From a university student to a chief academician

Chapter 4 dissertation nearing completion
Professor Lu Yishan's office!

Professor Lu Yishan is a middle-aged man in his 50s, with many wrinkles on his face and Mediterranean hair.

Mental workers generally have this style. If you have a few more hairs, others will think you are unprofessional.

Especially in mathematics, more hair proves that you think less.

A Fields Medal winner, more or less bald.

Unless the genes are good, the natural hair follicles are strong and can resist the power of mathematics.

Such as Terence Tao.

Professor Liu Yisheng walked in with his hands behind his back. He was the professor who taught Ye Fei and others.

He was not surprised to see Lu Yishan frowning tightly, there were too many people with this look in the university, especially university professors in the Department of Mathematics.

He sat beside Lu Yishan without speaking, waiting for Lu Yishan to finish thinking.

Science needs inspiration, especially mathematics. Interrupting a mathematician while thinking is like killing his wife and children.

Lu Yishan took out a pen and paper, found a stool and sat down, and also calculated his recent research.

After a long time, Lu Yishan stopped thinking, looked at Liu Yisheng, and said, "Why are you here?"

Liu Yisheng put down his pen and said with a smile, "Your student is teaching well!"

Lu Yishan took a sip from the water glass on the table, relieved his nervous thoughts, and said, "What do you mean?"

"Is there someone named Ye Fei among your students?"

"Yeah, what happened to him?"

"I asked him a question today, and he answered it perfectly, and he even answered it with super-class knowledge."

Lu Yishan asked: "What super-class knowledge?"

"He uses projection algorithms in Krylov subspaces to solve linear equations."

"Projection algorithm?" Lu Yishan was surprised: "When did he know this?"

"He said he learned it from reading a paper."

He looked at Lu Yishan puzzled, and asked, "Didn't you let him see it?"

Lu Yishan was confused, when did he let Ye Fei read such a paper?
The papers he asked Ye Fei to read were all part of the knowledge of Research [-] and Research [-], and the projection algorithm was the knowledge of Research [-], and he planned to let Ye Fei study it in the second semester.

Lu Yishan nodded and said, "I let him see it."

In any case, the thesis is of course for the tutor to let the students read.

In order to save some trouble, let’s just say yes, and it’s only good for students to read more papers, not bad.

Lu Yishan asked: "You came today and told me about this?"

"No!" Liu Yisheng shook his head and said, "Has there been any progress on your tiny tower issue recently?"

The minimal tower problem is one of the core problems in the theory of invariant cardinality, and it is also one of the research fields of set theory.

This problem appeared in 1940, and it has been 82 years since then, and it has not been resolved.

"No!" Lu Yishan shook his head tiredly: "It's too difficult. After studying for two full years, I just have a little clue, and I'm still far away from success!"

Liu Yisheng said: "Don't worry too much. For so many years, many people have studied the problem of extremely small towers, but no one has solved it yet."

"If you want me to say, put this in advance, you and I will study the paradox of ball distribution together. With the abilities of both of you and me, we will definitely be able to greatly speed up the research on the paradox of ball distribution."

The split-sphere paradox, also known as the Banach-Tarski paradox, is the most wonderful theorem in mathematics.

It is like magic, a three-dimensional solid ball, only through rotation and translation, can form two balls that are exactly the same as the original.

Lu Yishan shook his head: "I'm not interested in the ball-sharing paradox."

Mathematics is such a boring and brain-intensive subject, of course it is necessary to find a direction of interest to study.

Interest is the greatest motivation. If you lose interest, inspiration will not appear.

Lu Yishan asked: "How is your research on the ball-sharing paradox going?"

"Half of the research is done."

"En!" Lu Yishan nodded.

Half of the progress seems to be fast, and I think it can be researched.

But mathematics is not a manufacturing industry, half of it is made, and you know how long it will take to make it.

But this is not the case with mathematics. Even if you have researched 90% of mathematics, it is impossible to predict how long it will take to research it.

Maybe it's stuck at 99%, and only 1% is left. No matter how much you think about it, you can't research it.

And this 1% may be stuck for a few years, maybe for a lifetime.

"That's better than me." Lu Yishan sighed: "It took me two years to get started, and there is still a long way to go, let alone a successful research."

But he firmly believes that his research will be successful, and Liu Yisheng also firmly believes that his research will be successful.

Scientific research requires a belief, a belief that will never turn back.

If the faith is gone, we will not be able to persevere on the road of scientific research.

Persistence is very important for scientific research.

Maybe you don't have a strong talent, but you must persevere.

Of course, sometimes it is not just persistence, but also learning to give up.

If the same scientific research fails to come out all the time, but you still persist, then 99% of people will be useless on the road of scientific research.

1% of people may become enlightened one day and suddenly realize it, but the probability is too small.

If you study other things, you may be inspired by the previous research, and then go back to study.

Such things are often the case on the road of scientific research.

There is a famous saying in the scientific research community that everything is possible, and we must believe in miracles.

