"None of them?"
Molina was stunned.
She looked at Lu Zhou and said in a suspicious tone, "I know you're a genius … Although Goldbach's conjecture is not my field of research, if I'm not mistaken, you're not planning on redoing this century's worth of work, right?"
Lu Zhou smiled and spoke in a relaxed tone.
"The a + b problem is a complex expression of Goldbach's conjecture, which is that 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. When a = b = 1, the problem will eventually return to the original expression, which is any even number greater than 2 can be written as the sum of two prime numbers. "
If the number of prime factors was 1, then it was naturally a prime number.
Therefore, the form of 1 + 1 was still Goldbach's conjecture.
Molina said in a joking tone, "So you're saying that people who have been researching Goldbach's conjecture for the past century have been doing nothing?"
"Of course not," said Lu Zhou as he shook his head. He then asked an unexpected question, "Do you know anything about sports?"
Molina frowned and said, "Sports?"
Lu Zhou, "You know about the long jump, right?"
Molina pouted and said, "Of course."
Lu Zhou smiled and said, "Brown's a + b proof method is equivalent to the run-up before the long jump. Although the run-up time itself is not included in the score, is the run-up useless? In the same way, a + b is equivalent to the run-up of Goldbach's conjecture. If it wasn't for it, there would not be the large sieve method, which is full of potential and inspiring analytical number theory research tools. It can even be said that the value of the large sieve method has surpassed Goldbach's conjecture itself. "
Regardless of whether the large sieve method could really solve the 1 + 1 problem, it had completed its historical mission and played an important role in analytic number theory.
Even Lu Zhou benefited a lot from it.
Molina tucked her long hair behind her ear and looked at Lu Zhou. "So, how do you plan to prove it?"
Lu Zhou's lips curled into a confident smile.
"Of course, I have to prove it in my own way."
He did not know why.
Seeing the confident smile on his face, Molina's heart inexplicably sped up for two seconds.
Of course, for a woman who had already decided to marry a mathematician, her heartbeat only accelerated for a moment …
…
The solution of a mathematical conjecture required a lot of work and a creative genius.
Both of them were indispensable.
Just like Fermat's last theorem.
After the Taniyama – Shimura conjecture was proven, even though people could not see the specific prospects, everyone knew in their hearts that a tool to solve the problem had appeared. Sure enough, Andrew Wiles had finally completed this historic work.
But for Goldbach's conjecture, whether it was the large sieve method or the circle method, they both lacked this feeling.
The predecessors had done a lot of work, but whether it was Chen's theorem from "9 + 9" to "1 + 2" or Helfgott's proof of Goldbach's weak conjecture under odd conditions, they were only one step away. In fact, the significance of Chen's theorem was to let other mathematicians understand that the large sieve method had been taken to the extreme by Chen Jingrun. This path could no longer be taken.
The same was true for the circle method.
Because of the same reason, at the end of last year's speech, Helfgott used "we still have a long way to go to completely prove Goldbach's conjecture" as his closing remarks. He expressed that he did not have any hope of solving Goldbach's conjecture in the short term.
At least, he did not have any hope for the circle method.
Lu Zhou could not help but wonder if these two methods had reached a dead end.
When he was researching the twin prime number conjecture, he also faced a similar problem.
Zhang Yitang's research cleverly chose a lambda function and limited the distance between prime numbers to 70 million. His successors reduced this number to 246 within a year and could not go any further.
Lu Zhou's original idea was to choose an appropriate lambda function, but after countless attempts, he finally found out that this method did not work.
There were too many lambda functions to choose from, but no matter how hard he looked, he could not find the right one.
It was not until he was inspired and tried a completely different proof idea. He introduced topology theory into the concept of the sieve method. This opened the door to a new world.
Although this idea was first mentioned by Professor Zellberg in his 1995 paper on Goldbach's conjecture, it was he who improved it and introduced it into the prime number problem.
Later on, Lu Zhou introduced the knowledge of group theory on this basis and pushed the prime numbers from a finite distance to an infinite distance. This was the basis for solving the Polignac's conjecture. This method had been modified twice and completely deviated from the original sieve method.
Therefore, Lu Zhou engraved a new name for his own weapon, the "Group Structure Method".
However, when he was thinking about Goldbach's conjecture, his habitual thinking made him selectively ignore his own tool.
On the surface, the Group Structure Method seemed to have nothing to do with Goldbach's conjecture. However, it evolved from the sieve method and was always used to solve the prime number problem.
As long as he made some improvements, he might be able to use this tool on Goldbach's conjecture, which was also a prime number problem.
When this mathematical method was constantly perfected, perfected to the point where it could solve many problems, perfected to the point where it went from a toothpick to a Swiss army knife, its significance might no longer be a simple tool, but it would gradually evolve into a theoretical framework! And it was a theoretical framework in analytic number theory!
Just like the famous "chuunibyou" Shinichi Mochizuki, who created the "Intercosmic Teichmüller Theory" and "Alien Arithmetic Holomorphic Structure" while researching the ABC conjecture.
Whether it was establishing a theory and then proving the value of the theory, or developing a new theory while researching a specific mathematical problem, there were precedents to follow.
From Goldbach's conjecture, Lu Zhou saw a glimmer of hope.
…
After leaving the food club, Lu Zhou did not go to the library like usual. Instead, he went to the Princeton Institute for Advanced Study.
Although he didn't have an appointment, according to Professor Doehring, he would be here every night between 6 and 8 o 'clock if there were no accidents.
Lu Zhou knocked on the office door and walked in.
Professor Deligne put down the pen in his hand and looked at Lu Zhou, who was standing across from him. He spoke in a relaxed tone.
"You've thought about it?"
Lu Zhou nodded and spoke.
"Yes, I plan on completing my own research … I'm sorry, I may not be able to spare the extra energy to participate in your research project."
Deligné nodded and was not dissatisfied.
Sitting in his position, it was difficult for him to be narrow-minded like most PhD students. He would not use boring tests to test whether his students were "obedient". Like he said in the beginning, he gave Lu Zhou two choices.
Deligné: "I respect your choice, but as your supervisor, I need to know what your research project is?"
Lu Zhou answered truthfully, "Goldbach's conjecture."
Deligne nodded. Unlike Molina, Deligne wasn't surprised by Lu Zhou's research topic. Instead, Deligne's calmness surprised Lu Zhou.
Maybe …
Deligné also thinks that I'm the "best candidate" to solve this conjecture?
How can I do that?
Lu Zhou was a little proud.
Deligné: "Goldbach's conjecture is an interesting problem. I studied it when I was young, but I didn't go deep into it, so I might not be able to provide you with much help. Currently, the closest international research results are Chen's theorem and Helfgott's proof of the weak conjecture. I'm looking forward to you researching something new.
"Of course, in addition to your own research, I also need you to do some work outside of research. For example, teaching assistant. "
Lu Zhou nodded and said, "No problem … If it's a number theory or functional analysis course, I can still teach some."
"Mainly analytic number theory. I believe that with your ability, you are more than qualified for this job … Also, I prepared a gift for you."
After a pause, Mr. Deligné reached out and opened a drawer. He took out a certificate and placed it on the table with a smile on his serious face.
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