Mathematical guesswork crusher?
Hearing this title, Li Mu couldn't help but smile and said modestly: "That's not the case."
"I haven't solved many problems, just a few."
I can count them all on one hand.
Isa suddenly rolled her eyes.
There are only a few gods.
No matter how well-educated she usually is, she almost couldn't hold back her swear words at this moment.
For anyone, solving any mathematical conjecture is enough to last a lifetime.
For example, after Andrew Wiles proved Fermat's Last Theorem, he directly became the top mathematician in the mathematics world. Moreover, Perelman, who proved the Poincaré conjecture, even though he has a low-key nature, he has always avoided the world. Not surprisingly, his legend is still circulating in the mathematics community.
As a result, Li Mu is doing well now. He has solved so many conjectures, but now he just uses the words "just a few" to cover up all these great achievements.
"What you said is not humbling at all."
"Yeah?"
Li Mu laughed.
He was just telling the truth.
When he solves the Riemann Hypothesis, he will definitely not be modest.
Isa shook her head and did not continue to say more. She took out her own book and read it next to it.
Li Mu also returned to silence.
Although ambient music is playing in the library, it still feels extremely quiet.
Time passed quietly.
…
Research on Goldbach's conjecture did not happen overnight.
Li Mu's only first-mover advantage is that he has solved the same prime number problem, the twin prime number conjecture.
Although the two are still different, the use of the methods can also form a connection, after all, they all study prime numbers.
Of course, the only intersection between the two is just the prime numbers, so it doesn't provide much help.
Just like that, a few days passed.
On an ordinary morning, Li Mu woke up and simply made a glass of milk in his dormitory, boiled an egg, and added a few slices of bread, and that was it for breakfast.
Then he picked up his bag and prepared to go to the library.
For him, it doesn't matter where he studies, but the only good thing about the library is the atmosphere.
Just like when I was in college, there were many students who couldn't learn in the dormitory and settled down after going to the library.
However, as soon as he opened the door and walked out, he saw the door of the next door also opened.
Isha came out.
She closed the door, turned around and saw Li Mu.
Her eyes lit up: "Good morning, Li! I was just looking for you."
"Good morning." Li Mu nodded to her and asked, "What do you want from me?"
"Professor Richter also knows that you are studying Goldbach's conjecture, so he asked me to help convey to you, do you want to cooperate?"
"Of course, if you don't want to, that's okay. After all, you have independently researched so many conjectures. Maybe you can solve them by yourself."
Isa smiled.
Li Mu thought for a moment, and then said: "Since it is Professor Richter's invitation, it is okay to go and understand."
He is not resistant to cooperation. If the partner can bring him some inspiration, it is acceptable.
"Really? That's great! In this case, we will be in the same research group."
Isa immediately smiled and said: "Then I will take you to Professor Licht's office now! We usually do our projects there."
Without any nonsense, she and Li Mu left the graduate student apartment and headed to the teaching building of Merton College.
When I arrived at Professor Richter's office, there were many young people inside. Apparently, like Isa, they were students of Professor Richter.
Then, a middle-aged man about 50 years old came from the side, smiled and stretched out his hand to Li Mu: "Li, welcome to your arrival."
Li Mu quickly recognized this person, Lucas Richter, professor of mathematics at Merton College.
He also stretched out his hand to shake the other person's hand and said with a smile: "Professor Licht, nice to meet you."
"I heard from Isa that you are also studying Goldbach's conjecture, so I took the liberty of entrusting her to ask if you are willing to cooperate." Richter smiled slightly.
"I am also very honored to have your approval."
"Perhaps with the joining of your mathematical genius, we will be very close to the answer to Goldbach's conjecture."
"This is not necessarily true." Li Mu said modestly again: "In any case, Goldbach's conjecture is also the brightest pearl in the crown of number theory. It is still very difficult. It is not easy to solve it. thing."
This time he was truly humble.
Richter laughed: "Maybe so, but I believe you have magic power, just like your recent performance in physics."
Li Mu said helplessly: "Okay, I also hope I have such magic power."
