Mathematical conjecture grinder?

Hearing this title, Li Mu couldn't help but smile and said modestly: "That's not it." ”

"I haven't solved many problems, just a few."

I counted them on one hand.

Isa rolled her eyes.

There are only a few gods.

Rao is usual cultivation is good, and she almost couldn't help but burst out at this time.

For anyone, a mathematical conjecture or something, solving just one is enough to blow for a lifetime.

For example, after Andrew Wiles proved Fermat's theorem, he directly made him the top mathematician in the mathematical world, and Perelman, who proved Poincaré's conjecture, even if he was low-key by nature and has never been able to escape from the world, his legend is still circulating in the mathematical world.

As a result, Li Mu is now good and has solved so many conjectures, but now he just uses the sentence "just a few" to cover up all this great achievement.

"When you say this, it doesn't make people feel humble at all."

"Really?"

Li Mu snorted.

He's just telling the truth.

When he solves the Riemann conjecture, he will definitely not be modest.

Isha shook her head, didn't say anything more, took out her own book, and read it beside her.

Li Mu also returned to quiet.

Although ambient music is playing in the library, it also has a very quiet feeling.

Time passed quietly.

……

The study of Goldbach's conjecture did not happen overnight.

Li Mu's only first-mover advantage is that he once solved the same prime problem of twin prime conjecture.

Although the two are still different, the use of methods can also form a connection between them, since they both study prime numbers.

Of course, the only intersection between the two is just primes, so there's not a lot of help that can be provided.

And just like that, a few days passed.

One ordinary morning, Li Mu woke up, simply brewed a glass of milk in the dormitory, boiled an egg, and added a few slices of bread, and breakfast was dealt with like this.

随后他便拿上自己的包，准备前往图书馆。

For him, studying is the same everywhere, but the only good thing about the library is the atmosphere.

It's like when I was in college, there were many students who couldn't get into school in the dormitory, but after going to the library, they settled down.

However, as soon as he opened the door and walked out, he saw the door of the next room open as well.

Isha stepped out of it.

She closed the door, turned her head and saw Li Mu.

Her eyes lit up: "Good morning, Lee! I was looking for you. ”

"Good morning." Li Mu nodded to her and asked, "Is there anything to find me?" ”

"Professor Licht also knows that you are studying the Goldbach conjecture, so he asked me to help convey to you that you want to cooperate?"

"Of course, if you don't want to, it's fine, after all, you've already researched so many conjectures independently, maybe you can solve it on your own."

Isha said with a smile.

Li Mu thought for a moment, and then said, "Since it was Professor Licht's invitation, it is okay to get to know it. ”

He is not resistant to cooperation, and if the other party can bring him some inspiration, it is acceptable.

“真的吗？ That's great! In this case, we can be regarded as a research group. ”

Isha immediately smiled and said, "Then I'll take you to Professor Licht's office now!" That's where we usually do our projects. ”

Without nonsense, she and Li Mu left the graduate student apartment and went to the teaching building of Merton College.

When I came to Professor Licht's office, there were a number of young people in it, apparently all of whom, like Isha, were students of Professor Licht.

Then, a middle-aged man about 50 years old walked from the side and stretched out his hand to Li Mu with a smile: "Li, welcome to you." ”

Li Mu quickly recognized the man, Lucas Licht, a professor of mathematics at Merton College.

He also stretched out his hand and shook it with the other party, and said with a smile: "Professor Licht, it's a pleasure to meet you." ”

"I heard Isha say that you were also working on the Goldbach conjecture, so I took the liberty of asking her if you would like to cooperate." Licht smiled slightly.

"I'm honored to have your consent."

"Perhaps with you, a mathematical genius, we are close to the answer to Goldbach's conjecture."

"Not necessarily." Li Mu said modestly again: "In any case, the Goldbach conjecture is also the brightest pearl in the crown of number theory, and the difficulty is still very high, and it is not an easy thing to solve it." ”

This time it's a real humility.

