Chapter 359 Proving the Duffin-Schaeffer Conjecture
Xu Qingshan has no use for the results of these researchers, and he even doesn't care much about results.
He couldn't use up all the results he could produce, so he established this research team.
The purpose is to free up the energy and time Xu Qingshan spends on basic work and produce more results.
There are generally two situations in academic circles, whether domestic or foreign.
One is that the team leader's personal strength and domain knowledge are very deep, and he can accurately guide every mistake in every topic that the students and assistants in the team have arranged to do. This kind of team is led by super experts. The research team has an astonishingly high production efficiency of scientific research results.
The other is more conventional, and is currently the most common model in academia around the world. That is, professors are only responsible for formulating the big framework, but basically all the work is done by research assistants and students, who then start from the project. On the branches, I relied on the help of my junior brothers and sisters to complete my doctoral thesis. In the end, the most fruitful thesis was in the name of my supervisor. I spent several years of hard work in exchange for a generous letter of recommendation and a degree. There are also one or two small journal papers and graduation thesis that are difficult to evaluate.
Some people still think that academia is an ivory tower of purity.
But you must know that this is a group of people with such high IQs. They are all human beings, and as human beings they will have selfish motives and weaknesses. Every time selfish motives and weaknesses manipulate the loopholes in the mechanism, it is a blow to the entire system. .
Just like those descendants of academics who can publish many SCI papers while still in middle and high school.
Bosses like Xu Qingshan fall into the former category.
Jin Jing took Xu Qingshan's revision opinions and returned to her office. When she went out, she unexpectedly let out a small exclamation. There seemed to be someone outside the door, but they should all be acquaintances. Xu Qingshan He looked up curiously and found that Jin Jing breathed a sigh of relief and left with his things.
"Who is coming?"
Xu Qingshan asked aloud.
"Director Xu, me."
Li Guangzhi's reflective three-haired head stuck out from the door frame. If he hadn't spoken first, the scene would have been scary.
"Why are you standing there? Come in if you need anything, or do you want to go next door to see Senior Brother Ruochuan?"
"I'm here to find you, Director Xu."
Li Guangzhi, even though he has been encouraged, is still so submissive in life. When he walks, he seems to have a heavy turtle shell on his back.
"Then come in."
Xu Qingshan is sometimes speechless. Apart from doing academic work, this guy is like a fake at other times.
"Oh, okay."
Li Guang straightened up and stood in the door frame, then walked in cautiously.
Entering Xu Qingshan's office, he didn't dare to raise his head and look around, so he sat cautiously on the chair where Jin Jing had just sat, with his legs together and his hands folded on his lap, hesitantly. .
"Let's talk about something. Don't be so jealous. Our research team is all a family. There is nothing to be embarrassed to say."
Xu Qingshan patted Li Guangzhi on the shoulder.
"Hey, eh, good."
Li Guangzhi took out two pieces of crumpled paper from his arms and spread them out on Xu Qingshan's desk. Xu Qingshan took a few glances and found that these seemed to be facial tissues. The writing on them was slightly blurry, but he could still read it. Get clear.
"Director Xu, I just moved here recently and I feel it's drier here. I'm a little constipated. I've been squatting in the toilet just now, but I suddenly felt a fever while squatting. Fortunately, I brought a pen with me, so I quickly recorded it. Check this out, look at this.”
Li Guangzhi still looks excited when he talks about things in his field.
He did not realize at all that the two pieces of paper in his hand became very interesting once he mentioned their origin.
The corner of Xu Qingshan's mouth twitched. For this reason, he finally understood why Li Guangzhi didn't get along well with his boss and colleagues before.
To a certain extent, he is quite pure, but it also reflects the saying "high IQ, low EQ".
Fortunately, Xu Qingshan didn't mind this very much, so he nodded and listened to Li Guangzhi continue.
Just as he was talking about his attempt to use the graphical model method to more intuitively display and analyze the relationship between transcendental approximation and continued fractions, Xu Qingshan suddenly frowned.
"Wait a minute, you are thinking about the graphical model method here."
Xu Qingshan felt that some stars seemed to be gradually emerging in the space in the office. Every moment when white stars appeared in the space, Xu Qingshan's head was running crazily.
His wisdom is like a black hole, forming a whirlpool of inspiration.
