Technology invades the modern world

Chapter 218 I Saw the True God! (6k)

What exactly constitutes a top-tier thigh?

This is a top-tier thigh.

A self-taught mathematician from humble beginnings.

As a self-taught student who was able to stay in a mental hospital and do quite well, his intelligence and emotional intelligence are beyond doubt.

Arxiv only has Randolph's name on it; there are no other collaborators.

The news has spread throughout the mathematics community, and more and more leading figures are saying that this paper is very interesting and that the methods in it are very inspiring.

Even during their group meeting, their advisor mentioned that the paper was very well written and truly deserved to be the work of a master.

If it were a Chinese mathematician, then the mathematics community would have a new renowned Chinese mathematician.

All signs indicate that Lin Ran has no mentor or collaborators; he is entirely self-taught.

Are there any examples of this?

Of course there are.

Take Zhang Yitang, for example. He spent decades working on it, and finally made a huge leap forward in the twin prime conjecture.

Although Lin Ran is not a mathematics major, his aerospace engineering major at Shanghai Jiao Tong University and his doctoral studies in artificial intelligence at Stony Brook University demonstrate his undeniable self-learning ability.

Perhaps his years of dedicated study were all for the sake of making a name for himself in the world of mathematics.

This story is indeed bizarre, but that's how it actually happened.

Xu Xian had a deep impression of Lin Ran. In high school, Lin Ran's math scores were consistently around 140. He only went to study aerospace because he was interested in it.

Here we are back on the path of mathematics.

A wild, powerful woman, a high school classmate—why not take advantage of her?

Xu Xian thought to himself, "I'd be perfectly content with just getting a second authorship in a top-tier journal."

There are fewer and fewer teaching positions available, the competition is getting fiercer, and young scholars in mathematics are becoming increasingly competitive.

Mentor resources are limited, the guidance provided is limited, the questions offered are limited, and the opportunities to have your name listed on the faculty list are even more limited.

Lin Ran's sudden appearance was the biggest boon to his academic career! Xu Xian thought to himself with a smug smile.

Who says you can't have cheat codes in the real world! My own cheat code has arrived!
Xu Xian has already begun to fantasize about publishing a paper in one of the Big Four accounting firms, then happily finding a permanent associate professorship with a tenure at a 985 university in a second-tier city, while also demanding that his family members find jobs. With that, he can find a cute girl and live a blissful life at the pinnacle of success.

Life is so easy.

As for Ran-ge not taking me with him? How could that be! Xu Xian thought to herself.

On the other end of the WeChat message, Lin Ran smiled faintly as he read Xu Xian's praise.

He spent six years in 1960 and was a world-renowned professor.

In a true sense, who in the world does not know you?

President America, the Prime Minister of England, the Prime Minister of Italy, the Chairman of the Soviet Union—I've met them all, and we've chatted and laughed together countless times.

Lyndon Johnson had to rely on me, Nixon had to sit down and consult me ​​late at night, and now Fred obediently follows my script.

By 2020, the mathematics community had not even heard of Randolph.

Xu Xian was his high school classmate and had a talent for mathematics. In Lin Ran's opinion, he would definitely have no problem becoming a mathematician.

The other party's praise immediately brought me back to 2020.

"No problem, we're like family."

What problem are you facing right now?
Let's talk on the phone, I'll give you some pointers.

Xu Xian thought to herself, "Holy crap, are you serious?"
"No

燃哥
The problem I'm working on is elliptic partial differential equations.

It's not number theory, nor does it really belong to algebraic geometry.

In the 60s, there was a desire to unify mathematics.

In recent years, many mathematicians have also been working on this topic.

People are trying to combine different fields.

But as mentioned before, those who can combine these elements are all top-tier mathematicians.

Most researchers still focus on their own specific subfield.

At best, they're good at analysis and algebra.

As for more cutting-edge fields, the idea of ​​interdisciplinary collaboration isn't that most people don't want to, or don't know it's good, but rather that they can't.

I don't have the ability, let alone the energy.