Five days later!
Ye Fei watched the task progress bar reach 100%, he said excitedly: "Finally reached 100%, you can start preparing the thesis."

At this time, he already knew the paper he was going to write in his mind.

【Two Choices for the Axioms of Set Theory: Two Paths】

This paper mainly writes the axiom of large cardinality and force axiom.

The axiom of large cardinal numbers is one of the five axioms of set theory.

Force axiom is the basic theorem of force law.

Force method is an important method for constructing extended models in the study of axiomatic set theory.

Ye Fei wrote the topic and outline, then sent it to Professor Lu, and said it on WeChat.

In Professor Lu's office, seeing Ye Fei's message, he quickly opened his mailbox to check.

"Huh?" After seeing Ye Fei's topic selection and content introduction, he was a little surprised: "This content is not very easy to write!"

Because of the axiom of large cardinal number and the axiom of force, most of them are contradictory to each other, and only a few of them have similarities and can reconcile the contradictions.

Therefore, it is very difficult to write from the perspective of large base numbers and forced axioms.

He looked at the outline again, and was a little surprised: "When did this kid become so capable?"

As a tutor, he must know his own ability as a student.

But today, I found that Ye Fei's ability was beyond his estimation.

He recalled Professor Liu Yisheng's words again, and said, "Does he have extra studies?"

"It should be so."

"But the capacity is too much."

Professor Lu suppressed the doubts in his heart, it is naturally a good thing for students to be strong.

Every teacher hopes that their students are strong, especially graduate tutors and doctoral supervisors. Their students are strong and will help them a lot in scientific research. No graduate tutor or doctoral supervisor wants to bring a bottle of oil.

"He can't really write a paper in Area A!" Professor Lu was surprised.

Although he said that he wanted Ye Fei to write a thesis in Area A, it was actually just a wish. It is very good to write it, and it doesn't matter if it can't be written.

As for the grievances between him and Professor Li Jiguo, he didn't take it seriously.

After a while, he revised Ye Fei's outline and sent it to Ye Fei, asking him to write according to the outline first.

After writing, after he has read it, he usually still needs to revise it.

It is very difficult to pass the paper without changing it three or four times.

After Ye Fei received the tutor's information, he started writing the thesis that night.

He has classes during the day and homework at night, and only finds two or three hours a day to write papers.

The same is true for the other three roommates, and everyone is desperately writing papers.

The semester will be over in just over a month, and the thesis will be finished before the semester ends.

It seems that there is plenty of time, but it is actually very tense.

After the thesis is written, it needs to be revised, and then shown to the tutor, and then the tutor revises it, and then revises it according to the tutor's revision.

If you don't change it three or four times, it will be very difficult to pass the paper.

It will take at least half a month just to revise the thesis.

At night, in the dormitory, at eleven o'clock in the middle of the night!
Zhuang Nan looked at the manuscript full of words and felt helpless. He checked a lot of information and wrote almost 5000 words.

According to the requirements of the tutor, the thesis should be between [-] and [-] words.

Therefore, I have to write more than 5000 words, and this time will take at least half a month.

He sighed tiredly, looked at the other three who were desperately writing their thesis, and asked, "Brothers, how is your thesis going?"

"I've written more than 5000 words." Zhou Lin said.

"What about you, Xu Tian?" Zhuang Nan asked.

"I'm also over 5000." Xu Tian said.

"It looks like we're all about the same." Zhuang Nan said, "I'm also over 5000."

"Where's Ye Fei?" Xu Tian asked.

Zhuang Nan said with a smile, "He's still early. After all, his thesis is going to enter Section A, which is more difficult than ours."

Ye Fei said: "I'm almost done. I'm almost at [-] characters. I'll be done with another day of writing tomorrow."

"It's almost finished?" The three of them were taken aback.

"Impossible!" Zhuang Nan said.

"It's almost finished." Ye Fei said, "If you don't believe me, come and see."

The system acquires knowledge in a targeted manner, so he can write papers much faster.

The three of Zhuang Nan walked behind Ye Fei in disbelief, and saw that Ye Fei was writing a thesis as if he were writing a novel, very fast.

In the blink of an eye, three or four characters came out.

Zhuang Nandao: "Ye Fei, this is just the first draft, and it needs to be revised many times after it is finished."

The thesis is considered as the first draft after writing, and the final draft after several revisions.

"That's for sure." Ye Fei nodded: "But it should be finished soon."

"What you wrote is the choice of two axioms in set theory. It's very difficult to write. You wrote it so fast?" Zhou Lin asked in surprise.

"That's right!" Ye Fei said, "It's actually quite simple."

The three of Zhou Nan looked at each other, then turned around silently and sat down at their respective desks, hurrying to write their thesis.

Is Ye Fei cheating? He wrote such a difficult topic so quickly. Looking at our paper, it is easier than him, and he writes slower than him.

There is no harm without comparison, too curly.

(End of this chapter)