Chapter 131 The solution to Brother Guess’s solution
Terence Tao, who is used to being a genius, still admires those who can solve problems that he cannot solve.
For example, just one year after he entered Princeton University as a doctoral student, their professor Andrew Wiles claimed that he had proved Fermat's Last Theorem. This was a big shock to him, and his classmates also
He was always around him talking about the field of mathematics. At that time, he also admired these classmates, although later, these classmates admired him.
Now, this netizen he met on the Internet actually solved his problem, and he was also a little impressed.
Of course, it is not ruled out that this is an acquaintance that I know in real life.
So he looked at the person's name.
"XiaoLin?"
As a Chinese-American who was born in Australia, he can even speak Cantonese. When faced with this name, he naturally knew at a glance that it was a Chinese name.
"Then, his name should be Lin-Xiao?"
And with this name, he could easily think of another super genius in the world of mathematics this year.
"Is it the same Lin Xiao who solved the Mersenne prime distribution and proposed Lin's conjecture?"
Lin's conjecture caused a huge shock after it was proposed. Of course Terence Tao would also have some interest, 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 precisely because of this, he also had the idea of getting to know Lin Xiao, but he never had such an opportunity.
However, now it seems that geniuses are attracted to each other, don't they have a connection now?
He smiled slightly and replied below Lin Xiao.
"With such an exquisite answer and this ID, I believe you are the terminator of Mersenne's prime number distribution law, right? Your derivation process is perfect. If you are interested, add my ins and we can discuss it in depth.
, of course, if you don’t have Instagram, I can also download your international version of KouKou, and you can send me a private message with your contact information.』
Soon, after replying, he looked forward to Lin Xiao's reply. After all, Lin Xiao's reply was about twenty minutes ago, and it wasn't long ago. Maybe he would receive the message soon.
However, I don’t know how long it will take to wait.
Lin Xiao fell into an immersive state again because he was studying the following ideas. When Zheng Ren came to visit with his granddaughter, it was already around 7 pm, so it got 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 China, so it was only twelve noon in Terence Tao's place, and he had other things of his own to do, so he had no choice but to give up waiting in front of the computer.
So, time passed like this.
Until two weeks later.
Lin Xiao looked at the new screening method he had perfected.
In the problem of prime numbers, there are two methods that 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 certain asymptotic problems on sequence, and it is used on prime number problems.
It has also developed an extremely wide range of applications; the sieve rule is a classic case that has been born in the hands of ancient Greek mathematicians since more than 200 BC, and has been used to this day, and more methods with the same principle have been developed.
And it mainly 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 is always inevitable between screening methods?"
When Lin Xiao looked at his final result, he did not immediately become excited about it, but fell into a short period of thinking.
It took him more than two weeks to finally come up with this theory, which was quite a long time. This was also related to the fact that he was still studying French.
Of course, the reason it took so long in the end was actually because he changed his thinking in another direction.
He had been studying Tao Zhexuan's ideas for five days before, but finally found that he had encountered a problem that he could not solve. Finally, he found that it was an unsolvable problem, so he had to give up. But those days of research made him
An inspiration came to mind, that is, how to completely overcome one of the shortcomings of the sifting method.
That is, the parity problem. Most sieving methods are generally difficult to distinguish whether a number has an odd number of prime factors or an even number of prime factors. This is still a problem to this day, although some results have been achieved on this, such as a
This method is called parity-sensitive screening, 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 can even provide extremely important help in solving Goldbach's conjecture and another twin prime conjecture.
However, Lin Xiao has been thinking about this for a long time and still has not found a sure way.
As for the theory he has formed now, it is a new method that can more easily factorize a number and at the same time more approximately estimate the number of odd and even prime numbers.
This is why he has some hope of completely solving the parity problem.
"Would you like to take a look at other people's research?"
When Lin Xiao thought about it, he suddenly remembered the message he had replied to Terence Tao on that mathematics forum.
"Well, it's been two weeks, and I don't know if he has replied to me."
So he quickly logged in to mathoverflow. After logging in, he found that he had received a reply.
"Did you actually reply on the same day as me?"
