God's Crown

"Mr. Faltings, the previous calculations..." Schultz glanced at the previous draft, "There are no mistakes, we only have the last few pages. This is a difficult point, and it will probably take some time."

Faltings did not appear to be as shocked as Schultz, he just frowned slightly, "Will we be brought into his logic by An Yan? That is, he did not solve the BSD conjecture, but his The logic is too strong. We are also involved?"

"No professor, I have read this paper carefully, and there is no problem at all. I can only say-maybe he really solved the BSD conjecture?"

"It's still not sure whether he really made the BSD conjecture." Faltings said with a frown, "but we must pay attention to one thing, his calculations are very smooth, and his ideas... are somewhat different from those of the public. Same. How should I put it? This guy’s guess is like God’s idea.”

Faltins didn't know how to describe An Yan's magical strokes. Obviously, the previous calculations were very smooth, but the calculations had already reached the point where they could not be calculated.But I didn't expect that his magic stroke brought the whole calculation formula back to life, that is to say——his calculation formula brought the whole calculation back to life—it seemed that he really solved the BSD conjecture.

But Faltings is still a little confused, or rather, still a little confused.

It's just that he didn't have more time to think about these issues, such as how Anyan found a solution to the BSD conjecture, and why he was able to relate the arithmetic and analytical properties of Abelian varieties.The only thing he can be sure of now is - there is nothing wrong with the previous calculations.

However, there is no problem with the calculation, which is strange.Faltings frowned slightly, pondering for a while with the paper.Putting it aside, Schultz was still counting at this time.

There was a 'rustling' sound on the small blackboard. For more than half a month, he has been checking An Yan's thesis.It has to be said that in An Yan's thesis, he also seems to have learned a lot.Especially regarding the calculation of Abel clusters, he felt that An Yan was simply a genius among geniuses.

Why is there such an idea, this idea is really awesome.

While calculating, he pondered An Yan's thesis.This paper was very inspiring to him in algebra.

On An Yan's side, in more than half a month, he actually failed to produce anything.Hodge conjectured that the problem about algebraic varieties was really too difficult, and An Yan couldn't figure it out after thinking about it for a long time.

However, it has not been long since he solved the BSD conjecture, and he still has some time to make the Hodge conjecture, which is more than a year away from the two years given to him by Professor Hudson... Even if the Hodge conjecture cannot be made , at least BSD guesses that he has made phased results.So An Yan wasn't too flustered, he was slowly calculating.

Even though he has stayed in Bonn for nearly half a month now, he still doesn't know... how is the situation at Gu Weize's side.Originally, they had jet lag, but now Gu Wei seemed to be traveling and did not contact him every day.And now he is busy making Hodge's conjecture, and he really doesn't have much time to talk to Gu Weize every day.

He quietly wrote the calculation formula on the small blackboard, and Faltings had already reached the most important step with Schultz.If this step is correct, then there is one last page left. In fact, you can tell without looking at it that An Yan's calculation is correct.

While writing the most important calculation steps, Schultz was thinking wildly. If An Yan really solved the BSD conjecture, then next year's International Congress of Mathematicians will definitely be able to win An Yan's Fields Medal.

Perhaps there are still many prizes waiting for An Yan to claim.

"Peter." Faltings called Schultz, "Be more attentive, don't miscalculate the steps."

"Okay, Mr. Faltings." Schultz concentrated on writing the most important calculation steps on the blackboard.

…………

An Yan yawned, watching the sun outside had already set.He thought, he should go back and rest first.Just standing up, Schultz pushed the door and entered.His movements were so big that he even surprised An Yan.

"Mr. Schultz, what happened?" An Yan knew that Schultz was the person Faltings invited to check the calculation with him.Moreover, An Yan also knew how talented this Schultz was.Therefore, he saw Schultz enter the door in a panic, and said with a hint of surprise, "Mr. Schultz, it's my thesis. Did you make a mistake?"

"Ann." Schultz stared at An Yan and said, "Are you free now?"

"Of course." An Yan nodded slightly, "May I know what happened?"

"You'll know when you go with me." Schultz led the way, and An Yan followed behind him.Walking step by step, when he came to Faltings' office, Faltings was already sitting in his seat, drinking coffee slowly.

"Mr. Faltings." An Yan greeted Faltings very politely.

"Ann, you're here." Faltings smiled at An Yan, and pointed to the seat next to him, "Sit down, both you and Pete."

"Yes." An Yan didn't know if there was something wrong in his thesis.When he was sitting on the chair, he was still a little flustered.

"To be honest." Faltings put down the coffee in his hand and said, "Ann, you really surprised me. Pete and I have been counting for more than half a month."