Licht laughed, "Perhaps, but I believe you have magical powers, just like your recent performance in physics." ”

Li Mu said helplessly: "Okay, I also hope that I have such magic." ”

Licht patted him on the shoulder, and then said, "Okay, let's not say more, I'll show you how we're doing now." ”

Then, he took Li Mu to his desk, then took out a document from the side, handed it to Li Mu, and said, "I have been studying the Goldbach conjecture for about three years. ”

"I find that whether it's a separate circle method or a separate sieve method, it's a bit stretched to the surface when it comes to Goldbach's guess."

"And for now, both approaches seem to have come to an end."

"But if you can turn these two methods into one method, maybe there will be a huge improvement in dealing with prime numbers."

Hearing Licht's words, Li Mu looked at the information in his hand and thought: "Is it ...... to combine the circle method and the sieve method into one method?" ”

"Yes." Licht nodded.

"In the last century, the '1+2' form, which was also proved by Chen Jingrun from China, has been considered to be the ultimate in the sieving method, and although the circle method has not been brilliant in Goldbach's conjecture, we must not ignore the importance of the circle method."

Li Mu nodded slightly.

Licht's statement, although only a speculation, is also in line with the consistent thinking of the current mathematical community.

It is now generally accepted in the mathematical community that in order to prove the Goldbach conjecture about even numbers, it is necessary to make significant improvements in existing methods, and there are even those who believe that the proof cannot be completed based on the improvement of existing methods alone, and that new ideas or new mathematical tools are needed.

So, perhaps Licht's idea is also correct.

"The information I've given you includes some of my thoughts on combining these two approaches."

"See if there's anything else you can optimize?"

In front of Li Mu, as a professor, Li Het has always maintained an equal attitude to speak, and even has some meaning to ask for advice.

But no one in the office felt anything wrong with that.

When the students in Licht saw this, they were all but emotional.

"It's really Lee, I've never seen Professor Licht have such an attitude in front of a person our age."

"yes!"

"Don't say this kind of thing, when we see Lee, will you just treat him as a peer?"

"Uh...... It doesn't seem like so. ”

Maybe it's normal to treat Li Mu as a professor.

Others asked Isa Grosvenor: "Isha, how did you meet Lee?" ”

"Uh...... We both live in the dormitory provided by the school, and he and I are neighbors. ”

"Oh! Oh my God, I knew that living in the dormitory would be able to become neighbors with Li Mu, and I would have known that I would also live in the dormitory! ”

"Isha, why don't you go and live in my rental house, and then I'll live in your dorm?"

Merton College is limited in the number of graduate students who can 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 had reserved one for him.

Therefore, regarding the matter of changing the rental house to the dormitory, Isha directly said: "I refuse!" I don't want to live outside. ”

能够抢到墨顿学院的宿舍可不是一件简单的事情。

"Okay."

The man who said he was going to change houses could only sigh.

……

Of course, neither Li Mu nor Professor Li Het paid attention to their discussion.

Li Mu continued to look at the materials given by Licht, which were basically manuscripts.

This made Li Mu, who had gradually become accustomed to using his mental computer to directly connect to electronic devices and then download papers and books from the Internet, felt a little troublesome.

It would take him 5 seconds to read a page with his eyes, and 10 pages in 0.5 seconds if he downloaded it to his mental computer.

In addition, because the font of the manuscript is often not a special standard, when he looks at the information in his hand, he can basically only read one page in 10 seconds.

“有些慢了啊。”

Li Mu sighed slightly in his heart, but soon he shook his head with a smile, this is really easy to go from thrift to luxury, and from luxury to thrift.

A page of manuscript in 10 seconds was already very fast when he was still a third-level 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 few more moments before handing it back to Licht.

Licht was stunned for a moment, and then couldn't help asking, "...... Finished reading? ”

His manuscript is about more than 30 pages before and after, Li Mu read it so quickly?

Li Mu nodded: "I'm done." ”

"I think the idea you mentioned that you can use the method of finding quadratic extrema to improve the two in the same direction, I think it's worth trying."

