From university academician to chief academician

Professor Lu Yishan's office!

Professor Lu Yishan is a middle-aged man about fifty years old. He has many wrinkles on his face and Mediterranean hair.

Intellectual workers usually have this look. If you have a few extra hairs, others will think you are unprofessional.

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

Fields Medal winners are more or less bald.

Unless you have good genes and are born with strong hair follicles, they can withstand 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's frown. There were too many people with this look in the university, especially among university professors in the Department of Mathematics.

He sat next to Lu Yishan and said nothing, waiting for Lu Yishan to finish thinking.

Science needs inspiration, and mathematics even more so. Interrupting a mathematician while he is thinking is like killing his wife and children.

Lu Yishan took out a piece of paper and pen, found a stool to sit down, and calculated what he had studied recently.

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: "My student taught well!"

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

"Is there one of your students named Ye Fei?"

"Yeah, what happened to him?"

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

Lu Yishan asked: "What super knowledge?"

"He used the projection algorithm in Krylov subspace to solve linear equations."

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

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

Seeing Lu Yishan's confusion, he 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 part of the knowledge of the first and second years of graduate school, and the projection algorithm was the knowledge of the third year of graduate school. He planned to let Ye Fei read the second semester of the second semester.

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

No matter what, of course the thesis is what the instructor lets the students read.

In order to save some trouble, just say yes. Besides, there are only advantages and no disadvantages for students to read more papers.

Lu Yishan asked: "You will tell me this when you come today?"

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

The minimal tower problem is one of the core issues in cardinality invariance theory and one of the research areas of set theory.

This problem emerged in 1940 and has not been solved for 82 years.

"No!" Lu Yishan shook his head tiredly: "It's too difficult. I've been studying for two whole years, but I only have a little clue, but I'm still far from success!"

Liu Yisheng said: "Don't worry. Over the years, many people have studied the problem of minimal towers, but no one has solved it yet."

"If you ask me, let's put this aside in advance. You and I can study the ball distribution paradox together. With the abilities of you and me, we will definitely speed up the research on the ball distribution paradox."

The ball-splitting paradox, also known as the Banach-Tarski paradox, is the most amazing theorem in mathematics.

It's like magic. Just by rotating and translating a three-dimensional solid ball, you can form two identical balls.

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

Mathematics is such a boring and brain-consuming subject. Of course, you have to find the 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-pointing paradox going?"

"Half of the research is done."

"Yeah!" Lu Yishan nodded.

Half of them seem to be progressing quickly, and I think they can be researched.

But mathematics is not a manufacturing industry. You only know how long it will take to make half of the work.

But this is not the case with mathematics. Even if you study 90% of mathematics, you cannot predict how long it will take to study it.

Maybe it's stuck at 99%, with only 1% left, and you can't figure it out no matter how hard you try.

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

"That's better than me." Lu Yishan sighed: "I have only made a start in the past two years, and I am still far away from half of it, let alone successful research."

But he firmly believed that his research would be successful, and Liu Yisheng also firmly believed that his research would be successful.

Scientific research requires a belief, a belief without hesitation.

If you lose all your faith, you will not be able to persevere on the path of scientific research.

Persistence is very important for scientific research.

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

Of course, sometimes you don’t just persist, you also have to learn to give up.

If the same scientific research cannot be found, but you still insist on it, then 99% of people will be useless on the road of scientific research.

1% of people may have enlightenment one day and suddenly become enlightened, but this probability is too small.

If you study other things, you might be able to get inspiration from your previous research, and then go back to study it.

This is often the case in scientific research.

There is a wise saying in the scientific research community that everything is possible, you must believe in miracles.

Five days later!

Ye Fei saw that the task progress bar reached 100%, and he said excitedly: "It has finally reached 100%, and we can start preparing the paper."

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

[Two options for set theory axioms: two paths]

This paper mainly writes about the large cardinality axiom and the forcing axiom.

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

The forcing axiom is the basic theorem of the forcing method.

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

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

In Professor Lu's office, when he saw 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 most of the large cardinal axioms and forcing axioms are contradictory to each other, only a few of them have similarities, and the contradictions can be reconciled.

Therefore, it is very difficult to write from large cardinal numbers and forcing axioms.

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

As a tutor, he must know his students' abilities.

But today I discovered that Ye Fei's ability seemed to be beyond his expectation.

He thought of Professor Liu Yisheng's words again and asked, "Does he have extra study?"

"That's how it should be."

"But it's too much beyond my capabilities."

Professor Lu suppressed the doubts in his heart. It is a good thing for students to be capable.

Every teacher hopes that his students will be strong, especially graduate tutors and doctoral supervisors. If their students are strong, they will be of great help to them in scientific research. No graduate tutor or doctoral supervisor wants to be a dragster.

"He can't really write an A-area paper!" Professor Lu was surprised.

Although he said he asked Ye Fei to write an A-area paper, it was actually just a wish. It would be good if he could write it, and it didn't matter if he couldn't.

As for his grievances with Professor Li Jiguo, he didn't take it to heart.

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 he writes it, he usually still needs to revise it after reading it.

If you don’t revise your paper three or four times, it will be difficult to pass.

After Ye Fei received the information from his tutor, he started writing his thesis that night.

He had classes during the day and homework at night, so he only had time to squeeze in two or three hours a day to write a paper.

The same is true for the other three roommates. Everyone is working hard to write papers.

The semester will be over in just over a month, and the thesis must be written before the end of the semester.

It seems like there is plenty of time, but it is actually very tight.

After the paper is written, you need to revise it, and then show it to your tutor. After that, the tutor will revise it and then revise it based on the tutor's revisions.

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

Just revising the paper will take at least half a month.

At night, dormitory, eleven o'clock at night!

Zhuang Nan looked at the manuscript full of words and felt helpless. He checked a lot of information and wrote more than five thousand words.

According to the instructor's requirements, the paper should be between 30,000 and 50,000 words.

Therefore, I still have to write more than 25,000 words, and this time will take at least half a month.

He sighed tiredly, looked at the other three people who were working hard on their papers, and asked: "Brothers, how is your paper going?"

"I have written more than five thousand words." Zhou Lin said.

"Where are you, Xu Tian?" Zhuang Nan asked.

"I am also over five thousand." Xu Tian said.

"It seems that we are all about the same." Zhuang Nan said, "I also have more than five thousand."

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

Zhuang Nan smiled and said: "He's still early. After all, his paper is going to be in Area A, and it's more difficult than our papers."

Ye Feidao: "I'm almost done. I've almost reached 30,000 words. I'll finish it in another day tomorrow."

"Is it almost done?" The three of them were stunned.

"Impossible!" Zhuang Nan said.

"It was written really quickly." Ye Fei said, "If you don't believe me, come and take a look."

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

Zhuang Nan and the other three walked up behind Ye Fei in disbelief and saw that Ye Fei was writing a paper as if he was writing a novel, very fast.

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

Zhuang Nan said: "Ye Fei, this is just the first draft. It will need to be revised many times after it is written."

Once the paper is written, it is considered the first draft, and after many revisions, it is considered the final draft.

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

"What you wrote was about two choices of axioms in set theory. It's very difficult to write. How can you write it so quickly?" Zhou Lin asked in surprise.

"Yes!" Ye Feidao: "It's actually quite simple."

Zhou Nan and the three of them looked at each other, then turned around silently and sat down at their desks to write their papers.

Is Ye Fei cheating? He writes such a difficult topic so fast. Look at our paper. It is simpler than his paper, but it is written slower than him.

No comparison, no harm, it’s too curly.