"Finally finished calculating your thesis." After Faltings finished speaking, he fell silent, and An Yan's heart beat violently.He held his breath and looked at Faltings and said, "Mr. Faltings, is there a mistake in the calculation?"

"No." Faltins shook his head slightly and said, "A very good calculation, without any mistakes."

"Is that a problem with the theory?"

"The theory...has no problems, it can even be said to be perfect, both Schultz and I think so. You perfectly quoted theorems and built your own theory."

"So...Mr. Faltings, it's...I couldn't untie it in the end?" An Yan squeezed his hands nervously, looking worried.

Faltings smiled slightly, "No, An Yan. I want to tell you that after our checking and calculation, your thesis really has no problems at all, and you solved the BSD conjecture perfectly. This is really a major discovery , I didn’t know until today that you told me that you found some interesting things on the Abelian cluster, what kind of interesting things it is.”

"I can finally know now." Faltings stood up, stretched out his hand, and said gently to An Yan, "Congratulations, Ann, you really solved the BSD conjecture."

Really - solved the BSD conjecture?An Yan still stared at Faltings in disbelief, he took a breath and said, "Mr. Faltings, you just said that I really solved the BSD conjecture?"

"That's right, yours solved the BSD conjecture. You should publish your paper now, and submit it to the Annals of Mathematics, shouldn't you?"

"..." An Yan was too shocked to speak, although he had some confidence in himself.Maybe he can really solve the BSD conjecture, but wait until Faltings tells him that he really solved it.He still has an unbelievable, even dreamy feeling.

No, he never even dreamed that he could actually unravel the BSD conjecture.This is simply unimaginable.

"Congratulations Ann, you are already a very outstanding young mathematician. I believe that your name will be included in the Fields Medal next year."

Not to mention An Yan was shocked, even Faltins was very shocked.Unexpectedly, the person in front of him was only 20 years old, and he was not a very optimistic graduate student in the physics department, so he actually made the BSD conjecture.This was probably the first time in his lifetime that he lost his sight.

With such a powerful learning ability and thinking ability, even as a mathematical genius and proud Faltins believes that there may even be more unexpected situations in mathematics in Anyan in the future.It is even possible to solve more mathematical conjectures, such as the Hodge conjecture that An Yan is currently working on, and even other millennium prize puzzles are possible.

All in all, Faltings was very surprised and shocked, and An Yan was really terrible.He has never met such a person who can bring him such a shock.Even in his opinion, Searle, one of the most powerful mathematicians, is not as scary as An Yan.

It seemed that he had been able to see one of the world's great mathematicians on the rise.

"Thank you, Mr. Faltings." An Yan took a deep breath and said, "Without the verification of you and Mr. Schultz, I'm not sure if I can solve this conjecture."

"There is no doubt that you have succeeded. Moreover, you are already a very good mathematician. I am proud to invite you to the Max-Planck Institute of Mathematics." Faltins spoke a lot more kindly, a little It's not like he just met Faltings, he looks serious.

This is probably a mathematical genius, respect for another who is also a mathematical genius in his opinion.

"Ann, go get busy first. I seem to be able to see that the earthquake in the academic world is just because of your paper..." Faltins smiled, "Unraveling the BSD conjecture, an academic report will definitely be held Yes. It’s just the location of the symposium, which depends on whether you want to hold it at Stanford University or at the Max Planck Institute of Mathematics.”

"This..." An Yan thought for a while and said, "I haven't been able to figure it out yet."

"Mr. Faltings, please allow me to think about this issue first." An Yan bowed to the gentleman Faltings. He didn't even know how he left Faltings' office.

Go back to your office and sit down.An Yan took a deep breath, his excitement was beyond words.

How should I say it?It's like—no, it's like he's floating on clouds right now.That unreal feeling stunned An Yan.

This is really shocking. I believe that after he puts the paper on arXiv, everyone will also be very shocked.It might even be a lot more shocking than he imagined.

The BSD conjecture, a state-of-the-art puzzle on Abelian varieties.A conjecture that has an unusual connection to the Hodge conjecture.A conjecture that is eligible for the Fields Medal... It was difficult for An Yan to calm himself down. He kept walking back and forth in the office, seeming to be muttering something.

It took him a long time to calm himself down.

Upload the document that has been placed on the computer to arXiv, and the title is still about the correctness of the BSD conjecture.

It is afternoon in Deutschland, after An Yan uploaded the file.With arXiv closed, it is conceivable how intense the discussion will be in the next period of time.

But he wasn't ready to join the discussion.

Academic reports will definitely need to be held.It's just a question of where to hold it.When he was invited to be a researcher at the Max-Planck Institute of Mathematics, An Yan had no idea that he actually solved the BSD conjecture.But the conjecture has been solved, maybe... Maybe I can make some kind of contribution to Hodge's conjecture.

