When the time came to July, the international mathematical community still did not give a definite reply to Zhao Xiancai's proof of Goldbach's conjecture.

However, the two graduate students recruited by Zhao Xiancai came to report to him.

"This is Krag Appiah, and this is Yang Biwen. You are all familiar with it in the group, so I won't introduce you..."

When Yang Biwen and Krago Appiah came to report to Zhao Xiancai, Zhao Xiancai introduced them to each other.

Then, Zhao Xiancai said to the two of them: "There will be an assessment the day after tomorrow. There will be ten questions in total. Just be able to get five of them right.

If you have carefully read the books I recommended before, the final assessment results will definitely be within my expectations."

"Professor, what if the number of correct questions is less than five?"

Krager Appiah asked Zhao Xiancai that because he originally studied at Princeton University as an undergraduate, he had come to see Zhao Xiancai many times before Zhao Xiancai decided to recruit him as a graduate student.

Coupled with Krago Appiah's own personality, he would also ask directly about anything.

"If the number of correct questions is less than five, it only means that you did not do what I said. Then you have to continue to learn some basic knowledge in this first semester, and don't even think about getting involved in subject research.

I’ll see how you learn later. If you learn well, then I will let you get involved in research." Zhao Xiancai explained.

"So, professor, what is our topic? Goldbach's conjecture?"

Appiah asked again, but when he finally said Goldbach's conjecture, he immediately realized that it was impossible, because Goldbach's conjecture had been solved by his mentor.

And when he mentions this now, it seems that Zhao Xiancai's paper proving Goldbach's conjecture did not actually completely prove Goldbach's conjecture.

So after talking about Goldbach's conjecture, Appiah quickly explained to Zhao Xiancai: "Professor, what I mean is that our topic is about doing some sorting and explanatory stuff after you prove Goldbach's conjecture.

?”

For example, after Perelman published his article proving the Poincaré conjecture, many scholars began to analyze his paper, and many of them were full professor level scholars.

However, these professors are not doing useless work. The article Perelman published in the preprint library was the first of a series of articles.

Those articles did not simply prove the Poincare conjecture, but proved the geometric conjecture. A special case of this geometric conjecture is the Poincare conjecture.

The original research of those professors indeed helped more scholars better understand Perelman's paper that proved the geometrization conjecture.

Now it would make sense if Zhao Xiancai asked his two graduate students to study his paper on proving Goldbach's conjecture as their graduation project. After all, the new mathematical methods used in his article alone were enough for these two researchers.

Yes.

However, this was not the topic that Zhao Xiancai planned to arrange for them.

"I know what you mean, you don't need to explain, but the topic I'm going to assign you has nothing to do with Goldbach's conjecture.

After you take the exam the day after tomorrow, I will tell you the topic, and this will also be what you have to study before graduation."

Zhao Xiancai said that he did not directly mention the topics he planned to arrange for them.

Although Zhao Xiancai is currently doing some mathematical research, he can solve it in a few months in isolation.

But after all, there are very few people like him in the world, and there are even none alive now. Naturally, he will not think that these students of his can be like himself and only need a few to study a world-class mathematical problem.

The work of the moon.

If they were all like him, there would be no need for him as a mentor.

Hearing what Zhao Xiancai said, Appia became even more curious. Even Yang Biwen, who had been silent until now, was also a little curious. However, Yang Biwen did not ask. Anyway, he would know in two days.

Krag Appiah originally wanted to ask, but after he opened his lips slightly, he did not ask.

After communicating with his two students for a while, Zhao Xiancai asked them to leave. After all, they had just arrived at Princeton and needed to get familiar with the campus environment.

Soon, time came to the day when Zhao Xiancai would conduct an assessment on them.

The final assessment results were pretty good. Both Yang Biwen and Kraig Appiah answered more than five questions. No one needed to continue learning the basic content.

"It can be seen from the results of this assessment that you have indeed carefully read the books I recommended before, so I will tell you now what I plan to let you study...

What I am going to ask you to study is the Hardy-Littlewood second conjecture. Do you understand this conjecture?"

Zhao Xiancai explained.

"learn."

Yang Biwen looked at Zhao Xiancai seriously, nodded and said.

Kragg Appiah on the side was a little confused. He knew the Hardy-Littlewood Conjecture, which was proposed by British mathematicians Godfrey Hardy and John Littlewood in 1921.

So its name is also named after these two proposers.

The Hardy-Littlewood conjecture is a conjecture similar to the Polignac conjecture. It is often called the "strong twin prime conjecture" because this conjecture not only proposes that there are infinite pairs of twin primes, but also gives

Its asymptotic distribution form.

However, what Kragg Appiah didn't know was that the conjecture he knew was also called the Hardy-Littlewood first conjecture, and the Hardy-Littlewood second conjecture was also a conjecture in the field of number theory.

"Okay, then you tell me." After hearing what Yang Biwen said, Zhao Xiancai also said to her, just in time for Appia on the side to listen.

"The Hardy-Littlewood second conjecture, like the twin prime conjecture and Polignac's general conjecture that you solved before, is also a conjecture in number theory. It was proposed by the mathematicians G.H. Hardy and John.

Unther Littlewood proposed that it is related to the number of prime numbers in the interval.

The content of this conjecture is that when assuming that π(x) is a prime number in an integer less than or equal to x, π(x y)≤π(x) π(y) is true for x, y≥2..."

Yang Biwen said.

"Well, yes, it is indeed the case. The conjecture means that the number of prime numbers between x 1 and x y is always less than or equal to the number of prime numbers between 1 and y...

You probably won't be able to solve this topic in one year, but you can solve it as much as you can. Anyway, as long as you can publish at least one article in the "Annals of Mathematics" or a journal of similar quality.

Because if you don’t solve it, I will let your junior brothers and sisters come in from behind to continue studying this topic.”

Zhao Xiancai said.

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Chapter completed!