Chapter 191 Mathematical Miracles
"According to the sieve formula just mentioned, Theorem 28 is obtained from (8), Lemma 9 and Lemma 1."

"Therefore."

“（1，1）及Px（1，1）≥……（logx）2”

"Proof completed."

In the main venue of the Mathematics Exchange Conference, in the largest lecture hall, Xu Yuan’s report finally came to an end.

While giving the final narration, he picked up a pen and quickly wrote mathematical formulas on the blackboard next to him.

When the final conclusion was reached, all the mathematicians in the lecture hall stood up spontaneously and paid tribute to Xu Yuan with the warmest applause.

Although everyone present was much older than Xu Yuan, they were all convinced at this moment.

He was still immersed in the content of the report just now.

Long lasting aftertaste.

At the same time in other lecture halls, although they could only see the real-time broadcast, they also stood up and applauded enthusiastically, with excitement visible on their faces.

The applause lasted for several minutes before gradually dying down.

But many people still had happy smiles on their faces.

Professor Wells, Fields Medal winner Terence Tao, and other well-known scholars in the academic community, including representatives of the International Mathematical Union, also came over to talk with Xu Yuan.

Unfortunately, Deligne could only communicate via satellite conference and was unable to be present to witness the presentation.

“It’s really wonderful.”

"Whether it is the improved combination of sieve methods or the clever use of group theory, the perfect combination of them is simply a mathematical miracle."

Wells's area of ​​expertise is not number theory, but after listening to Xu Yuan's report, he could still feel the subtlety of it.

Without having time to think about the words of praise, I blurted out these two sentences subconsciously.

Originally, he considered that number theory was not his forte, so he organized a number theory group in the institute to verify the paper, so he did not read much of the specific content of the paper.

After listening to Xu Yuan’s live report today, he finally realized how brilliant this paper is.

I want to combine different sieving methods and branches of mathematics together to complete the proof of a certain problem.

Any unreasonable loophole will make it impossible to solve the Goldbach conjecture.

And other people will also find the mistakes and falsify the proof process of the entire paper.

But Xu Yuan solved this problem perfectly.

Almost a month has passed since the paper was published in the Journal of Mathematics and the Mathematics Exchange Conference was held today, but no one in the mathematics community has been able to prove that there are errors in Xu Yuan's paper.

This is enough to illustrate the problem.

Terence Tao, who was standing next to him, was also quite moved after Wells finished speaking.

He raised his eyes to look at Xu Yuan and said solemnly: "My mathematical thinking and level in the field of number theory are not as good as yours."

"When I was studying the Goldbach conjecture, I was still using a more traditional proof method, so I had no clue for a long time."

"I couldn't even determine the general direction, and wasted a lot of time."

"After reading your paper, and especially listening to today's detailed report, I finally realized how wrong I was."

At this moment, he had a very clear understanding of the gap between himself and Xu Yuan.

It's not just the level of knowledge.

It is more of a gap in mathematical thinking.

For example, even when Xu Yuan was studying the Goldbach conjecture for the first time, he dared to use a bold proof method with unpredictable results, and was not afraid of wasting time and failing to prove it in the end.

Instead, he started from the experience left by his predecessors and his proof method was relatively conservative.

And it is precisely because of the completely different mathematical thinking that the results are so different.

Xu Yuan was bold and innovative and solved the Goldbach conjecture in just one year, but his conservatism prevented him from even getting started.

So he was the only one who wasted time.

But the thought stayed here. To some extent, he should even thank Xu Yuan.

After all, if Xu Yuan hadn't solved the Goldbach conjecture so quickly, he would have wasted a lot of time on it.

Now that things have come to this, there's no need for him to keep it a secret and then take it back.

So he smiled awkwardly, and after organizing his words, he continued, "I should thank you. At least now I don't have to waste time on the Goldbach conjecture, and can focus on problems in other fields."

However, when Wells heard this, a look of joy instantly appeared on his face and he leaned forward.

"You've won the Fields Medal in your thirties, so your mathematical talent is pretty good. If there aren't any new mathematical topics, I suggest you study the Millennium Prize problem."

"If you can really solve one of these problems, your reputation in the mathematics community might surpass Xu Yuan's."

Wells did not miss this good opportunity and immediately tried to direct Tao's focus to the Millennium Problem.

Although Xu Yuan has completely surpassed Terence Tao in terms of mathematical talent and strength, the fact that he is called the Mozart of mathematics by the academic community is enough to prove that his level has reached the level of mathematical genius.

If we study the Millennium Prize problem, perhaps we can really get some results.

In addition, what he said was indeed correct, as long as Terence Tao can prove the problem of the Millennium Prize.