An Yan's eyes suddenly focused on Hodge's conjecture.

…………

Algebraic varieties are somewhat different from Abelian varieties in terms of expression. An Yan took a pen and began to calculate on the scratch paper.

At night, he returned to his room to eat and sleep.No one seems to have contacted him all day today. It seems that the controversial discussion will have to wait until tomorrow's paper published on arXiv.

The BSD conjecture is really important. Although Faltings has calculated this conjecture empirically, no one can guarantee that this conjecture will be solved [-]% by An Yan.Unless, An Yan can really post in the academic report meeting.After clarifying all the problems in the paper, Faltins thinks that An Yan is completely fine.

The paper itself was written by An Yan himself.

He didn't believe that anyone else would help An Yan write such a paper.This is a paper that can compete for the Fields Medal, the highest honor in mathematics, even if it is Professor Hudson-come on, even if Hudson wants to help An Yan.I'm afraid it can only hold back.

As a professor at Princeton University, Faltings still has some understanding of Hudson.This guy is indeed good in physics, but in mathematics, it is already very remarkable to have one-fifth of him.There is even less research on Abelian varieties.

You know, when he solved the Modal conjecture, he also thought about solving the BSD conjecture in one go.Unfortunately, his attempt failed.

Today, he saw a young mathematician try the BSD conjecture for the first time, and he gave the answer very successfully and perfectly.This is simply an incredible thing.Faltings sat in his seat and thought for a while, when suddenly the office phone rang.

It was so late, I looked back at the sky.It is now night shrouded in the entire city of Bonn.He frowned slightly, picked up the phone and said coldly, "Hello."

"Faltings?" The person on the other end of the phone looked a little unbelievable.

"Yes, it's me. Hudson?"

"Yes." Professor Hudson took a deep breath, "I just saw a paper on arXiv, it's Ann's. It's about the arithmetic and analytical properties of Abelian varieties."

"In short, it's the BSD conjecture." After Professor Hudson finished speaking, he paused.Then he said doubtfully, "Is it because of this problem that he went to Germany to visit you?"

"Your student is not small." Faltings said indifferently, "He gave me the unpublished paper."

"It seems that he trusts you very much, so he solved the BSD conjecture?"

"That's right." Faltins said in a deep voice, "He did solve the BSD conjecture, and made some other things based on the conjecture."

"Some other things?" Hudson was obviously puzzled.

Faltings said silently, "Obviously, I don't know how to tell you about this matter. All in all, he made some changes in the calculation of the Abel cluster. At this time, you didn't even sleep."

"I'm browsing his thesis, and I just want to know how correct his thesis is."

"For the sake of his academic reputation, I suggest that he hold an academic report as soon as possible." Faltins thought for a while and said, "I think his excellence is enough to show that he can graduate there, right?"

"If he sets his graduation project as the BSD conjecture, I won't be too happy, but I don't think I can refute it, can I?" Professor Hudson said rather helplessly, "I just think he should be in physics. It takes a lot of time and effort to learn."

"No, in my opinion, he has actually spent a lot of time on physics. He even spent several times more time on physics than mathematics."

"Really? Why didn't I see it." Professor Hudson said suspiciously, "I can only say that he is really talented in mathematics. Although he is my student, I want him to There is more in-depth research on high-energy physics and gauge field theory. But obviously, he does not seem to have such plans now."

"I think he is enough to be a professor of mathematical physics at Stanford University." Faltins added, "Don't forget that algebraic varieties themselves are one of the important theories that construct M-theory and quantum topology."

"Sorry, Faltings, personally. I don't like Witten's doctrine very much..."

"Ah……"

Faltings chatted with Hudson for a while, then hung up.

He thought about it, what is it like on arXiv now?An Yan should have been uploaded to arXiv for a while before. At this time, probably many people are still seriously reading An Yan's paper.

If someone who jumped out to object at this time, Faltings would definitely think that this person hadn't read An Yan's paper.After all, it took him and Schultz nearly half a month to check and calculate the entire thesis.

An Yan uploaded the thesis for a few hours at most. If someone claims that he has read the thesis at this time and thinks that An Yan's thesis is right or wrong, it is a lie.I believe that on arXiv, such people are still in the minority.

Use your own account, log in to arXiv, and search for keywords.

Sure enough, An Yan's thesis had been uploaded for several hours, and the discussion was not bad at this time, everyone was quietly looking at An Yan's thesis.

Faltings thought about it, and began to read the paper again.

After he finished reading, he tidied up and went straight home.This paper is destined to cause heated discussions and debates...