Chapter 4 Thesis is about to be completed

Author: Big fish eats small fish

Chapter 4 Thesis is about to be completed

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.

For example, 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 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 when 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 you 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 used super-class knowledge to answer it."

Lu Yishan asked: "What super-class 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 all 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 it again next 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, it is only good for students to read more papers, not bad.

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 issue 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 appeared 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 it 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."

"Let me tell you, let's put this aside in advance. You and I will study the ball-sharing paradox together. With the abilities of you and me, we will definitely speed up the research on the ball-sharing paradox."

The ball-splitting paradox, also known as the Banach-Tarski paradox, is the most wonderful 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, so of course you have to find the direction of your interest to study it.

Interest is the biggest 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. Once you make half of it, you know how long it will take to make it.

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 may be stuck 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 done, 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 gain inspiration from your previous research and then go back to study it.

Things like this often happen in the field of 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 time, he already knew the paper he wanted to write in his mind.

[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 this capability is too much."

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 also 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 that 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.
To be continued...