Chapter 23 proves the problem of the smallest tower
After returning to school, Ye Fei went to the tutor's office.
"It's back!" Seeing Ye Fei come in, Lu Yishan said with a smile.
"Mentor!" Ye Fei sat down and said, "I have already proved p=t, do you know about this?" ”
Lu Yishan's expression froze, do I know? Of course I do.
Because of you, I have no goal to strive for.
Lu Yishan nodded and said, "I know." ”
"I went to the School of Mathematics of Fudan University to give a lecture in the past few days, and later entered their small library, and saw a lot of literature that is not published to the public, including the knowledge of set theory, which allowed me to find the remaining proof ideas for the minimum tower problem."
Lu Yishan looked at Ye Fei in surprise and said, "You have found the idea of p=t under ZFC in the past few days?" ”
"yes!" Ye Fei nodded and said with a smile: "But I haven't verified it yet, if the verification is successful, our very small tower problem will be proven." ”
Lu Yishan sighed in his heart, from the beginning of the research, in less than two months, you have solved the problem of the extremely small tower.
So what is my research for so many years?
Lu Yishan felt a strong malice from a genius.
Lu Yishan said: "When are you going to write your thesis?" ”
"I'll write it right away, I'm here to talk to my mentor."
Lu Yishan complained in his heart, did you come to hit me!
Lu Yishan nodded.
After leaving the tutor's office, Ye Fei began to check what he was thinking about under ZFC p=t.
Three days later, the library!
Ye Fei said in surprise: "My idea is really right. ”
"Let's start writing my paper!"
At this time, what Ye Fei didn't know was that many people around the world knew the proof idea of p=t after listening to his explanation of the proof of p=t.
The most difficult of the smallest tower problems is p=t.
p=t under ZFC is not too difficult.
After all, p=t has been proven, and all that remains is to convert p=t and put it under ZFC.
Faced with the temptation of the world's problems, many people want to be the first to prove the problem of the smallest tower.
Perhaps, this is the only chance in their lives that they can prove the world's problems.
They had to prove the problem of the Extremely Small Tower before Ye Fei, otherwise they would have no chance.
They're kind of cheeky about it.
After all, the most difficult ones were solved by Ye Fei, and as long as they proved the simple part, they could prove the problem of the extremely small tower.
Then they complete the paper and publish it to Arxiv, and they can become the authors who prove the problem of the smallest tower.
Of course, there must have been people who accused them of being cheeky afterwards.
But in the face of the temptation of the world's problems and the temptation of being famous in the world of mathematics, be cheeky and be cheeky!
Kyoto University, Library!
Rollo, a master's student in the Department of Mathematics, came to the library around 9 a.m. this weekend.
But the library was overcrowded, and it took a long time to find a place to sit down.
As soon as he sat down, he opened Arxiv, a website frequented by math students.
Suddenly, his eyes widened and he exclaimed, "Ye Fei has proved the problem of the Extremely Small Tower." ”
It's loud and a lot of people hear it.
Many people were disturbed from their studies and looked at him irritably.
But Luo Luo didn't seem to notice, and he excitedly clicked on Ye Fei's newly published paper.
"It's too fast, it's only been half a month!"
"It is worthy of Ye Fei, it has been proved in such a short time that p=t under ZFC."
Many people in the library heard Luo Luo's words, and some people who knew Ye Fei went online to check it out.
Soon, they also found Ye Feixin's published paper.
University of Cambridge, England!
"Ye Fei has already proved the problem of the extremely small tower." Kumas looked at Ye Feixin's published papers, and then looked at his own efforts in the past few days, and his heart ached.
Ever since he saw Ye Fei explain p=t, he has been working hard to prove that p=t is under ZFC.
wanted to prove it before Ye Fei, but now his proof is not half there, and Ye Fei has already proved it.
"How could he be so fast?"
Princeton, North Beauty!
"It proved so quickly." Perry said desperately: "There is no chance, Ye Fei's proof must be right, after all, he has already proved the most difficult part of the extremely small tower problem, and the easy part should not be difficult for him." ”
"Ouch......" Perry looked at his efforts on the table for days, and he pushed all the manuscript papers on the table to the ground, scattering them all over the floor.
Toeikoku, University of Tokyo!
"Baga ......" Taro Yoshikawa looked at the computer screen angrily: "Why, I've tried so hard, but I still haven't caught up, why are you so fast?" ”
"I'm so slow, such a good opportunity is gone." He clenched his fists in reproach.
When Ye Fei proved the problem of the smallest tower, the paper was published on Arxiv.
Many people who are working on the p=t problem under ZFC are full of despair.
No one would think that Ye Fei's proof was wrong.
After all, the most difficult part was solved by Ye Fei, and the easy part should not be difficult for Ye Fei.
On this day, countless people around the world were defeated by Ye Fei's talent.
Of course, there are also many people who are shocked and surprised by Ye Fei's talent, especially Xia Guoren.
After all, Ye Fei is a native of Xia Kingdom, and Ye Fei's achievements make them proud.
At this point, the set theory section on Stack Exchange!
A lot of posts are about Ye Fei's proof of the very small tower.
"Calculating the time, Ye Feiyi spent two months to prove the problem of the extremely small tower."
"It can't be counted like this, he didn't do all the research in the past two months, I heard that during this period, he also went to Fudan University to give a lecture and stayed at Fudan University for three days."
"Anyway, Ye Fei's scientific research speed is too fast, I have never seen such a fast man."
"Why are men so fast, women are not so fast!"
"Can you talk about it, please don't drive, we're talking about scientific research."
"His speed is much faster than when he studied the Strange Cardinality, he should have spent four months researching the Singular Cardinality, and now he has only spent half the time on the Exotic Cardinal Problem on the Smallest Tower."
"I've never seen anyone like this, the odd cardinal and the Tiny Tower are the same difficult problems, and he is studying faster and faster."
“……”
In the evening, Ye Fei took a walk in the playground while thinking about the next research.
He has to write two papers, one is p=t and the other is p=t under ZFC.
He only published one article, which is p=t under ZFC.
The other one, he will write in half a month.
The reason why p=t under ZFC was published first was because he had hung the proof process of p=t on Arxiv, and he was afraid that someone would prove the minimum tower problem before him.
That's why p=t under ZFC was published first.
Of course, the ZFC written now under p=t, just the first draft is hung on Arxiv, and it will take a few days to revise the paper many times before sending it to the journal.
"Since I have chosen set theory, then I should continue with set theory in my next research."
"Topological Ott conjecture? Typical in-model problem with supertight cardinality? Two Problems in the High-Level Limited Borel Equivalence Relationship? Continuum Determination Problem? Turing Equivalence Problem? Or is it a question of the decidability of real number theory with exponential functions? ”
These questions are all the remaining problems in set theory except for the continuum hypothesis.
Ye Fei's subsequent research still started from these questions.
As for the continuum hypothesis, it is the most difficult ultimate problem.
At least these problems are not solved, and he will not start with the continuum hypothesis.
At this time, Ye Fei's mobile phone rang!
"Hey, Mentor!"
"Ye Fei, come to my office and tell you good news."
"Okay!"