His reputation as the Mozart of mathematics may soon surpass Xu Yuan's reputation as the Prince of Mathematics.

When Terence Tao heard Wells's words, he didn't know whether to laugh or cry, but he didn't directly deny it.

"Thank you very much for Professor Wells's advice. I will definitely consider it carefully when I return." "Oh!"

"There are still too few mathematicians studying the Millennium Prize problems." Wells sighed and waved his hand.

I remember when the Clay Mathematics Institute first proposed the Millennium Prize, the entire mathematics community was shocked.

After all, in the field of mathematics, there has never been a mathematics prize with such a generous prize money.

Therefore, when the news came out, it immediately attracted the interest of many mathematicians, and they all devoted themselves to proving the Millennium Prize problem.

Although everyone was full of confidence at the beginning and believed that with the strength of the entire mathematics community, they would definitely be able to achieve results and win the award.

However, only after truly getting involved did you realize how difficult it was.

All we can say is that since these seven difficult mathematical problems in the world can be listed, they are not easy to prove.

After all, many of these difficult problems have been raised for many years.

But no one has been able to prove it.

After finally being hit by the reality, fewer people chose to study the Millennium Prize problem.

Up to now, only Perelman has completed the final proof of the Poincare conjecture.

After listening to the conversation between the two, Xu Yuan calmed down Tao Zhexuan's mood a little.

I’m afraid that the other party will be too stimulated and dare not study the problem anymore.

"I chose to use the sieve method and group theory to prove the Goldbach conjecture, which was quite bold. In order to ensure the rationality and rigor of the formula, the difficulties that needed to be overcome far exceeded my imagination."

"But at that time, I had no choice but to go all the way and continue to deduce."

"I was able to successfully solve the Goldbach conjecture. I guess I owed a bit of luck to it."

Tao Zhexuan listened to everything Xu Yuan said and naturally understood that this was done to take his feelings into consideration.

After all, he was not stupid enough to really believe that Xu Yuan proved the Goldbach conjecture by luck.

However, the two of them understood each other tacitly, and they smiled at each other and temporarily ended the topic.

At this time, the member of the International Mathematical Union who had been silent all this time finally made a comment for the first time.

"You're growing up fast."

"I heard your report at the last International Congress of Mathematicians, and today's report is much better than the last one in every aspect."

"It looks like the Fields Medal will soon have its youngest winner in history."

To be honest, with Xu Yuan's current level of mathematical achievement, he is no longer so concerned about the Fields Medal.

Even if I win this award, it is only to fulfill my previous promise.

Received a gold medal in mathematics.

Therefore, when he heard that he had a high probability of winning the Fields Medal, his expression did not show much emotion.

Just turn around and thank the other person.

On the contrary, other domestic mathematicians in the lecture hall showed visibly joy on their faces when they heard this.

After all, the Gauss Prize that Xu Yuan won was the first medal awarded to the mathematics community, so its influence naturally cannot be compared with the Fields Medal.

You have to know that the Fields Medal has been awarded so many times since its establishment, but there is still no record in China.

If Xu Yuan wins the Fields Medal as the youngest winner, it will completely fill the gap in this field in China.

Since Xu Yuan's report lasted for several hours, there were no other arrangements for the conference that day.

However, people can communicate and discuss on their own in branch venues and outside venues.

It is also worth mentioning that the content of Xu Yuan’s report was uploaded to the Internet by the conference organizers, which can be regarded as satisfying the regrets of those mathematicians who were unable to attend the conference for various reasons.

But the most watched people are ordinary netizens outside the mathematics community.

Even though I couldn't understand it at all, it didn't affect the playback.

Many people even left messages in the comment section, making it a gathering place for fans to build a group and check in.

"Is this Professor Xu's report on the proof of the Goldbach conjecture? I really don't understand a word of it."

"At least you need to be a mathematics graduate student to understand this, right?"

“I, a PhD in mathematics, can’t figure it out.”

"I took a look and it's only a little over two hours long. I'll finish it to support Professor Xu."

"I've decided to play it for my one-year-old son after get off work. Maybe it will help him develop mathematical abilities."

"Who am I, where am I, what am I doing..."

“I can only describe it in a few words: I didn’t feel the clear calendar, but seeing so many mathematicians applauding for so long, I suddenly felt very proud.”

……

This evening, Xu Yuan did take some time to surf the Internet. Seeing that everyone was willing to take the initiative to learn about mathematics, he felt very happy because at least he knew that he was not wasting his time.

In a blink of an eye, it was the second day of the mathematics conference, and Xu Yuan arrived at the main venue early to prepare.

After all, he had to guide the selected scholars in writing papers, and the workload was much greater than yesterday's report.

(End of this chapter)