Chapter 228: Tools, or your own use

"neither?"
Molina froze.
After setting her mind, she looked at Lu Zhou and said in a skeptical tone: "I know that you are a genius ... Although Goldbach's conjecture is not my field of research, if I heard correctly, you wouldn't intend to change this. A century of work overthrow and redo? "
Lu Zhou smiled lightly and said in a relaxed tone.
"In the final analysis, the problem of ab is a complex expression of Goldbach's conjecture, that is, each large even number n can be expressed as ab, where the number of prime factors of a and b does not exceed a and b, respectively. When ab1, After all, this question will return to the original formulation, that is, any even number greater than 2 can be written as the sum of two prime numbers. "
The number of prime factors is 1, which is naturally a prime number.
So the form of 11 is ultimately Goldbach's conjecture.
Molina said in a ridiculous tone, "Do you mean that people who have studied Goldbach's conjecture for this century have been doing nothing?"
"Of course not," Lu Zhou shook her head, suddenly throwing up an unexpected question, "Do you know sports?"
Molina frowned slightly and frowned, "Sports?"
Lu Zhou: "Look at the long jump."
Molina pouted her lips and said, "Of course."
Lu Zhou smiled slightly and said, "Brown's ab proof method is equivalent to a run-up before a long jump. Although the run-up time itself is not included in the score, is the run-up useless? In the same way, ab is equivalent to brother The run-up of the Debach conjecture. If it were not for it, there would not be a later sieve method, an enlightening and potential analytical number theory research tool. It can even be said that the value of the sieve method has surpassed the Goldbach conjecture itself."
Regardless of whether the large sieve method can really cross the last 11, it has completed its historical mission and played an important role in analytical number theory.
Including Lu Zhou, they have benefited a lot.
With long hair in her ears, Molina looked at Lu Zhou: "So, how are you going to prove?"
The corner of Lu Zhou's mouth evoked a confident smile.
"Of course, it is proved by your own method."
do not know why.
Seeing a confident smile on his face, Molina's heartbeat accelerated inexplicably for two seconds.
Of course, for a woman who has decided to marry mathematics, the so-called heartbeat acceleration is only a moment ...
...
The solution of a mathematical conjecture requires the accumulation of workload and a creative genius.
Both are indispensable.
Just like Fermat's Last Theorem.
When the Gushanshi Village conjecture was proved, although people still can't see the concrete prospects, all people have counted it, because a tool to solve the problem has already appeared. Sure enough, Andrew Wiles finally completed this historic work.
But for Goldbach's conjecture, whether it is the large sieve method or the round method, this feeling is almost the same.
The predecessors' work has made a lot of groundwork, but whether it is the Chen's theorem from "99" to "12" or Helfgot's proof of Goldbach's weak conjecture under odd conditions, it is only the last step. Even the significance of Chen's theorem is to let other mathematicians understand that the road of the big sieve method has been achieved to the extreme by Chen Jingrun, and this road is no longer viable.
The circle method is the same.
For exactly the same reason, in his speech at the end of last year, Helfgot used "there is still a long way to go to fully prove Goldbach's conjecture" as the final conclusion, expressing his own short-term Can't solve Bach's conjecture without hope.
At least, no hope for the circle method.
Lu Zhou could not help but start to reflect on whether these two methods had entered the dead end.
When he first studied the twin prime conjecture, he also faced similar problems.
Zhang Yitang's research cleverly selected the lambda function to limit the spacing of prime pairs to 70 million. Successors reduced this number to 246 within a year, and then couldn't move further.
Lu Zhou's original idea was to choose an appropriate lambda function, but after countless attempts, he finally found that this road did not work.
There are too many lambda functions to choose from, but no matter how he looks, he can't find the right one.
It was not until he tried a totally different proof of thought in the heuristic state that he introduced topology theory into the concept of the sieve method, which opened the door to a new world.
Although this idea was first mentioned in Professor Zellberg's 1995 paper on Goldbach's conjecture, it was himself who improved it and introduced it to the problem of prime pairs.
Later, Lu Zhou introduced the knowledge of group theory on this basis, pushed the prime pairs of finite distance to infinity, and solved the Polignac conjecture on this basis. This method has been transformed by two magical reforms. Unrecognizable, completely deviated from the original appearance of the sieve method.
Therefore, Lu Zhou engraved his own weapon with a new name, namely the "group formation method".
But when thinking about Goldbach's conjecture, inertial thinking made him selectively ignore his tools.
On the surface, the group construction method seems to have nothing to do with Goldbach's conjecture, but from the root, it has evolved from the sieve method, and always goes to solve the prime problem.
As long as improvements are made, it may not be possible to use this tool for the Goldbach conjecture, which is also a prime problem.
When this mathematical method is constantly perfected, enough to solve many problems, and perfected from a toothpick to a Swiss Army Knife, its meaning may no longer be a mere tool, but gradually evolve into a theoretical framework! And it is the theoretical framework in analytical number theory!
Just like the famous "Second Disease" in the mathematics world, Mochizuki Shinichi, the "intercosmic teichmuller theory" and the "pure structure of extraterrestrial arithmetic" created when studying the abc conjecture.
Whether setting up a theory first to prove its value, or developing a novel theory while studying specific mathematical problems, there are precedents to follow.
From Goldbach's conjecture, Lu Zhou vaguely saw hope.
...
After coming out of the food club, Lu Zhou did not go to the library for a while after eating, but went to the Princeton Institute of Advanced Studies.
Although he didn't make an appointment, according to Professor Delin himself, it should be no surprise that he would be here every day from 6 to 8 pm.
Knocking on the office door, Lu Zhou entered.
Stopping the ball-point pen in his hand, Professor Deligne looked at Lu Zhou, who was standing across the desk, and asked easily.
"Have you considered it?"
Lu Zhou nodded and said.
"Yes, I plan to continue my research ... I'm sorry, I may not be able to spare extra energy to join your project."
Deligne nodded, not dissatisfied.
Sitting in his position, it is difficult to be as narrow-minded as the boss of a doctoral student, and to test whether the student is "obedient" with some boring tests. As he said at the beginning ~ EbookFREE.me ~ he offered Lu Zhou two options.
Deligne: "I respect your choice, but as your mentor, I need to know what your research topic is?"
Lu Zhou answered truthfully: "Goldbach's conjecture."
Deligne nodded, not as surprised as Molina was about the subject he was studying. The looseness and calmness on his face actually surprised Lu Zhou, who had thrown this proposition.
Is it ...
Old DeLigne also thought that he was the "best candidate" to solve this conjecture?
How sorry this is.
Lu Zhou was a little proud of himself.
Deligne: "Goldbach's conjecture is an interesting question. I also studied it when I was young, but it did not go deep and may not provide you with much help. At present, the closest research results in the world are Chen's theorem With Helfgot's proof of the weak conjecture, I am looking forward to your research on something new. "
"Of course, in addition to your own research, I also have some work outside of my research that you need to do. For example, work such as teaching assistants."
Lu Zhou nodded: "No problem ... if it is a course in number theory or functional analysis, I can still talk about some."
"It's mainly analytic number theory. I believe that with your ability, it is more than adequate for this job ... In addition, I have prepared a meeting gift for you."
After a pause, Mr. Deligne reached out and opened the drawer, took out a certificate-like thing from it, and put it on the table, with a smile on his serious face.
"I heard you say that your family conditions are not good. When I helped you with the admissions procedures yesterday, I helped you to solve the problem of the grant. By the way, you can take this thing to the educational affairs office, and by the way The tuition matter is resolved. "