From Xu Xian's perspective, Lin Ran's ability to thoroughly research his own topic in his spare time, to have studied the prime number problem in number theory and algebraic geometry, and to produce results that even impressed Terence Tao, already makes him a top-tier expert.

Even in the mental hospital, he was a top-tier figure.

The partial differential equations I worked on have very little relevance to the problem you're working on.

The message Lin Ran sent seemed to say that no matter what direction you take, I can give you guidance.

Even a master probably wouldn't dare to be so arrogant, Xu Xian thought to himself.

Little did they know, the person on the other end of the WeChat conversation was a master among masters.

He is a top master who has returned from cultivating in the past and in the virtual world.

In the past, someone who wanted to hear Lin Ran's teachings was a doctoral student who wasn't even qualified to erase the blackboard.

Xu Xian was quick-witted enough not to think that Lin Ran was bragging and therefore had no intention of testing or making things difficult for him.

After all, what you want is to be carried by the experts, not to be jealous and try to prove that the experts are not good enough.

Lin Ran didn't waste any words and immediately made a WeChat call:
"Go ahead."

The tone conveyed an unquestionable certainty.

Xu Xian thought to himself, "When did Brother Ran become so domineering?" He organized his thoughts and said, "Brother Ran, I'm working on an elliptic partial differential equation problem."

The main issue is the separable solution to the eigenvalue problem on the ring. How about we use zoom?

Shall I share the problem with you?

It's true that it's very difficult to explain mathematics clearly just by talking.

Because some formulas, especially cutting-edge mathematical formulas, are too difficult to express in words.

"Okay," Lin Ran said.

Using screen sharing, Seohyun quickly explained what he was doing and the progress.

However, he didn't expect Lin Ran to actually understand.

After all, every profession has its own secrets.

Mathematics is like a completely different world when you try to cross different fields.

"When you work on eigenvalues ​​over a ring domain, you inevitably have to consider the Laplace operator."

Since that's the case, and you just said that a single Bessel function cannot satisfy two boundary conditions at the same time, why don't you consider constructing a solution through a linear combination of Jn and Yn?
First, substitute the eigenvalues ​​to construct a special solution.

We are constructing a homogeneous linear system of equations. For the system to have non-zero solutions c1 and c2, the determinant of the coefficient matrix must be zero.

This is a transcendental equation. I think we can probably use the Newton iteration method to solve for λ to the power of 1/2, and thus obtain the eigenvalues ​​λ.

The corresponding characteristic function is

"

Lin Ran skillfully typed out one formula after another using LaTeX.

Xu Xian was not surprised; the Randolph that the mathematics community had been searching for for a week was Lin Ran.

However, what shocked him was...

He had been working on his doctoral questions for over a year, and Lin Ran's thinking progress was now on par with his.

I only heard him mention this issue.

"Okay, it seems that Newton's iterative method is feasible, but it is still difficult to find the analytical solution this way."

Then we use numerical methods to find an approximate solution.

It will still be done step by step.

First, discretize the annular domain into a grid, and then divide it on r and θ.

Then, the Laplace operator is discretized using the central difference formula:
The discretized equation is written in matrix form Au=λu, where A is the discretized Laplace operator matrix.

Finally, numerical linear algebra methods are used to solve for the eigenvalues ​​and eigenvectors of the matrix.

Of course, calculations are required, or an approximate solution can be obtained using computer programming.

In computer programming, editing and verification can be difficult when you publish a paper. Therefore, we can use the rotational symmetry of a toroidal domain to simplify the problem.

One hour later:

"In summary, due to the complexity of boundary conditions, analytical solutions to eigenvalue problems on a ring domain are difficult to obtain directly."

Using a linear combination of Bessel functions and combining it with numerical methods to solve transcendental equations is a feasible analytical-numerical hybrid strategy.

By combining this with the finite difference method, we have provided a general numerical solution.

You can then choose appropriate methods to further explore based on your specific needs, such as accuracy, computational resources, or theoretical insights.

Seohyun was truly numb.

The person was completely numb.

They belong to the type who don't know who they are, where they are, or what they are supposed to do.

