "Annual Review of Mathematics" was my senior. Like me, he came from Peking University.

I also know something about his paper and the views of his method in the mathematical community.

From the time his paper was made public on the Internet on May 14, to February of the following year, the gap of 70 million had been narrowed to 246 by other mathematicians, but that was all."

Zhao Xiancai had already known about Professor Deligne's suggestion.

After that, Deligne talked with Zhao Xiancai about other things. In fact, before Zhao Xiancai came, professors from Princeton University had talked together, and they all wanted Zhao Xiancai to join their projects.

…

Before conducting research on the twin prime conjecture, Zhao Xiancai was ready to get his driver's license from the United States first, so he quickly found Zhang Ruixiang.

"I have to trouble you again, senior brother." After finding Zhang Ruixiang, Zhao Xiancai said to him with some embarrassment.

"It's nothing troublesome, and I feel it's much more useful to talk about math with you than in class.

However, don’t say this everywhere. Some professors in our school are a bit petty. If they listen to me, I won’t feel good about it.

In fact, the attitude of the professors towards us graduate students is pretty good. Some Princeton professors look down on undergraduates, or rather they don’t look down on them, but they don’t really like teaching to them. They prefer to do their own research, and teaching is important to them.

It's just a necessary task to stay here and do research.

But they are quite tolerant of us graduate students, because we graduate students can help them do a lot of things.

In fact, compared to some other private universities in the United States, the one-to-one communication time between Princeton teachers and students is actually relatively small.

Although each professor is obliged to define 90 minutes of tutoring time every week, and all students can go to the professor's office to seek study help during this time, but... haha, you know, there are policies and countermeasures, this

This applies everywhere.

Forget it, let’s not talk about this, let’s talk about getting a driver’s license...”

Soon, Zhang Ruixiang and Zhao Xiancai talked about the rules for taking the driver's license here.

next chapter
Chapter completed!