Li Guangzhi did not dare to speak. He paused, shrank back from the state of wanting to share his gains, and looked at Xu Qingshan longingly.
After Xu Qingshan stopped Li Guangzhi's words, he suddenly opened the drawer inside his desk and rummaged through a pile of messy manuscripts inside.
Li Guangzhi watched from the side. He didn't know what Xu Qingshan wanted to do, but the boss was the boss, and he kept the rank suppression in the academic workplace in mind.
It didn't take long for Xu Qingshan to dig out a manuscript from the pile of manuscripts that he had been leaving unused.
[Duffin-Schaeffer conjecture] and [Wirsing-Schmidt conjecture].
In this manuscript, Xu Qingshan explained in detail the possible ideas of the entire conjecture. However, when completing this part of the work, Xu Qingshan was temporarily stuck in one place.
Li Guangzhi's words made Xu Qingshan subconsciously find this core point, so he immediately found the manuscript, hoping to confirm his thoughts.
The Duffin-Schaeffer conjecture was jointly proposed by physicist Richard Duffin and mathematician Albert Schaeffer in 1941.
This conjecture occupies a central position in the field of metric Diophantine approximation, which explores how rational numbers can effectively approximate irrational numbers.
Li Guangzhi watched Xu Qingshan take out a pile of blank draft paper after someone took out a manuscript, and began to write frantically.
At this moment, he felt more and more that he was right to come here, because Xu Qingshan's state at this time could be said to be the plus version of himself.
Although he can sometimes enter this kind of thinking, just like a group of people in a smooth research state.
But it is still difficult to reach as fast as Xu Qingshan.
Xu Qingshan decided to adopt a complex and innovative method. He decided to intuitively display the relationship between the denominator and the approximated irrational numbers by building a graphical model.
Before completing a definite proof, he wanted to be able to simply verify and try to find the answer.
As he was writing, Li Guangzhi saw Xu Qingshan open his computer and start typing codes quickly. This was where Li Guangzhi was stunned.
Li Guangzhi, a mathematical researcher who prefers traditional methods, is actually not very good at using computer codes to assist his mathematical calculations.
That's not to say he can't.
In many paper proofs, mathematical research cannot be separated from the help of computers, but he prefers a traditional conservative research style and theoretical discussion, so many of his derivation parts do not require the use of high-end computer calculation methods.
So when he saw Xu Qingshan quickly typing out a long series of codes on the computer with his fingers flying, he tried to use it to find the rational number p/q of the inequality to approximate a given irrational number.
He suddenly understood the meaning of Xu Qingshan's laboratory. Why is the Information Technology Laboratory next to the Mathematics Laboratory?
Although the development of computers has been rapid, the influence of supercomputers on science is rapidly expanding around the world.
Xu Qingshan's work pace is very fast, and he also uses relatively detailed previous results in his name correction.
For example, Pollington and Vaughan tried to use a simple sieve method in 1990 to give a more refined estimate of the measure, and used it to prove the natural generalization of the Duffin-Schaeffer conjecture in high dimensions.
The application of this simple sieve method gave future generations a major breakthrough in the study of the Duffin-Schaeffer conjecture.
Xu Qingshan is now using computers to make a more refined average estimate of this measure through their screening method and obtain new results under stronger development conditions.
The obstacles to analytical independence he had encountered before served as the key to the final solution.
When Xu Qingshan tried to use graph theory as a solution tool, he successfully broke through this point.
"Oh, it really works!"
Mr. Xu stopped and looked at the results on the computer and the estimated answers he had drawn on the manuscript, although there is no complete paper to prove the entire process.
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But in Xu Qingshan's case, his thinking was clear, which meant that this conjecture was completely proved by him.
Li Guangzhi on the side looked a little dumbfounded. He had not yet realized what Xu Qingshan was doing, but he looked at the several pages full of manuscripts on Xu Qingshan's desk and the programs running on the computer.
He suddenly discovered that the mathematical research methods that seemed to be at the forefront of the times were no longer the traditional ones.
"Director Xu, this is"
Li Guangzhi wanted to ask, but he was too embarrassed to ask. He could only subconsciously point to the manuscript on the table. After all, the topic that could make the boss suddenly speak, calm himself down, and then enter a state of concentrated research must be done. It won't be simple.
