Chapter 169 Studying the Goldbach Conjecture

"You should have an idea of ​​the topics for the Young Elite Scientists Program, but you must ensure that they can be completed on time."

When Xu Yuan heard Tang Shihong's words in the car, he naturally understood that this was a sign of concern for him.

Although the other party had not asked about the subject before, in order to reassure the other party, he answered the question truthfully without hesitation.

“It’s a topic in the field of number theory.”

Tang Shihong was worried that he would influence Xu Yuan, so he did not express his opinion on the Young Elite Scientists program.

But he knew very well how much Xu Yuan liked to challenge himself, and his previous graduation thesis was the best proof of this.

In addition, Xu Yuan did not rely on the team in the process of studying mathematics. If he had really chosen a difficult topic, applying for the Young Elite Scientist award might have become a bad thing. But now he is relieved.

Number theory is the branch of mathematics that Xu Yuan is best at. Even the twin prime conjecture can be proved to be less than 246 prime number pairs.

At this level, it seems safer to choose number theory as the topic of the Young Elite Scientists Program.

Relaxed, Tang Shihong's face lit up with a smile.

"I feel much more relieved that you can choose the field of number theory, which you are good at, as your research topic."

"I was worried that you would choose another unfamiliar branch of mathematics."

"Once the project is officially approved, with your ability and some new discoveries, I think you can finish it ahead of schedule."

Xu Yuan's lips moved slightly when he heard this, but since he didn't find the right time to speak, he finally chose to remain silent.

Anyway, we have already arrived, so it won’t be too late to talk about other things after the defense is over at the meeting.

that's it.

Soon Xu Yuan and Tang Shihong came to the National Natural Science Foundation of China.

After parking the car and entering the building, Tang Shihong went to the special lounge as an accompanying person.

Xu Yuan had to go to the Department of Mathematical and Physical Sciences to wait for his defense.

"I won't say anything more, just go over there quickly."

Tang Shihong did not say any words of encouragement to Xu Yuan. After all, the person standing in front of him was a Gauss Prize winner, not just an ordinary doctoral student in science.

In response, Xu Yuan just nodded and temporarily separated from Tang Shihong.

With his various documents, Xu Yuan walked into the waiting area and found that many people were already sitting there.

There is no doubt that they are all here to participate in the defense.

However, Xu Yuan knew that the mathematics and physics projects were not as good as those in other academic departments every year.

There will be more people who want to come to other places to participate in the defense.

Of course, being able to attend the defense meeting only means you are qualified to receive the Young Outstanding Scientist award.

Whether the final project topic can be passed depends on the performance of the defense, the applicant's level and academic achievements, and the value of the project.

After all, the establishment of the Young Elite Scientists Program is mainly to cultivate academic leaders and enable the country to have more outstanding talents.

If the project you apply for is worthless, then even if you are excellent, you will most likely not be approved.

Otherwise, what is the difference between that and defrauding funds?

The doctoral students present at the Department of Mathematical and Physical Sciences waiting for their thesis defense were naturally familiar with Xu Yuan.

It is no exaggeration to say that many people even regard Xu Yuan as an idol.

When he saw that Xu Yuan had also applied for the Young Outstanding Scientist Program, he stood up from his chair excitedly.

However, due to the on-site discipline, I could only express my inner emotions through facial expressions.

Xu Yuan also didn't say anything about this.

With a warm smile on his face, he responded to these people with his eyes.

After finding a seat and sitting down, everyone calmed down and focused on the defense.

Review in your mind what you are going to say next.

Being able to complete a doctorate and be qualified to attend the defense meeting can be said to be very outstanding among his peers. He must have gone through a lot of similar defenses and has rich experience.

But now that I was about to go in, I couldn't help feeling nervous.

But there is nothing that can be done about it. After all, the value of the outstanding young talent is there.

The defense judges are mainly academicians, so even if a professor comes, you have to be fully prepared.

Looking at the entire waiting area, Xu Yuan was the only one who remained calm.

Have confidence in yourself.

Time passed by minute by minute, and as people walked into the lecture hall to defend their thesis and then came out again, it invisibly put a lot of pressure on the people behind them.

At this moment, the on-site assistant came out and called out a name that everyone was very familiar with.

"Next is Xu Yuan."

When Xu Yuan heard his name, he immediately stood up and answered, then followed the other party into the lecture hall.

When others saw this scene, they were extremely envious.

I wasn't worried about Xu Yuan at all.

After all, if Xu Yuan couldn't get the Young Elite Scientist award despite his academic achievements in mathematics, then these people could just leave.

-

Soon Xu Yuan walked into the defense site, and was stunned when he saw the figures on the judges' panel.

Ma Zhiming, who was sitting in the middle, was not surprised, but most of the others had attended the Mathematicians' Congress, which was unexpected. The judges at the defense were all acquaintances, and to some extent, it was no different from a formality.

Ma Zhiming naturally noticed the change in Xu Yuan's expression, and then he put on a smile and spoke something.

"Don't be nervous, just start your speech."