Seeing that the two published on the same date, Lin Xiao couldn't help but be startled. He originally thought Tao Zhexuan would reply after a few days.
Then, seeing Tao Zhexuan's message, Lin Xiao added the other person's ins.
He had already registered accounts on these foreign social platforms before. After all, after he visited the International Congress of Mathematicians, many mathematicians naturally wanted to communicate with him in the future, so he simply registered these things.
, we can’t let dozens of mathematicians all download Kuokou or Weixin together.
Soon, after adding the other party's Instagram, Lin Xiao received a notification that the friend addition was approved.
Then, Tao Zhexuan sent a message.
"Mr. Lin, it's really not easy to contact you."
Lin Xiao replied: "Professor Tao, I'm sorry, I haven't visited mathoverflow in the past two weeks, and then I forgot about it."
"It's okay, we are still friends now :)"
Lin Xiao smiled and then replied: "Actually, I have been researching the idea you shared during this period. After I solved the problem, I wrote a lot more, 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 continued writing along the train of thought. I also found a problem. In the end, we could not determine the range of k. After that,
I will not continue my research."
Lin Xiao: "Yes, but I have thought of another method from my thoughts."
After that, Lin Xiao sent his new idea. He was not worried that Terence Tao would steal his results. Such a well-known mathematician would never have such an idea, even just thinking about his reputation.
Wouldn't do such a thing.
"Let me see"
After Tao Zhexuan replied, there was no news. It was not until ten minutes later that he sent a message that looked very surprised: "Incredible! It turns out that this can be possible! He is indeed the most famous mathematical genius in our time."
,Why didn’t I think of that!』
Seeing that his results received such a surprised reaction from a Fields Medal winner, Lin Xiao felt... it seemed quite refreshing?
I usually see comments on the Internet saying that he is awesome, except that he felt pretty good at the beginning, but now, I have become used to it and don’t care anymore.
Just because Yang Lao praised him so much before, and now this Mozart in mathematics has such a surprised reaction, he can feel a sense of recognition.
This is probably because recognition from peers is more satisfying.
Then he replied with a smile: "It is really an honor for me to be able to surprise Professor Tao so much. In addition, I think the method I used can be further extended to completely solve the parity problem."
Tao Zhexuan: "No, no, you don't have 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 solve this problem of yours."
Thank you for your help. As you can see, I haven't even solved the problem I encountered before. This shows that my interest in this matter has been exhausted. Now that I know you, I suddenly have another interest in Lin's conjecture.
I became interested in it—even though I had studied it for several weeks before, I ultimately failed.』
Lin Xiao: "Okay, maybe it has something to do with the reason why I have a cat? If you don't have a cat, I recommend you to get one. If you encounter a problem, just touch it and maybe you can figure it out."
Terence Tao: "Really? I will try it later, but I don't know if my wife likes it."
After finishing the wave of Amway, Lin Xiao felt a sense of satisfaction in sharing. She turned her head and looked at the breast next to her, then reached out and stroked it again.
However, at this time Terence Tao replied: "Of course, I once had a bold idea, that is, why not combine the circle method and the sieve method. If it succeeds, I believe there will be amazing discoveries."
Lin Xiao was stunned: "Can these two be combined?"
"In mathematics, the Langlands Program can unify number theory and algebraic geometry. Who knows if these methods can all be unified? Let me recommend a few papers to you."
『doi:10.2307/196……』
After a while, Lin Xiao saw a bunch of identifiers sent by the other party, which were all papers, and the time span of these papers spanned from seventy or eighty years ago to the past few years.
"Thank you, I'll go take a look now."
"Well, no problem. Oh, by the way, if possible, please post your new screening method on arxiv. I hope I can take a more detailed look at your steps."
"No problem at all."
Lin Xiao had almost sorted it out a long time ago, and the one he just sent to Terence Tao was also a simplified version.
So he spent some time sorting it out, and 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 attracted.
This paper comes from Radmacher, a German mathematician in the last century. In the process of studying the sieve method, it extends the combination of the circle method. Although there are no results, it is only discussed somewhere in the paper.
However, for Lin Xiao, it brought him an inspiring effect.