From Almighty Scholar to Chief Scientist

"Yes, there is! Can you try to construct a new sequence!"

So he immediately threw Mimi on the table again, and immediately began to write on the draft paper, expressing the hint that came from inspiration with words as a carrier.

And Mimi looked at this owner who didn't know what was going on, just picked her up and masturbated for a minute, but then put herself back down again.

It made a "meow?", expressing its own questioning, but obviously, its new owner had no time to answer it.

Just like that, another 10 minutes passed. Lin Xiao let out a sigh of relief when he saw the result he got.

"It's still quite difficult. It's a problem that can get Tao Zhexuan stuck."

However, he finally got it done.

"Then, after proving this formula, I can continue to perfect this sieve method."

Now he can continue to study this mathematical tool following Terence Tao's thinking in this formula.

"But... After all, it was Tao Zhexuan's achievement a month ago, maybe he has already solved it?"

Lin Xiao thought about it, and decided to post his method under Tao Zhexuan's comment. No matter whether Tao Zhexuan solved the problem, but after all, he also used his idea, so he should let him know.

So he posted his derivation process under Tao Zhexuan's reply, and then continued to study.

He also didn't expect to get Tao Zhexuan's response immediately. After all, this happened a month ago, so it doesn't matter whether he still pays attention to it or not.

……

Across the Pacific, UCLA, UCLA.

As a world-renowned school, UCLA has a prominent position in mathematics, ranking No.7 in the world, and what supports its position in mathematics is naturally related to its faculty. There are three Fields Medal winners Serving as a teaching post here, Terence Tao, works here.

At this time, in Tao Zhexuan's office, he was surfing the Internet.

Although he is a famous mathematician, he is still very interested in surfing the Internet, just like their president. They have fought each other.

Of course, the place where he surfs is usually a place for mathematical academic discussions. At this moment, he is discussing problems with others on mathoverflow.

"Huh? Someone replied to me... Goldbach guessed that post."

That was all a month ago. To Zhexuan Tao, he doesn’t have much impression of him anymore. He studies things, and he just studies things if he is interested. That’s why Charles Fefferman of Princeton University would say, “If you meet If you have any problems, go to Terence Tao, as long as you can make him interested'.

Just like the other form of the weak Goldbach conjecture he proved at the beginning, it was also because he became interested and studied it carefully, so he accidentally completed the proof.

Of course, he has also seriously thought about a new screening method he discussed in this post.

However, since there were too many people replying to this post, he didn't pay much attention to it at first, but after glancing at it, he couldn't help but raise his eyebrows.

"Has it actually solved the problem I encountered?"

He would be interested to take a look at it.

So he entered the post and read the reply.

And soon, he couldn't help being surprised.

"So it can be like this! Why didn't I find out before?"

Chapter 1

Tao Zhexuan, who is used to being a genius, still admires those who can solve problems that he cannot solve.

Just like when he just entered Princeton University for a year as a Ph. He always talked about the field of mathematics by his side, and he also admired these students at that time, although later, these students became the admirers of him.

Now, this netizen he met on the Internet has actually solved his own problem, and he also admires it.

Of course, it is not ruled out that this is an acquaintance I know in reality.

So he looked at the person's name.

"Xiao Lin?"

As a Chinese born in Australia, he can even speak Cantonese. When faced with this name, he naturally recognized it as a Chinese name at a glance.

"So, his name should be Lin-Xiao?"

And with this name, he can easily think of another super genius in the mathematics world this year.

"Could it be Lin Xiao who solved the distribution of Mersenne prime numbers and proposed Lin's conjecture?"

Lin's conjecture caused quite a shock after it was put forward, and Tao Zhexuan, of course, also became interested, so he also studied it, but in the end he gave up, the conjecture that shocked the algebraic geometry world, The difficulty is a bit too high.

But because of this, he also wanted to get to know Lin Xiao, but he never had such an opportunity.

However, now it seems that geniuses are attracted to each other, so don't they have a connection?

He smiled slightly, and then replied under Lin Xiao.

"Such an exquisite answer, and this ID, I believe you are the terminator of the law of distribution of Mersenne primes, right?"Your derivation process is perfect, if you are interested, add my ins, we can discuss in depth, of course, if you don’t have an ins, I can also download your international version of Koukou, you can send me a private message to contact me』

Soon, after replying, he looked forward to Lin Xiao's reply. After all, Lin Xiao's reply was twenty minutes ago, and he might receive the news soon.

However, this wait, I just don't know how long it will take.

