Chapter 218: I’ve Met A True God!
What do you call top-tier big legs?
This is top-tier big legs.
Wild mathematician self-taught genius.
As a self-examinee who can stay in the asylum and do quite well there, his IQ and EQ are beyond doubt.
Arxiv only has Randolph’s name, no other collaborators.
The mathematics community is all abuzz, more and more big shots are coming out saying this paper is very interesting, the methods inside are very inspiring.
Even in their group meetings, their mentor mentioned it, saying this paper is written very well, as expected from a master’s hand.
If he’s Chinese people, then the mathematics community will have a new famous Chinese mathematician.
All signs indicate that Lin Ran has no mentor, no collaborators, purely self-taught genius.
Are there examples like this?
Of course there are.
Like Zhang Yitang, didn’t he just huff and puff on his own for several decades, and finally advance the Twin Prime Conjecture a big step forward.
Lin Ran certainly isn’t a mathematics major, but Shanghai Jiaotong University’s aerospace major plus Stony Brook University’s current PhD student in artificial intelligence, his self-study ability is beyond doubt.
Maybe these past few years he’s been studying diligently in seclusion, just to make a splash in the mathematics community.
This kind of story is indeed very bizarre, but reality is just like that, it happened.
Xu Xian has a profound impression of Lin Ran; in high school, the other’s math scores were always fluctuating around 140, he just went to study aerospace because he was interested in aerospace.
Now he’s back on the mathematics main road.
Wild big legs, high school classmate, no hug is wasted.
Casually getting second author on a top journal would be more than satisfying, Xu Xian thought to himself.
Faculty positions are getting fewer now, competition is getting fiercer, young scholars doing mathematics are getting more intense.
Mentors’ resources are limited, guidance given is limited, problems given are limited, opportunities to put your name on are even more limited.
And the heaven-sent Lin Ran is the biggest golden finger on his academic path! Xu Xian thought happily.
Who says the real world can’t have golden fingers! His own golden finger hasn’t come just like that!
Xu Xian has already started fantasizing about publishing a paper in one of the top four with him, then happily finding a permanent associate professor position with establishment in a second-tier city 985, plus requiring them to solve work for family members, then finding a cute girl, and walking into peak life happiness.
Life is just that easy.
As for Brother Ran not taking me flying? How is that possible! Xu Xian thought.
On the other end of WeChat, looking at Xu Xian’s flattery, a faint smile appeared on Lin Ran’s face.
He stayed in 1960 for a full 6 years, he was a professor renowned globally.
Truly, in the world who doesn’t know you.
US President, England Prime Minister, Italy Prime Minister, Soviet Union Chairman, which one haven’t I met, which one wasn’t chatting and laughing casually.
Lyndon Johnson had to rely on me, Nixon had to get up in the middle of the night and humbly ask for advice, now Fred is obediently acting according to my script.
By 2020, the mathematics community surprisingly hasn’t even heard of Randolph.
Xu Xian is his high school classmate, has some talent in mathematics; in Lin Ran’s eyes, becoming a mathematics worker is definitely no problem.
The other’s flattery immediately pulled him back to 2020.
“No problem, we’re buddies.
What problem are you working on now?
Let’s chat on the telephone, I’ll give you some pointers.”
Xu Xian thought, damn, you’re serious?
“No
Brother Ran
The problem I’m
It’s not number theory, nor does it really belong to algebraic geometry”
In the 1960s, everyone hoped to unify mathematics.
In recent years, many mathematicians have also been working in this area.
Everyone is trying to combine different fields.
But as I said before, those who can achieve combination are all first-class mathematicians.
More researchers still focus on their own subfield.
At most, analysis and algebra are good.
As for more cutting-edge fields, attempting to do interdisciplinary work, most people aren’t unwilling or unaware that it’s good, but simply unable to do it.
Without this ability, let alone this energy.
In Xu Xian’s view, for Lin Ran to use his spare time to thoroughly understand his own topic, to have research on prime number problems in number theory and algebraic geometry, and to produce achievements that could even shock Terence Tao already made him a top big shot.
Even in the asylum, he was a big shot among big shots.