I've never felt so numb before.

"Brother Ran, a pathetic, thick barrier has already formed between us," Xu Xian said after Lin Ran finished his final summary.

His roommate in the next bed turned his head and glanced at him, thinking that Seohyun was really acting strangely.

"What? Are you a country bumpkin?" Lin Ran immediately knew what joke Xu Xian was making.

Xu Xian then remembered that she still had roommates in the dormitory.

Currently, some universities have not yet started classes, and those that have are urging students not to leave campus.

Yenching University is better, but there aren't many good ones; most people are crammed into the library.

If you can't get a seat in the morning, you'll have to stay in the dorm.

There are two people in their dorm room today.

Unfortunately, I couldn't get a seat and had to stay in the dormitory.

Xu Xian whispered, "No, Ran-ge, you're exaggerating too much. Everyone says the rich rely on technology, and the poor rely on mutation."

Although I've never been able to tell whether you're rich or poor, did you use technology or mutation to do this?

You know, this is a major problem that my supervisor assigned me to work on during my five years of doctoral studies.

You finished the calculations for me in just an hour and a half, and you even did all the numerical calculations by hand.

Isn't this a bit too perverted?
Although I can't tell whether what you said is right or wrong right now, it's already quite outrageous.

I've been thinking about this problem for over half a year, and I can't find anything wrong with the method you mentioned.

This is a question my supervisor treasures. He said it's a question for young PhD students to level up, and that it would be good if I could solve it in five years and graduate smoothly from Yenching University.

You shouldn't have known this before.

If what you did is correct, it means that I only need to solve one more small problem in my five years of PhD studies to graduate from my supervisor's program.
That's like graduating in less than three years! Seriously, Brother Ran, I just said you'd take me with you, and you skipped the Qi Refining stage and went straight to the Golden Core stage! Are you some kind of mutant or some kind of advanced technology?

Generally speaking, if you go to study for a PhD in mathematics, a good supervisor will give you two problems: a big problem and a small problem. The big problem will be the content you need to work on throughout your PhD studies. In the end, it is best to publish a good and valuable paper in a reputable academic journal.

For minor issues, treat them as practice problems; once completed, they can be posted.

Then, if you solve the small problems quickly, your tutor will give you one or two more small problems.

In this way, even if you can't solve a major problem or publish a good paper before graduating with your doctorate, you can still have a few smaller papers in hand, so that you won't be left with nothing to show for your postdoctoral application or a junior faculty position at a university.

However, such mentors are very rare. They can guide you step by step, provide you with questions, help you grow gradually, and consider your future development after graduation. Such mentors are absolutely rare in Chinese universities.

Because this requires not only a conscience, but also sufficient ability to judge the difficulty of a problem.

Many mentors have easy problems, so they huff and puff and puff, picking all the fruits of their labor, leaving the students with problems they can't solve themselves. Then they say, "This is a difficult task, so I'm handing it over to you. Although it's hard, I believe you can do it," followed by a barrage of psychological manipulation.

The reason why it's so difficult to graduate with a PhD in mathematics is because there are so few such students. They are given a lot of problems whose difficulty level is unknown, and they know they can't solve them themselves, so the students dive right in.

I've been thinking about this for years, but I can't come up with anything. I'm graduating without a single thesis in hand.

That's already considered good.

Even more despicable ones will wait until the student has almost finished working on the problem and made a breakthrough, when all that's left is some finishing touches. Then they'll jump in and say, "This problem is very difficult. Let me help you think about it." After thinking about it together, they'll finally ask for your name to be listed as an author on the paper.

Yenching University is good. Xu Xian's mentor is a rare breed, and Xu Xian has always been grateful. However, he feels that his mentor is still not rare enough. How did his former high school classmate, who is thousands of miles away in New York, become a mythical creature?

"What technology, what mutation, can't it all be the result of my hard work!" Lin Ran said righteously, thinking to himself that he could tear apart the Navier-Stokes equations with his bare hands, so what was this?

"Brother Ran, I already regret it." Xu Xian became serious after hearing this and said with a wry smile.

