Just turned over a new leaf and became a wise and intelligent student

Chapter 359 Proving the Duffin-Schaeffer Conjecture
Xu Qingshan has no use for the results of these researchers, and he himself doesn't even care much about such things.

He had more than he could use up all the results he could produce, so he set up this research team.

The purpose is to free up Xu Qingshan's energy and time spent on basic work and produce more results.

There are generally two situations in the academic circle, regardless of whether it is domestic or overseas.

One is that the team leader has very deep personal strength and attainments in the field, and can accurately guide every mistake in every topic done by the students and assistants arranged by him in the team. This kind of research team led by a super expert has an astonishingly high efficiency in producing scientific research results.

The other is more conventional, and is also the most common model in the global academic community. That is, the professor is only responsible for formulating the big framework, but basically all the work is done by research assistants and students. The students then start from the branches of the project and rely on their junior colleagues to help them complete their doctoral dissertations. In the end, the most fruitful paper is under the name of the tutor, and the tutor himself gets a heavy letter of recommendation and a degree for several years of hard work, as well as one or two small journal articles and a graduation thesis that is difficult to evaluate.

There are still people who think that academia is a pure ivory tower.

But you have to know that this is a group of people with such high IQs, but they are all human beings, and as human beings they have selfishness and weaknesses. And every time selfishness and weakness manipulate the loopholes in the mechanism, it is a blow to the entire system.

Just like the descendants of academic tycoons who can publish many SCI papers while still in junior high and high school.

A boss like Xu Qingshan belongs to the former.

Jin Jing took Xu Qingshan's revision suggestions back to her office workstation. When she was leaving, she unexpectedly let out a small cry of surprise. There seemed to be someone outside the door, but they should be acquaintances. Xu Qingshan looked up curiously and found that Jin Jing breathed a sigh of relief and left with the things.

"Who's coming?"

Xu Qingshan asked.

"Director Xu, I..."

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? If you need anything, come in, or do you want to go next door to see Senior Brother Ruochuan?"

"I'm here to see you, Director Xu."

Li Guangzhi is a guy who, even though he has been encouraged, is still timid in life, and when he walks, it seems as if he is carrying a heavy turtle shell on his back.

"Then come in."

Xu Qingshan was sometimes speechless. This guy was like a fake person except when he was doing academic work.

"Oh, good."

Li Guang stood up straight in the door frame and walked in carefully.

After entering Xu Qingshan's office, he didn't dare to look up or around. He sat down stiffly on the chair that Jin Jing had just sat on, with his legs together, his hands folded together, and placed on his legs, hesitating.

"If you have something to say, just say it. Don't be so distant. We are all family in the research team. There is nothing to be embarrassed about."

Xu Qingshan patted Li Guangzhi on the shoulder.

"Hey, eh, good."

Li Guangzhi took out two crumpled pieces of paper from his arms and spread them out on Xu Qingshan's desk. Xu Qingshan took a few glances and found that these things seemed to be facial tissues. The writing on them was a little blurry, but still clear enough to see.

"Director Xu, I just moved here recently and it feels a bit dry here. I'm a bit constipated. I was just squatting in the toilet, but I suddenly felt it while squatting. Luckily I brought a pen with me, so I quickly recorded this. Take a look at this."

Li Guangzhi still looked excited when talking about things in his field.

He had no idea that the two pieces of paper in his hand became very interesting once his origins were revealed.

The corners of Xu Qingshan's mouth twitched. Just from this thing, he finally understood why Li Guangzhi had not gotten along well with his leaders and colleagues before.

To some extent, he is quite pure, but he also reflects the saying "high IQ, low EQ".

Fortunately, Xu Qingshan himself didn't mind these things very much, so he nodded and listened to Li Guangzhi continue.

Just as he was talking about his attempt to use graphical modeling to more intuitively demonstrate and analyze the relationship between transcendental approximation and continued fractions, Xu Qingshan suddenly frowned.

"Wait, you came up with the idea of ​​graphical modeling."