Lin Xiao fell into an immersive state again because of studying the following ideas. When Zheng Ren brought his granddaughter to visit, it was already around [-]:[-] p.m., so it was getting dark soon. As for his reply It was after nine o'clock in the evening when Tao Zhexuan heard the news, and he fell asleep until twelve o'clock in the evening.

The time in the United States is twelve hours behind that in Huaguo, so Tao Zhexuan's place is only twelve o'clock at noon, and he still has his own affairs, so he can only give up waiting in front of the computer.

So, time passed like this again.

until two weeks later.

Lin Xiao looked at the new screening method he had perfected.

In the problem of prime numbers, two methods are often used, one is called the circle method, and the other is called the sieve method.

The Hardy-Littlewood circle method is the most commonly used method in the field of analytic number theory in the past 100 years. It is mainly used to solve some asymptotic problems on number sequences, and it is also used in It has developed an extremely wide range of applications; and the sieve method is a classic case that has been born in the hands of ancient Greek mathematicians since more than 200 BC, and has been used until now, and more methods with the same principle have been developed, and its main It plays a role in the study of prime number problems.

"In this way, it seems that there is hope to solve the parity problem that cannot be avoided between sieve methods?"

But Lin Xiao looked at his final result, and didn't immediately get excited about it, but fell into short-term thinking.

It took him more than two weeks to finally come up with this theory, which is relatively long, and this is also related to the fact that he is still learning French.

Of course, it took so long in the end because he changed his thinking in a new direction.

Before he followed Tao Zhexuan's thinking for five days, he finally found that he encountered a problem that he could not solve. Finally, he found that it was an unsolvable problem, so he had to give up. However, those days of research made him An idea came to mind about how to completely overcome one of the shortcomings of the drop-out method.

That is, the problem of parity. Most of the sieve methods are generally difficult to distinguish whether a number has an odd number of prime factors or an even number of prime factors, and it has always been a problem until today, although there have been some achievements on this, such as a A method called parity-sensitive sieve, but it still has limitations.

And if this problem can really be solved, it will undoubtedly be a very important achievement for the number theory community, and it can even provide extremely important help for solving Goldbach's conjecture and another twin prime number conjecture.

However, Lin Xiao has been thinking about this for a long time, but he still hasn't found a sure way.

As for the theory he has formed now, it is a new method that can more easily decompose a number into prime factors, and at the same time estimate the numbers of odd prime numbers and even prime numbers more approximately.

That's why he had some hope of solving the parity problem once and for all.

"Do you want to look at other people's research?"

When Lin Xiao thought about it, he suddenly remembered that he had replied to Tao Zhexuan's message on that mathematics forum.

"Uh, it's been two weeks, and I don't know if he has replied to me."

So he quickly logged in to mathoverflow, and after logging in, he found that he had received a reply.

"Did you reply on the same day as me?"

Seeing that the two published on the same date, Lin Xiao couldn't help being taken aback. He thought Tao Zhexuan would reply after a few days.

Then, seeing Tao Zhexuan's message, Lin Xiao added the other party's ins.

He has already registered the accounts of these foreign social platforms before. After all, after he went to the International Conference of Mathematicians, many mathematicians hoped to communicate with him in the future, so he simply registered these things , can't let those dozens of mathematicians all download QQ or prestige together.

Soon, after adding the other party's ins, it didn't take long for Lin Xiao to receive a notification that the addition of friends was approved.

Afterwards, Terence Tao sent a message.

"Mr. Lin, it's really not easy to contact you."

Lin Xiao replied: "Professor Tao, I'm sorry, I haven't looked at mathoverflow for the past two weeks, and then I forgot. 』

"It's okay, we're still friends now :)"

Lin Xiao smiled, and then replied: "Actually, I have been doing research on the idea you shared during this period of time. After I solved that problem, I wrote down a lot, but in the end I found that it was not successful."

Tao Zhexuan: "Yes, after seeing that you solved the problem I encountered before, I also wrote down along the line of thinking, and also found a problem. We could not determine the range of k in the end, and after that I didn't continue my research. 』

Lin Xiao: "Yes, but I came up with another method from my thoughts"

Afterwards, Lin Xiao sent his new idea to the past. He was not worried that Tao Zhexuan would steal his results. Such a well-known mathematician, let alone would not have this idea, even if they just think about their own reputation, they would Will not do this kind of thing.