Lin Ran asked, "What are you regretting?"

Xu Xian said, "No, you've solved my problem. What am I supposed to do during my doctoral studies?"

I can verify your solution in a month at most. If it is correct, I will spend another month writing the paper, and another month showing it to my supervisor. If there are any problems, I will revise it; if not, I will send it out.

In other words, ideally, I could solve this problem in three months.

The problem is, frankly speaking, you're the one who caused this problem; you're at least 90% responsible, while I'm only 10%.

I'm really embarrassed to put my name on your work; at most, I'd just be a co-author.

It's like I have to ask my supervisor for a new topic again, and all the work I did over the past year has been for nothing. If he doesn't have a suitable topic, then I'll have to wait.

"It's true that my Golden Core is at the Golden Core stage, but the Golden Core inside me belongs to you, you understand? This feeling is very strange."

As a devoted fan of online novels, Xu Xian is used to using this strange metaphor.

Lin Ran wore the expression of an old man on the subway: "Stop, stop, stop! What do you mean 'mine' and 'your'? Your description is too strange. It makes it sound like I stuffed my things into your place."

Seohyun couldn't take it anymore: "Stop! What you're saying is way more disgusting than what I'm saying!"

Lin Ran said, "No, no, no, this is still your problem. I just gave you a little help."

I don't need to sign my name.

Xu Xian was still hesitating: "No, Brother Ran, no, God Ran, is this just a little bit of help?"

Isn't that a bit too modest?

A low-key and humble way of showing off is indeed your style, but it's definitely not a small help.

Lin Ran said, "Okay, you can just sign your name. For me, papers on this issue really have no value."

If my approach is correct and I can solve it in an hour and a half, would I value this paper?
If my line of thinking is wrong, then you can think about it again.

If you still can't get over it, you can treat this paper as a backup plan, and ask your advisor for a big question to think about slowly in the remaining time.

Just take the results of your thinking on that big question and try to get into a domestic university's "publish or perish" program.

He met the "publish or perish" requirement in his first year and became an associate professor.

Aren't you thrilled?

Xu Xian stared wide-eyed at Lin Ran on the screen, "No, Ran God, is that American PhD really that effective?"

It's been said online that a PhD in pure mathematics should be pursued abroad, preferably in America or France, followed by Russia or England, and lastly, staying in one's home country. Germany and Japan are about the same as staying in one's home country, although Japan might be slightly better.

If you exclude the third language, then it's just American and English.

You've changed so much since you went to America!

Let's not even talk about math; I can't even fathom your abilities anymore. I feel like even my supervisor isn't as strong as you.

How did you manage to become so comprehensive in your way of thinking after only a year or so with the Americans?

"Is this kind of environment in America really that demanding of people?"

Lin Ran thought for a moment, and a bitter smile appeared on his face, just like Xu Xian's. Indeed, America was a tough place to hone one's skills.

However, it's not the America of 2020, but the America of 1960.

"Burning God, I'll keep it to myself as a brother and stop worrying about it. You're right, this is indeed a trivial matter for you."

For me, it would save a lot of time, and who knows, it might even help me get a teaching position at a top-tier university. I'm so grateful, I'll treat you to dinner sometime when I come to Yenching University.

Don't even think about getting me involved in anything like "take me flying" or "get me credited"—I'm too embarrassed to accept those offers.

Lin Ran nodded: "It's nothing."

During his conversation with Seohyun, he felt a sense of alienation from this time and space gradually disappear, and he was slowly pulled back to this era on a psychological level.

Because this feeling is just so wonderful.

He went to the 1960s and lived there for six years, transforming himself from an unknown unregistered person into a professor known to everyone, and even playing the role of Mr. V, who is omnipresent in conspiracy theories.

What's even more absurd is that after 2020, bad news was everywhere on TV, social media, and in my WeChat Moments.

There were no cars, no pedestrians, and of course no dogs on the road.

It's as if, because I went to 1960 and then returned to 2020, it felt like a different world, as if the end of the world had begun.