After hearing this, Xu Yuan did not think any more and immediately opened the presentation he had prepared long ago, ready to explain the topic of his Young Elite Scientists project.

Both Ma Zhiming and other judges on the scene were very aware of Xu Yuan's mathematical talent.

A single undergraduate thesis can study optimal transmission theory.

Now that they are applying for Young Elite Scientists, they are naturally looking forward to what the project topics will be.

Therefore, after the speech officially began, everyone's eyes were focused on Xu Yuan, and it can be said that he seemed very serious.

If other PhDs outside saw this scene, they would probably think that Xu Yuan was giving a lecture to a group of bigwigs.

When Xu Yuan's presentation appeared on the screen, everyone's eyes widened when they saw the title on the homepage, and Academician Ma Zhiming couldn't help but exclaimed.

"Proof of the Goldbach conjecture!"

Yes.

The topic that Xu Yuan decided to study was the Goldbach conjecture, which is also the ultimate problem in number theory.

As a difficult problem that has existed for more than two hundred years, it was first raised by Goldbach, who wrote a letter to the then famous mathematician Euler for advice, hoping that Euler could help prove it.

Unfortunately, it was not proven until Euler's death.

This has become an unresolved problem in the mathematical community.

The last progress was half a century ago, when Chen Jingrun proved that 1+2 was valid through the sieve method.

That is, any sufficiently large even number can be expressed as the sum of two prime numbers, or the sum of a prime number and a semi-prime number.

The so-called Goldbach conjecture, if studied using the almost prime number approach, assuming N is an even number, although it cannot be proved that N is the sum of two prime numbers, it is sufficient to prove that it can be written as the sum of two almost prime numbers.

Expressed as N=A+B
Therefore, every large even number N can be expressed as A+B, where the number of prime factors of A and B does not exceed a and b respectively.

In this way, the Goldbach conjecture can be written as 1+1.

But unfortunately, half a century ago, Chen Jingrun only proved the Goldbach conjecture to 1+2 by using the sieve method.

The Goldbach conjecture has not been completely solved.

However, even though he only proved 1+2, Chen Jingrun's name is still widely known among mathematicians.

Xu Yuan chose to study the Goldbach conjecture because he wanted to completely complete the proof and make up for Mr. Chen Jingrun's regret.

After all, when he published his first paper proving the problem of the intervals between infinite Carmichael numbers, he was improving on Chen Jingrun's sieve method.

The twin prime conjecture and the Goldbach conjecture are both known as the ultimate problems in number theory.

Although he made some progress in twin primes by chance and proved that there were less than 246 prime pairs, he failed to win the championship and complete the final proof.

This is also a pity for him.

Since there is no clue about the subsequent proof of twin primes, it is better to take a different approach and choose the Goldbach conjecture.

In addition, he chose this conjecture as his research topic after careful consideration.

First of all, number theory is the branch of mathematics he is best at, and he has made many improvements and innovations in the sieve method.

With the experience in studying the twin prime conjecture, it is perfect for proving the Goldbach conjecture.

The project cycle of the Young Elite Scientists Program is several years, which is the most prosperous battle he has ever experienced since he started studying mathematics. He is even confident that he can complete the project ahead of schedule with deep learning.

But the Goldbach conjecture is the ultimate problem in number theory after all, and it has been weighing on the shoulders of mathematicians for many years.

One can imagine what kind of uproar his research topic will cause in the academic community once it is made public.

No matter how confident he is, I believe there will certainly be many voices of doubt in the academic community.

Because of this, when Tang Shihong asked him about specific topics in the car, he only answered the field of number theory in which he was good at.

It is not pointed out that it is Goldbach's conjecture.

Otherwise, Tang Shihong would definitely be worried.

At this time, Ma Zhiming and other judges on the jury saw that Xu Yuan's outstanding young scholar project was really about studying the Goldbach conjecture, and they didn't know what to say for a moment.

Xu Yuan’s mathematical talent and level are indeed very strong, but this is, after all, the ultimate problem in the field of number theory.

What's more, Chen Jingrun has already advanced it to 1+2.

It stung Xu Yuan that he could prove it thoroughly and push the result to 1+1, otherwise his achievement would probably not be as good as the progress on the twin prime conjecture.

However, if Xu Yuan can really prove the Goldbach conjecture, it will undoubtedly be good news for the Chinese mathematics community.

The benefits that can be brought are absolutely unimaginable.

And the most crucial point is that as judges, they naturally cannot ask Xu Yuan to change the topic.

So I can only continue to listen patiently.

In addition, there is no reason to deny Xu Yuan's topic, so it is basically the same as being finalized.

Xu Yuan had no idea what the judges were thinking at the moment. After getting into the state, he immersed himself in his presentation. He gave a relatively detailed explanation of the importance of the Goldbach conjecture, as well as the initial ideas and research directions.

After finishing his speech which took dozens of minutes, he waited patiently for questions from the judges.

Anyway, he was very confident in his topic and was not worried that the judges would ask questions that he could not answer.

(End of this chapter)