"Let me see"

After Tao Zhexuan replied, there was no news, until more than ten minutes later, he sent a sentence that seemed very surprised: "Unbelievable!It turned out to be okay!He really deserves to be the most famous math genius of our time, why didn't I think of it! 』

Seeing his achievements received such a surprised response from a Fields Medal winner, Lin Xiao felt...it seemed quite cool?

I usually see those comments on the Internet saying that he is great, except that he felt pretty good at the beginning, but now, I'm used to it, and I don't care.

It's just that Mr. Yang praised him so much before, and the surprised reaction of this Mozart in the mathematics world now makes him feel a sense of recognition.

This is probably because the recognition from peers is more satisfying.

Then he smiled and replied: "It is my honor to surprise Professor Tao so much. In addition, for the method I used, I think it can be extended to completely solve the parity problem." 』

Terence Tao: "No, no, you don't need to call me Professor Tao, just call me 'Tao'. I admire the two prime number problems you solved before."However, I may not be able to help you with your problem. As you can see, I haven't even solved the problem I encountered before, which means that my interest in this has been exhausted. Now I After meeting you, I suddenly became interested in Lin's conjecture again - although I had studied it for a few weeks before this, I failed in the end. 』

Lin Xiao: "Well, maybe, it has something to do with the reason I have a cat?If you don’t have a cat, I recommend you to get a cat, and if you encounter problems, touch them, and you might be able to figure them out.』

Terence Tao: "Really?I'll try it later, but I don't know if my wife likes it or not.』

After completing a wave of Amway, Lin Xiao felt a sense of satisfaction in sharing. He turned his head to look at Mimi next to him, and stretched out his hand to rub it again.

However, Tao Zhexuan replied at this time: "Of course, I once had a bold idea, that is, why not combine the round method and the sieve method. If it can be successful, I believe there will be amazing discoveries." 』

Lin Xiao was taken aback: "Can these two be combined? 』

"Mathematics, the Langlands program can unify number theory and algebraic geometry, who knows if these methods can be unified?Let me recommend a few papers for you to read.”

"DOI: 10.2307/196..."

After a while, Lin Xiao saw a bunch of identifiers sent by the other party, all of which were some papers, and the time span of these papers spanned from seven or eighty years ago to recent years.

"Thanks, I'll check it out now. 』

"Well, no problem, oh yes, if possible, you can post your new screening method on arxiv, I hope to take a look at your steps in more detail. 』

"Of course, no problem. 』

Lin Xiao had sorted it out a long time ago, and the one he sent to Tao Zhexuan just now was also an abbreviated version.

So it took him a while to sort it out. After about a day or two, after the system detection was completed, he could query it.

Then, he read the paper sent by Terence Tao.

After reading the first paper, he was drawn in.

This paper comes from a German mathematician Rademacher in the last century. In the process of studying the sieve method, he extended the combination of the circle method, although there was no result, and it was only discussed somewhere in the paper. Talked about it, but for Lin Xiao, it brought him an enlightening effect.

Gradually, Lin Xiao sank into it.

Chapter 131 Going to Paris

Time passes quickly.

Academician Tang Qing's project is almost at the final finishing touch, and it is quite close to the final goal.

Needless to say, Lin Xiao's role in it, Academician Tang Qing has already planned to give Lin Xiao a second author position, and Professor Cao Chengqing also agreed with this decision. I am also embarrassed to ask for the position of this second work.

Although Lin Xiao shied away from this at the beginning, he had no choice but to accept the insistence of the two professors in the end.

However, compared with the research on this topic, his research on Goldbach's conjecture is still stuck halfway.

He had to admit that the difficulty of this conjecture was a bit beyond imagination.

Of course, this is also true in fact. In 1921, British mathematician Hardy once said: "The difficulty of Goldbach's conjecture can be compared with any known mathematical problem."

And Hardy is one of the proponents of the round method. Even he thinks that Goldbach's conjecture is so difficult, which is enough to show the difficulty of this problem.

Comparing Goldbach's conjecture with Riemann's conjecture, Goldbach's conjecture is not as important as Riemann's conjecture in terms of status, but it can still be called the jewel in the crown of mathematics, and if you compare Goldbach's conjecture with Regarding the relationship between the twin prime number conjectures, Terence Tao, as a mathematician who is interested in everything, once said that the former is more difficult than the latter.

Therefore, Lin Xiao, who plunged headlong into this pit, could only use his brain with less than 4% development to try to meet the requirements of this peerless beauty named 'Goldbach's conjecture'.

Only when the requirements are met, can he enjoy the joy of harvest - in front of mathematicians, the temptation to solve these mathematical conjectures is no less than that of a peerless beauty.