Talking to Seohyun helped me overcome this feeling of unfamiliarity.

After the Zoom remote meeting ended.

Seohyun took off her headphones.

My roommate next to me asked, "Which big shot are you talking to?"
Why is it about technology and mutation all the time?

His roommate is also a PhD student in mathematics, but not in pure mathematics; he works in applied mathematics. His name is Li Yiqing.

“I saw God,” Seohyun said.

Li Yiqing is also a direct PhD student.

To be precise, the School of Mathematical Sciences at Yenching University admits either undergraduates or graduate students, with only the Finance and Big Data majors accepting applications.

"No, isn't everyone in the Mathematics Department a god?"

"Don't people usually shout 'God, God' all the time?" Li Yiqing asked.

From undergraduate to doctoral studies, isn't that how everyone talks about it all the way through?

He had heard of Li Shen, Yi Shen, and Qing Shen.

Seohyun said, "No, these are fake, but what I saw today is real."

Holy crap! I've seen a god!

I have a feeling he has a chance to become the first Fields Medal winner who grew up in China.

Xu Xian said.

Now it was Li Yiqing's turn to be puzzled.

It's normal to shout "God!"

After all, in the School of Mathematical Sciences, there's only one standard for calling you a god: if you're human, people will call you that.

But he's rarely heard of anyone being able to get Fields.

At most, during class, the professor would say, "You are very talented." Even when Fields was mentioned, it was only when discussing the history of mathematics, and he would just mention it briefly, saying, "There are no Fields Medal winners who grew up in China yet. I hope everyone will work harder."

Yau Shing-Tung is both included and excluded, because he spent a long time growing up in Hong Kong, before Hong Kong was returned to China.

It belongs to a Schrödinger-like state.

"Really? Is it that exaggerated?"

"You mean, the person you were video chatting with just now can surpass Xu Chenyang, Zhang Wei, and Yun Zhiwei to become the first Chinese Fields Medalist?" Li Yiqing asked doubtfully.

Wei Shen is very impressive, and he's equally famous on social media, but his research achievements are far inferior to his competition results, and he's quite a distance from the Fields Medal.

The three individuals Li Yiqing mentioned were all graduates of Yenching University, known as the "golden generation" of Yenching University's School of Mathematics. They were all born between 1980 and 1982 and were considered the hope of Chinese people for the Fields Medal.

Unfortunately, Fields will have to say goodbye to all three of them in 2022, as he is already over forty years old.

Seohyun was still savoring the moment: "That's right, I think it's very likely."

If you just mentioned that the golden generation has a 30% chance of winning an award, then the person I was talking to on the phone earlier has at least a 70% chance of winning.

He seems even more awesome to me than Lao Li.

Old Li is Xu Xian's mentor. Because Li Yiqing also has the surname Li, they call him Old Li in private.

Li Yiqing sat up straight: "No, Xu Xian? Who's that? Is he that awesome? Have I ever heard of him?"

Xu Xian nodded and said, "Of course I've heard of him. Recently, everyone in the mathematics world knows him."

After a moment's thought, Li Yiqing asked, "Randolph Lin?"

Everyone in the world knows you, and we also need to add Randolph Lin, who has been making headlines in the mathematics world recently because of Terence Tao.

After the paper was posted on arXiv, Terence Tao first posted a message looking for Randolph, then Helfgott came out and said that Randolph's results were too beautiful and much more elegant than his own. Then the editors of the four top journals said that Randolph should submit his paper to them as soon as possible.

In addition, many PhD students and professors in the mathematics department at Stony Brook University came forward to say that they had no students, professors, or visiting scholars named Randolph Lin.

The involvement of four top journals, Goldbach's Conjecture, Terence Tao's strong support, the original author's self-deprecation, and the mystery surrounding Randolph's true identity—all these signs have fueled the already heated discussion on this topic.

"That's right!"

　Here's a total of 10,000 words. I skipped the 520 holiday to write for you all, so asking for a monthly vote isn't too much to ask, right? Waaaaah~
　　
　
(End of this chapter)