From university academician to chief academician

Chapter 14 Finding the Proof Idea

MIT, library!

Gao Fei looked at Ye Feixin's published paper.

"Condition (H4) is equivalent to b(0)N={1, 2, 3, .}, and it will be seen that condition (H4) is the only necessary condition for the existence of formal power series solutions..."

"Power series solution, power series solution..." Gao Fei murmured to himself, his eyes getting brighter and brighter.

"Yes!" He suddenly clenched his fists excitedly and pumped his fists: "That's how it works."

People around him looked at him irritably when he interrupted their reading.

Gao Fei realized that he was speaking too loudly and was disturbing others' reading, so he shrank his neck.

He said excitedly in his heart: "I found a way, this is the solution."

"Ye Fei is really my lucky star. Two months are about to expire. I have found a solution. Ye Feifei is doomed."

"I don't believe he can find the solution from Ye Fei's paper."

Gao Fei is blindly confident in himself. This is because he has never failed in studies since he was a child.

Long-term victory brings great confidence.

Ten days later!

Ye Fei glanced at the system and saw that the progress of the task of exploring the singular cardinality problem had reached 95%.

When he published the paper on the basis of singular cardinal numbers, the progress of the task reached 40%.

When the first solution was published, the task progress reached 50%.

The solution for the second part is 60%, the solution for the third part is 70%, and the solution for the fourth part is 90%

After another week of study, the task progress reached 95%

"Only 5% is left." Ye Fei let out a breath and said distressedly: "But what to do next?"

The road to scientific research becomes more difficult the higher you go.

This 5% Ye Fei has made no progress after three days of hard work.

This is like a natural chasm, blocking his research on strange cardinal numbers.

"Two months are up. Ask Gao Gaofei if he has found it."

Ye Fei sent a message to Gao Fei through Stack Exchange: "Gao Fei, have you thought of the proof of singular cardinal numbers?"

Gao Fei gave it a try and asked, "What about you?"

"Haven't thought of it yet."

Gao Fei was very excited when he saw Ye Fei's answer. As he expected, he did not find the proof of the singular cardinality.

Gao Fei replied: "I have found ideas from a type of function space."

"Isn't it a proof method?" Ye Fei asked.

"What are you thinking about?" Gao Fei curled his lips and continued to reply: "You still want to solve the problem that Singularity has not solved in 149 years in two months!"

Ye Fei shook his head regretfully after seeing it. He had his own ideas, but what he wanted now was a method of proof.

Ye Feidao: "Then tell me your thoughts."

"OK!" Gao Fei replied: "My idea is found from the Tribel-Lizhokin space in a type of function space, the weighted Mori-type Bisol space and the Tribel-Lizhokin space. Fourier’s Multiplier Theorem.”

"The boundedness of a class of pseudodifferential operators with non-regular signs can be found."

"Then we get the real Euclidean space and Schwartz space..."

Ye Fei looked at Gao Fei's explanation and saw that Gao Fei said that the low frequency part should be considered by the previous lemma and only need to focus on the high frequency part.

Suddenly, his mind felt like a small universe exploding, and an idea suddenly appeared in his mind.

"Yes, that's it. We introduce it from low frequency to high frequency, and then use space to find differential operators."

Ye Fei connected the five papers on singular cardinality he wrote during this period with the ideas he just thought of to form a complete method of proving singular cardinality.

The first paper was the foundation of singular bases and four papers on solutions to singular bases, which all led him to the door of singular bases.

But there is still a key missing, and now he has found the key, which is to use space to find differential operators.

“So, both my method and his method prove that singular bases are correct.”

"My method is to take the road and send me to the door of the strange cardinal number, and his method is to make a key to open this door."

"So we can't say who loses and who wins?"

Ye Fei smiled in his heart and said, "But without my path, I wouldn't be able to reach this door!"

"Of course, I can't open the door without his key."

"Also, his current thinking is not able to create the key. With his help, I used my own method to create the key."

Ye Fei took a look at the system and saw that the task progress was 100%.

He said in surprise: "Sure enough, my idea is right."