Li Het patted him on the shoulder, and then said: "Okay, we don't need to say more. Let me show you our current progress first."
Then, he took Li Mu to his desk, took out a piece of information from the side, handed it to Li Mu, and said, "I have been studying Goldbach's conjecture for about three years."
"I found that whether it is the circle method alone or the sieve method alone, it is a bit difficult to deal with Goldbach's guess."
"And right now, both approaches appear to be at the end of the road."
"But if these two methods can be turned into one method, perhaps there will be a huge improvement in dealing with prime numbers."
After hearing Li Hete's words, Li Mu looked at the information in his hand and thought: "Combine the circle method and the sieve method into one method...?"
"Yes." Li Het nodded.
"In the last century, the sieve method used in the '1+2' form proved by Chen Jingrun, who is also from China, has been considered to be the ultimate sieve method. Although the circle method has not always been We don’t shine on Goldbach’s conjecture, but we must not ignore the importance of the circle method.”
Li Mu nodded slightly.
Although Richter's statement is just a speculation, it is also consistent with the current thinking in the mathematics community.
It is generally believed in the mathematical community that if you want to prove the Goldbach conjecture about even numbers, you must make significant improvements in the existing methods. There are even some people who think that the proof cannot be completed based only on the improvements in the existing methods. New ideas or new mathematical tools.
So maybe Richter has the right idea too.
"The information I gave you contains some of my thoughts on combining these two methods."
"Can you see if there is anything that can be optimized?"
In front of Li Mu, Li Hete, as a professor, always spoke with an equal attitude, and even had some intention of asking for advice.
But no one in the office saw anything wrong with this.
When Li Heter's students saw this scene, they just sighed.
"As expected of Li, I have never seen Professor Richter have such an attitude in front of a person of our age."
"yes!"
"Stop saying that. When we see Li, is it possible that you just regard him as a peer?"
"Uh...it seems like I really can't."
Perhaps it is normal to regard Li Mu as a professor.
Others asked Isa Grosvenor: "Isa, how did you meet Lee?"
"Uh... we all live in the dormitories provided by the school. He and I are neighbors."
"Oh! Oh my god, if I had known that I could live in the dormitory and be neighbors with Li Mu, I would have lived in the dormitory too!"
“Isa, how about you go live in my rental house, and then I’ll live in your dormitory?”
The graduate student dormitories that Merton College can provide are limited and cannot accommodate all graduate students, so at least half of the graduate students live in rented houses outside.
Li Mu was able to have a dormitory because the college reserved one specifically for him.
Therefore, regarding the matter of renting a house to change into a dormitory, Isha directly said: "I refuse! I don't want to live outside."
It is not an easy thing to grab the dormitory of Merton College.
"All right."
The person who said he wanted to change his house could only sigh.
…
Of course, neither Li Mu nor Professor Richter paid attention to their discussion.
Li Mu continued to look at the information given by Li Heter, which was basically all manuscripts.
This caused some trouble for Li Mu, who had gradually become accustomed to using his brain computer to directly connect electronic devices and then download papers and books from the Internet.
If he reads it with his eyes, it takes him 5 seconds to read one page, but if it is downloaded to the computer in his mind, he can read ten pages in 0.5 seconds.
In addition, because the fonts of manuscripts are often not particularly standard, when he looks at the information in his hand, he can basically only read one page in 10 seconds.
"It's a little slow."
Li Mu sighed slightly in his heart, but soon he shook his head with a smile. It is really easy to go from frugality to luxury, but it is difficult to go from luxury to frugality.
A page of manuscript took 10 seconds, which was already very fast when he was still a level 3 mental computer.
So it didn't take long for him to finish reading the information in his hand.
He held it in his hand and thought for a moment before handing it back to Li Heter.
Li Heter was stunned for a moment, then couldn't help but ask: "Have you... finished reading?"
His manuscript has about 30 pages in total. How could Li Mu read it so quickly?
Li Mu nodded: "I've finished reading."
"You mentioned the idea of using the method of finding the extreme value of a quadratic form to improve both of them in the same direction. I think it is worth a try."