"This? Diophantine approximation and Duffin-Schaeffer conjecture. Thanks to you, you wanted to use graph theory to solve this problem, and it suddenly occurred to me that I can also use it to prove analytic independence at this point. Sexual disorders ”
Xu Qingshan picked up his manuscript, looked at it, and handed it to Li Guangzhi.
Li Guang passed the manuscript directly, like a devout worshiper holding a holy object in his hand, and read it with eyes eager for knowledge.
Xu Qingshan is not worried that Li Guangzhi will engage in plagiarism or preemptive registration after getting his first-hand proof.
Not to mention, Li Guangzhi's research field is not here, but his current scientific research status at home and abroad. Regarding this kind of thing, Xu Qingshan said one is one and two is two.
Not to mention that Li Guangzhi is from Xu Qingshan Research Institute.
As we all know, in the industry, for ordinary scientific research staff, the achievements you make within the project will belong to your research institute by default.
In particular, Li Guangzhi can only be regarded as Xu Qingshan's scientific research assistant and assistant researcher now.
"This proves that the process is so beautiful. I can't think of more words to describe it. Maybe elegant?"
Li Guangzhi murmured to himself.
Is this the talent gap?
Xu Qingshan smiled. He looked very relaxed, as if he was not the one who had just quickly solved a scientific research problem.
Li Guangzhi swallowed hard.
He seemed to understand what kind of place he had entered and what kind of leader he had met. Xu Qingshan's level of terror in the field of scientific research is far higher than what he knows from the outside world and what he has learned from these few days of contact.
"Although this is not quite your field, at least it is the inspiration and inspiration you gave me. Well, I agreed to give this topic to Xiao Xue. You lead her to fill in all the processes of perfecting this paper. I will also list three works for you.”
This subject was created by Xu Qingshan, so naturally it could only be him, and the communication must have his name on it.
The remaining two and three games are purely for the assistants in my research team.
Although the second and third works of the paper are not very useful, for Xue Xuequing, such a high-quality conjecture proves that the second work of the paper is enough to surpass many first works in the SCI area and can open many doors for her. For Li Guangzhi, the role of three top-ranked works can also satisfy some of his assessment indicators.
"Oh, okay, okay, okay!"
Li Guangzhi looked like a robot, but the excitement and excitement on his face could not be concealed.
With a boss like Xu Qingshan, are you afraid that you won't be taken away?
Li Guangzhi is now extremely grateful that he was able to summon up the courage to express himself immersedly during the interview, defeat those strong competitors, and finally stand by Xu Qingshan's side.
"Then tell me more about your idea for the topic just now, and let me take a look."
Xu Qingshan stretched.
He was quite happy to solve a topic so casually today and to be able to bring new results to his newly established research team immediately. While he was in good condition, he decided to help Li Guangzhi find out the direction, so let's talk about the key points. , and then take a look at the Wirsing-Schmidt conjecture that I left behind.
"This is me."
Li Guang looked directly at his two crumpled facial tissues, and then at Xu Qingshan's full manuscript, and for a moment he felt an inexplicable feeling of inferiority complex.
With what little I have, I feel like I can’t handle it in front of the boss.
Does he think I don't even understand these things?
"Don't be jabbering here. Did you forget what I just told you? Come and get it, I'll write it, you read it, and if you don't understand, just ask."
Xu Qingshan was as domineering as an old master at this time, so he slapped Li Guangzhi.
In the office, Li Guangzhi was obedient and answered Xu Qingshan's questions seriously from time to time. He watched Xu Qingshan's pen tip simulate an almost complete derivation with his own thoughts on the white paper.
He's a little numb now.
The boss has done the most fulfilling work, so what exactly is his subject?
"Tsk, it seems that I accidentally proved the whole process. It's not a big problem. This topic is still yours. You can just ignore it. You can be an independent author yourself."
Xu Qingshan waved his hand nonchalantly. In fact, Li Guangzhi's topic was not bad.
Not to mention being a top international mathematics journal, the probability of being reviewed in a first-class international mathematics journal is not low.
But Xu Qingshan no longer needs it.
"I"
"Don't worry, mother-in-law, go quickly, go quickly, and arrange Diophantu's work for Xiao Xue. I'll go do other things."
(End of chapter)