Gao Fei said: "I've finished what I said, how about it, now you are convinced!"

Ye Feidao: "I'm convinced, of course I'm convinced."

He complained in his mind: "Looking at this person's ability, he must have been involved in mathematics for a long time. He must be in his thirties, but he talks like a twenty-year-old girl."

Gao Fei said: "Then use my method to explore singular cardinal numbers!"

"Okay, no problem." Ye Fei said: "But you explore first. I have to wait for half a month. I have been very busy with some things recently. We will continue after half a month."

He was going to write a paper on proving singular cardinal numbers, but he couldn't tell anyone else about it.

After you write it down and post it on Arxiv, it will be useless for others to know.

Is this plagiarism?

No, there are many papers on Arxiv.

If your own paper contains a small portion of other people's papers, it will be counted as citations at most.

Besides, when a paper is sent to a journal, the journal also has to review the duplication rate.

If the repetition rate is high, it will not pass the first review.

Gao Fei pouted, a little unhappy. We had agreed to explore the strange cardinal numbers together. Why is this person like this!

But he also knows that people always have three urgent needs. Maybe the other person is really busy with something, and he can't stop him.

He replied: "Okay, hurry up then."

"OK!" Ye Fei replied.

End the conversation with Gao Fei and exit Stack Exchange.

Gao Fei looked at Ye Feifei's head that turned into black and white, and suddenly said: "By the way, I haven't asked him who he is yet, forget it, next time!"

He remembered the task assigned to him by his mentor.

Ye Fei quickly opened Word, wrote down the ideas that came to his mind, and then started planning the outline.

This paper is about proving singular cardinal numbers.

It is very important, so he needs to plan it carefully.

[Algorithm of non-regular graph isomorphism to prove singular cardinalities]

On September 1st, university starts!

Many new and former students, undergraduates, master's and doctoral students, began to enter the school.

When they entered the school gate, they all saw a banner above the school gate.

[Congratulations to Ye Fei, a graduate student from the School of Mathematics of our school, for his five papers entering SCI Area 1]

When many people saw this banner, they were blinded and filled with envy.

After seeing this, many parents pointed fingers and told their children to follow this person named Ye Fei as a role model.

Even some parents are illiterate and don’t know what SCI is.

But your children always know, ask them what SCI is.

After some popular science among their own children, they knew what it means to enter SCI.

Many university professors saw this banner and felt envious and jealous.

Why don’t their academy have a genius like Ye Fei!

Before they even came to school, they heard that a genius had emerged from the mathematics academy.

In just one holiday, five papers entered SCI Area 1.

They are all about set theory, and one of them is very important, as it is the basis for proving singular cardinal numbers.

It's like a holiday has passed and the whole world has changed.

Zhuang Nan walked with a group of people. He turned his back to the door and said excitedly: "Let me tell you, my roommate Ye Fei is amazing. He has published five papers, all of which have entered SCI Zone 1."

Zhuang Nan is indeed a little expert in intelligence. He has been paying attention to Ye Fei's paper since he learned that Ye Fei's paper entered the SCI area.

He has read all the papers Ye Fei posted on Arxiv, and he also went to Stack Exchange to support Ye Fei.

Of course, he accidentally leaked some information about Ye Fei.

For example, Ye Fei's age, Ye Fei is his roommate, and Ye Fei has a good relationship with him...

A person next to him pointed to the banner on the gate and said, "Zhuang Nan, we all know about Ye Fei, look."

Zhuang Nan turned around and looked, dumbfounded, and then said: "The school is too licky!"

Zhou Lin said: "If you can complete five SCI area one papers in a short period of time, the school will do the same."

Zhuang Nan said in frustration: "Forget it, I can't do it."

On this day, Ye Fei became famous at Zhonghu University.

Freshmen, old students, lecturers, professors, deans, principals.

As we all know, Ye Fei from the School of Mathematics at Zhonghu University has five papers entered into SCI Area 1.

This is a dazzling achievement. It is difficult for ordinary people to enter the first area of ​​SCI with one paper, let alone five papers.

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