He thought for a moment, then found a piece of scratch paper from the side, "This scratch paper should work, right?" ”

"Of course...... OK. ”

Li Hutt hadn't reacted from the fact that Li Mu had finished reading his manuscript, and subconsciously said a word.

Li Mu didn't talk nonsense, took out a pen directly from his pocket, and then began to write on it.

"For non-zero integer m, loop integration ...... along a unit circle as a path"

【∫e^(2πimt)dt=0】

"If and only if the integer m=0......"

"If you consider integral ......"

【D（N）=∫S^2(t，N)e……】

Li Mu wrote while introducing his thoughts and ideas.

"So, if we were to combine the sieve method with the circle method, the Goldbach conjecture about even numbers would be reduced to substituting the trigonometric polynomial e^(2πipt) with prime numbers in integral equations D(N) and T(N) into the sieve function S(u,P,z)." ”

"Ultimately, let's show that when λ = 2, the sieve function combined with the trigonometric polynomial is greater than zero."

"That's it."

Seeing this scene, Licht was stunned for a moment.

He just showed Li Mu his manuscript, and as a result, Li Mu directly deduced it to this extent?

Even the final proof conditions were found.

"You...... I ......"

He opened his mouth, a little speechless for a moment.

李牧疑惑地看了他一眼，问道：“李赫特教授？ ”

Licht said helplessly: "Listening to your analysis, I'm really a little embarrassed, maybe even if you don't cooperate with me, you should be able to do 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 brought me a little hint." ”

Licht shook his head and didn't say anything, just looked at Li Mu's scratch paper again, glanced at the analysis listed on it, and then said, "That is to say, as long as this goal is completed, it will be fine." ”

"Yes." Li Mu nodded: "After the combination of the two, the change of this sieve function, I am willing to call it the sieve circle function." ”

"It's a little bit more convenient than the previous sieve function alone."

"But the problem is still at the forefront—"

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?" ”

Licht touched his chin: "Hmm...... Indeed, this is the most critical question. ”

The formula given by Li Mu is actually carried out under the premise that the sieve method and the circle method can be used together, so their next work needs to truly combine the sieve method and the circle method.

Li Mu smiled: "But no matter what, we have indeed found a direction to success." ”

李赫特一笑，并没有抢功劳：“是你，不是我们。 ”

Then he said solemnly: "Li, I have to tell you first, although it is now the cooperation I invited you to make, but if the proof is really completed, and I have not made any meaningful contributions, I will cancel the cooperation between us at any time." ”

"This honor should be yours, it's yours."

……

当李牧离开了李赫特教授的办公室后，他就不由对旁边的伊莎说道：“李赫特教授可真是一个好人啊。 ”

Taking the initiative to do something that doesn't take credit is really rare in the academic world.

Academia is no less flawed than elsewhere, let alone the honor of proving Goldbach's conjecture.

People like Licht are rare.

"Professor Licht comes from a hereditary aristocracy, and he did this to preserve his family glory." Isha said with a smile.

Li Mu was stunned for a moment: "Hereditary nobles? How come I've never heard of it? ”

"Professor Licht has hardly revealed anything to anyone else."

"That's right."

Li Mu couldn't help but sigh, he had only heard of this kind of hereditary aristocrat in various works before, but he didn't expect to see one with his own eyes now.

Then he couldn't help but ask curiously, "But how do you know?" ”

"I ...... I also knew about it by chance. Isha explained, then asked, "Shall we go to lunch together?" ”

They had gone to Licht's office in the morning, and it was time for dinner.

Li Mu thought for a while, and then nodded: "Of course you can." ”

"Okay!" Isha smiled.

But at this time, they passed a corner, and Li Mu saw Yun Rongshang coming over.

When the two met, they were both stunned.

Then Li Mu greeted with a smile: "Senior Sister Yun." ”

Yun Rongshang nodded at him, "Li Mu, I was about to come to you." ”

Then she turned her head again, looked at Isha next to her, narrowed her eyes, and asked with a smile, "Who is this......?" Your classmates? ”

……

Kavenka's discomfort

(End of chapter)