He thought for a while, then found a piece of scratch paper from the side, "This scratch paper should be usable, right?"
"sure."
Li Heter had not yet reacted to the fact that Li Mu had read his manuscript, so he subconsciously said something.
Li Mu didn't waste any time. He took out a pen from his pocket and started writing on it.
"For a non-zero integer m, the loop integral of the path along the unit circle..."
【∫e^(2πimt)dt=0】
"If and only if the integer m=0..."
"If you consider the integral..."
[D(N)=∫S^2(t,N)e...]
As Li Mu wrote, he also introduced his thoughts and ideas.
Until the end, "So, if we want to combine the sieve method and the circle method, the Goldbach's conjecture about even numbers can be reduced to the trigonometric polynomials with prime numbers as variables in the integrals D(N) and T(N) e^(2πipt), substitute it into the sieve function S(u, P, z)."
"Ultimately, we are going to prove that when λ=2, this sieve function combined with a trigonometric polynomial is greater than zero."
"That's it."
Seeing this scene, Li Hete was stunned.
He just gave Li Mu a glance at his manuscript, but Li Mu directly deduced it to this extent?
Even the final proof conditions were found.
"You and I……"
He opened his mouth and was speechless for a moment.
Li Mu glanced at him doubtfully and asked, "Professor Li Heter?"
Li Hete said helplessly: "Listening to your analysis, I'm really embarrassed. Maybe even if you don't cooperate with me, you should be able to handle it on your own, right?"
Li Mu smiled and waved his hand: "No, no, the idea of combining the sieve method and the circle method you provided also gave me some tips."
Li Heter shook his head and said nothing. He just looked at Li Mu's draft paper again, glanced at the analysis listed above, and then said: "In other words, as long as this goal is achieved, it will be fine."
"Yes." Li Mu nodded: "After combining the two, the change of this sieve function, I would like to call it the sieve circle function."
"It is more convenient than the previous separate filter function."
"But the problem now is still at the front-"
Li Mu pointed to the previous formula: "How can we prove that the sieve function in this sieve method and the trigonometric polynomial in the circle method can be combined?"
Li Heter touched his chin: "Well... indeed, this is the most critical question."
The formula given by Li Mu is actually based on the assumption that the sieve method and the circle method can be used in combination, so their next work needs to truly combine the sieve method and the circle method.
Li Mu smiled and said: "But no matter what, we have indeed found a direction towards success."
Li Hete smiled and did not take any credit: "It's you, not us."
Then he solemnly said: "Li, I have to tell you first. Although I am inviting you to cooperate now, if the proof is really completed and I have not made any meaningful contribution, I will Cancel our cooperation at any time."
"This honor should be yours, it's yours."
…
When Li Mu left Professor Richter's office, he couldn't help but said to Isa next to him: "Professor Richter is such a good person."
It is so rare in academia to proactively propose things without taking credit.
There are no less cunning in academia than elsewhere, let alone the honor of proving Goldbach's conjecture.
People like Richter are rare.
"Professor Richter comes from a hereditary noble family. He does this to maintain the honor of his family." Isa said with a smile.
Li Mu was stunned: "Hereditary noble? Why have I never heard of it?"
"Professor Richter has basically never disclosed anything to others."
"That's it."
Li Mu couldn't help but sigh. He had only heard of this kind of hereditary nobleman in various works before, but he didn't expect to see one in person now.
Then he couldn't help but asked curiously: "But how did you know?"
"I...I also know it accidentally." Isa explained, and then asked: "Would you like to have lunch together?"
They went to Li Heter's office in the morning, and it was already dinner time.
Li Mu thought for a while, then nodded: "Of course."
"Okay!" Isa suddenly smiled.
But at this moment, they passed a corner, and Li Mu saw Yun Rongshang approaching.
When the two met, they were immediately stunned.
Then Li Mu smiled and said hello: "Senior Yun."
Yun Rongshang nodded towards him, "Li Mu, I was just coming to find you."
Then she turned her head again, looked at Isa next to her, narrowed her eyes, and asked with a smile: "Is this... your classmate?"
…
Kavinka's discomfort
(End of chapter)