Xu Qingshan felt that some stars seemed to gradually emerge in the space of this office. Every moment the white stars appeared in the space, Xu Qingshan's mind was working frantically.

His wisdom is like a black hole, forming a vortex of inspiration.

Li Guangzhi didn't dare to speak. He paused, and withdrew from the state of wanting to share his gains, and looked at Xu Qingshan eagerly.

After Xu Qingshan stopped Li Guangzhi from speaking, he suddenly opened the drawer inside his desk and began to rummage through a pile of messy manuscripts inside.

Li Guangzhi was watching from the side. He didn't know what Xu Qingshan wanted to do, but the boss was the boss, and he kept in mind the rank suppression in the academic workplace.

Not long after, Xu Qingshan found a manuscript that had been left idle from the pile of manuscripts.

[Duffin-Schaeffer conjecture] and [Wirsing-Schmidt conjecture].

In this manuscript, Xu Qingshan explained in detail the possible ideas of the entire conjecture, but when he was completing this part of the work, Xu Qingshan was temporarily stuck in one place.

Li Guangzhi's words made Xu Qingshan subconsciously find the core point, so he immediately found the manuscript, hoping to confirm his idea.

The Duffin-Schaeffer conjecture was 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 efficiently approximate irrational numbers.

Li Guangzhi watched as Xu Qingshan took out a pile of blank draft paper and began writing frantically after someone took out a manuscript.

At this moment, he felt more and more that it was right for him to come here, because Xu Qingshan's state at this time could be said to be a plus version of himself.

Although he could sometimes enter this kind of thinking, just like a group of people in a smooth research state.

However, it is still very difficult to reach the same speed as Xu Qingshan.

Xu Qingshan decided to adopt a complex and innovative approach. He decided to build a graphical model to intuitively demonstrate the relationship between the denominator and the irrational number it approximated.

Before completing the exact proof, he wanted to be able to do a simple verification and try to find the answer.

As he was writing, Li Guangzhi saw Xu Qingshan open his computer and start typing code quickly. This is what made Li Guangzhi stunned.

As a traditional mathematical researcher like Li Guangzhi, he is actually not very good at using computer codes to assist his mathematical calculations.

That's not to say he can't.

In many proofs in papers, mathematical research is actually inseparable from the help of computers, but he prefers a traditional conservative research style and theoretical discussion, so many of his derivations do not require the use of high-end computer calculation methods.

So when he saw Xu Qingshan quickly typing out a long string of code on the computer with his fingers flying, trying to use it to find the rational number p/q of the inequality to approximate a given irrational number.

He suddenly understood the significance of Xu Qingshan's laboratory. Why is the Information Science Laboratory next to the Mathematics Laboratory?

Although computers have been developing rapidly, the influence of supercomputers in science is rapidly expanding around the world.

Xu Qingshan works at a very fast pace, and he also uses relatively detailed previous results in his rectification of names.

For example, Pollington and Vaughan attempted in 1990 to use a simple sieve method 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 sieving method has enabled future generations to make a major breakthrough in the study of the Duffin-Schaeffer conjecture.

Xu Qingshan is currently using computers to make a more refined average estimate of the measure through their screening method and obtain new results under stronger development conditions.

The obstacles to analytical independence that he had encountered before were the key to finally solving the problem.

When Xu Qingshan tried to use graph theory as a solution tool, he successfully broke through this point.

“Wow, it really works!”

Mr. Xu stopped and looked at the results on the computer and the estimated answers he had obtained in the manuscript, although there was no complete paper to prove the whole process.

But for Xu Qingshan, his train of thought was clear, which meant that this conjecture was completely proved by him.

Li Guangzhi, who was standing by, was a little stunned. He hadn't yet figured out what Xu Qingshan had done, but looking at the several pages of manuscripts on Xu Qingshan's desk and the programs running on his computer.

He suddenly discovered that the most cutting-edge mathematical research methods were no longer the traditional ones.

"Director Xu, this is..."

Li Guangzhi wanted to ask something, but he was too embarrassed to do so, so he could only subconsciously point his finger at the manuscript on the table. After all, the topic that could make the boss suddenly speak and allow him to calm down and enter a state of focused research must not be simple.

