Professor Lu Yishan's office!

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

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

Especially math, more hair, proves that you think less.

Fields Medal winners, more or less bald.

Unless you have good genes, you are born with strong hair follicles that can resist the power of mathematics.

For example, Tao Zhexuan.

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

It was not surprising that he saw Lu Yishan's frowning appearance, there were too many people with this style in the university, and it was even more common for university professors in the Department of Mathematics.

He sat next to Lu Yishan and didn't speak, waiting for Lu Yishan to finish thinking.

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

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

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

Liu Yisheng put down his pen and said with a smile: "Your students teach well!" ”

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

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

"yes, what's wrong with him?"

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

Lu Yishan asked, "What supernatural knowledge?" ”

He used a projection algorithm in Krylov's subspace to solve linear equations.

"Projection algorithm?" Lu Yishan was surprised: "When will he do this?" ”

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

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

Lu Yishan was puzzled, 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 one and two, and the projection algorithm was the knowledge of research three, and he was going to let Ye Fei read it again in the second semester.

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

In any case, the dissertation is, of course, for the tutor to have the student read.

In order to save some trouble, let's just say yes, and besides, there is only benefit and no harm in students reading more papers.

Lu Yishan asked, "You came here today to tell me about this?" ”

"It's not!" 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 cardinal invariance theory, and it is also one of the research fields of set theory.

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

"Nope!" Lu Yishan shook his head tiredly: "It's too difficult, I've been studying it for two whole years, but I just have a little clue, and I'm still far from success!" ”

Liu Yisheng said: "Don't worry, for so many years, how many people have studied the problem of the extremely small tower, and no one has solved it yet." ”

"If you want me to say, let this go in advance, you and I will study the ball-sharing paradox together, and with the ability of you and me, we will definitely be able to greatly speed up the study of the ball-sharing paradox."

The part-sphere paradox, also known as the Banach-Tuski paradox, is the most fantastic theorem in mathematics.

It's like magic, taking a three-dimensional solid ball, just by rotating and translating, you can form two balls that are exactly the same as the original.

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

Mathematics is such a boring and brain-consuming study, of course, you have to find a direction that you are interested in to study.

Interest is the biggest motivator, and if you lose interest, inspiration will not appear.

Lu Yishan asked, "How is your research on the ball-splitting paradox?" ”

"I'm halfway there."

"Hmm!" Lu Yishan nodded.

Half of it seems to be progressing quickly, and I think I can study it.

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

But that's not the case with mathematics, and even if you get 90% of your math work, you can't predict how long it will take to figure it out.

Maybe it's stuck at 99%, only 1% is left, and no matter how much you try to research, you can't study it.

And this 1%, maybe card for a few years, maybe card for a lifetime.

"That's better than me, too." Lu Yishan sighed: "I have only had a beginning in the past two years, and I am still very far from half, let alone the success of the research." ”

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

Scientific research requires a conviction and a belief that does not hesitate.

If you don't have any faith, you can't stick to the road of scientific research.

Persistence is very important for scientific research.

You may not have a strong talent, but you must be able to persevere.

Of course, sometimes it's not just about persevering, it's also about learning to give up.

If you can't do the same scientific research, but you still insist on it, then 99% of people will be abandoned on the road of scientific research.

1% of people may open their minds one day and suddenly come to their senses, but this probability is too small.

If you study something else, you may be inspired by what you have researched before, and then you can come back to it.

This is often the case on the road to scientific research.

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

Five days later!

Ye Fei looked at the task progress bar reaching 100%, and he said excitedly: "It's finally 100%, and you can start preparing your thesis." ”

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

[Two Options for the Axioms of Set Theory: Two Paths]

This dissertation is mainly about the axiom of large cardinality and the axiom of force.

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

The axiom of force is the fundamental theorem of force and force.

The forced forcing method is an important method for constructing extended models in axiomatic set theory research.

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

In Professor Lu's office, when he saw Ye Fei's news, he hurriedly opened his mailbox to check it.

"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 cardinality and the axiom of force, most of them are contradictory to each other, and only a few have similarities that can reconcile the contradictions.

Therefore, it is very difficult to write from the large cardinal number and the axiom of force.

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

As a mentor, he must know his own student abilities.

But today, I found that it seemed that Ye Fei's ability exceeded his own estimates.

He remembered Professor Liu Yisheng's words again and said, "Does he have additional learning?" ”

"It should be."

"But that's too much more than that."

Professor Lu suppressed the doubts in his heart, and it is naturally a good thing that students are capable.

Every teacher hopes that their students are strong, especially graduate supervisors and doctoral supervisors, their students are strong, and they are also very helpful in scientific research.

"He's not really going to be able to write a section A paper!" Professor Lu was surprised.

Although he said that he asked Ye Fei to write a paper in Area A, it was actually just a wish, and it was very good to write, and it didn't matter if he couldn't write it.

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

After a while, he made some revisions to Ye Fei's outline, and then sent it to Ye Fei and asked him to write according to the outline first.

After it is written, he has read it, and he generally has to revise it.

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

After Ye Fei received the information from his supervisor, he began to write his thesis that night.

He attended classes during the day and had homework at night, and only found time to squeeze out two or three hours a day to write papers.

The other three roommates are the same, and they all work hard to write papers.

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

It seems like a lot of time, but it's actually very stressful.

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

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

It takes at least half a month to revise the paper.

In the evening, in the dormitory, eleven o'clock in the evening!

Zhuang Nan looked at the manuscript full of words, feeling helpless, he checked a lot of information, and almost wrote more than 5,000 words.

According to the supervisor's requirements, the thesis is between 30,000 and 50,000 words.

Therefore, I 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 desperately writing their papers, and asked, "Brothers, how is your paper?" ”

"I've written more than 5,000 words." Zhou Lindao.

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

"I'm also more than five thousand." Xu Tiandao.

"Looks like we're all about the same." Zhuang Nandao: "I am also more than 5,000. ”

"What about Ye Fei?" Xu Tian asked.

Zhuang Nan smiled: "He is still early, after all, his thesis is going to enter Area A, which is more difficult than our papers." ”

Ye Fei said: "I'm almost done, I'm almost 30,000 words, and it's almost enough to write for another day tomorrow." ”

"Almost ready?" The three of them were stunned.

"Impossible!" Zhuangnan Road.

"It's almost written." Ye Fei said: "I don't believe you come and see." ”

The system has a targeted acquisition of knowledge, so he writes papers much faster.

Zhuang Nan and the others walked 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 words came out.

Zhuang Nandao: "Ye Fei, this is just the first draft, and it will have to be revised many times after writing." ”

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

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

"You're writing about two axiomatic choices of set theory, it's hard to write, and you're writing so fast?" Zhou Lin asked in surprise.

"That's right!" Ye Fei said: "Actually, it's quite simple. ”

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

Ye Fei is not open, such difficult topics are written so quickly, look at our paper, it is simpler than him, and it is slower than him.

No comparison, no harm, too rolly.