"This? Diophantine approximation and Duffin-Schaeffer conjecture. It's all thanks to you that you wanted to use graph theory to solve this problem, and it suddenly occurred to me that I could also use it to prove the obstacles to analytical independence at this point."

Xu Qingshan picked up his manuscript, looked at it, and handed it to Li Guangzhi.

Li Guang went straight through the manuscript. He read it with a thirsty look, like a devout pilgrim holding a holy relic.

Xu Qingshan was not worried that Li Guangzhi would plagiarize or register his trademark after obtaining his first-hand proof.

Not to mention that Li Guangzhi's research field is not here, even as for his current scientific research status at home and abroad, as for this kind of thing, Xu Qingshan's words are one and 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 and results you produce within a project will belong to your research institute by default.

In particular, Li Guangzhi can now only be regarded as Xu Qingshan's scientific research assistant and assistant researcher.

"This demonstration process is so beautiful, I can't think of any other words to describe it. Perhaps elegant?"

Li Guangzhi muttered to himself.

Is this the difference in talent?
Xu Qingshan smiled, and he looked very relaxed, as if he was not the one who had just quickly solved a difficult 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 was far more terrifying in the field of scientific research than he knew from the outside world and from what he had known in the past few days.

"Although this is not really your field, it is still the inspiration and enlightenment you gave me. Let's put it this way. I promised to give this topic to Xiao Xue. You can help her fill in all the processes of perfecting this paper, and I will also list you as the third author."

This project was done by Xu Qingshan, so naturally he has to be the first author and his name must also be on the correspondence.

The remaining two and three works were purely for sharing with the assistants in his research team.

Although being the second or third author of a paper does not play a big role, for Xue Xueqing, being the second author of such a high-quality conjecture proof paper is enough to surpass many first authors in SCI Zone 1 and can open many doors for her. And being the third author of a top journal can also meet some of Li Guangzhi's assessment indicators.

"Oh, okay, okay, okay!"

Li Guangzhi was like a robot, but the excitement and excitement on his face could not be concealed.

With a boss like Xu Qingshan, are you still afraid that you can’t be led by him?

Li Guangzhi now began to feel extremely fortunate that he had the courage to express himself and show himself during the interview, defeating those strong competitors and finally standing by Xu Qingshan's side.

"Then tell me more about your idea for the topic. Let me see."

Xu Qingshan stretched lazily.

He just casually solved a problem today and was quite happy to be able to bring a new achievement to his newly established research team. While he was in good shape, he decided to help Li Guangzhi find the direction, so he talked about the key points, and then took a look at the Wirsing-Schmidt conjecture that he had left behind.

"Here."

Li Guangzhi looked at his two crumpled tissues, then looked at Xu Qingshan's full manuscript, and for a moment he inexplicably developed a sense of inferiority.

With what I have, I feel a little embarrassed to show it in front of the boss.

Will he think that I can’t even think these things through?

"Don't waste your time here. Have you forgotten what I just told you? Come here and take it. I'll write it down for you to read. If you don't understand, just ask."

At this time, Xu Qingshan was as domineering as an old scholar and patted Li Guangzhi.

In the office, Li Guangzhi was timid and answered Xu Qingshan's questions seriously from time to time, watching Xu Qingshan's pen tip simulate a nearly complete derivation of ideas on the white paper with his own ideas.

He's a little numb now.

The boss has done the most fulfilling work, so what exactly does my project amount to?

"Tsk, it seems like I accidentally proved the whole process. It's not a big problem. The topic is still yours. You can just not fail it. You can keep it and become an independent author."

Xu Qingshan waved his hand nonchalantly. In fact, Li Guangzhi's topic was quite good.

Not to mention the top international mathematics journals, the probability of passing the review in a first-class international mathematics journal is not low.

But Xu Qingshan no longer needs it.

"I"

"Don't be so fussy. Go quickly and assign Diophantus's work to Xiao Xue. I'm going to do something else."

(End of this chapter)