The partial differential equations I work on and the problem you work on have very little relevance, right.
Mainly, what Lin Ran sent over seemed to say that no matter what direction you’re working in, I can give you pointers.
Even a master probably wouldn’t dare to be so arrogant, Xu Xian thought.
Little did he know, on the other end of WeChat was a master among masters.
It was a top master who had cultivated in the past and the virtual and returned.
In the past spacetime, to hear Lin Ran’s teaching, someone like him, a current PhD student, wouldn’t even qualify to wipe the blackboard.
Xu Xian was also clever enough and didn’t have any thought of thinking Lin Ran was bragging, so he wanted to test and make things difficult for the other party.
After all, what you want is for the big shot to lead the way, not to become jealous and try every means to prove the big shot can’t do it.
Lin Ran didn’t waste words and directly made a WeChat telephone call:
“Speak.”
His tone carried an unquestionable certainty.
Xu Xian thought, when did Brother Ran become so dominant? He organized his words: “Brother Ran, what I’m working on is an elliptic partial differential equation problem.
Mainly, separable solutions for eigenvalue problems on the annulus. How about we start a Zoom?
I’ll share the problem with you?”
Mathematics is indeed very difficult to explain clearly just by talking.
Because some formulas, especially cutting-edge mathematical formulas, are too hard to express through language.
“Okay.” Lin Ran said.
Relying on screen sharing, Xu Xian quickly explained what he was working on and the progress.
However, he didn’t expect Lin Ran to really understand it.
After all, different fields are like different mountains.
Mathematics is such that different fields are like different mountains.
“For eigenvalues on the annular domain, you can’t avoid considering the Laplace operator.
Since that’s the case, you just said a single Bessel function can’t satisfy both boundary conditions at the same time, so why not consider constructing the solution through a linear combination of Jn and Yn?
First, substitute the eigenvalue to construct a particular solution.
What we’re constructing is a homogeneous linear system of equations, so for nonzero solutions c1 and c2, the determinant of the coefficient matrix must be zero.
This is a transcendental equation. I think it can probably be solved using Newton’s iterative method for the square root of λ divided by two, thereby obtaining the eigenvalue λ.
The corresponding eigenfunction is
“
Lin Ran skillfully typed out formula after formula using LaTeX.
Xu Xian wasn’t surprised. The Randolph that the mathematics community had been searching for for a week was Lin Ran.
But what shocked him was.
The PhD problem he had been working on for over a year, Lin Ran’s thinking progress had already caught up to his.
Just from hearing him describe this problem.
“Alright, it seems Newton’s iterative method is feasible, but doing it this way is still hard to find that analytic solution.
So use numerical methods for an approximate solution.
Still step by step.
First, discretize the annular domain into a grid, dividing in r and θ.
Then use the central difference formula to discretize the Laplace operator:
Write the discretized equation in matrix form Au=λu, where A is the discretized Laplace operator matrix.
Finally, use numerical linear algebra methods to solve for the eigenvalues and eigenvectors of the matrix.
Of course, for computation, either use computer programming for the approximate solution.
For computer programming, it’s difficult for the editor to verify when you submit your paper, so let’s utilize the rotational symmetry of the annular domain to simplify the problem.”
One hour later:
“In summary, due to the complexity of boundary conditions, the eigenvalue problem on the annular domain makes analytic solutions hard to obtain directly.
Using a linear combination of Bessel functions combined with numerical methods to solve the transcendental equation is a feasible analytic-numerical hybrid strategy.
And by combining finite difference methods, this provides a general numerical solution approach.
Subsequently, you can further explore suitable methods based on specific needs, such as precision, computational resources, or theoretical insights.”
Xu Xian was truly numb.
The person was completely numb.
It was the kind of numbness where he didn’t know who he was, where he was, or what he was supposed to do.
He had never been so numb before.
“Brother Ran, there’s already a tragic thick barrier between us.” After Lin Ran gave his final summary, Xu Xian said.
The roommate in the bed next to him turned his head to look, thinking Xu Xian was really inexplicable.
“What’s wrong? You’ve turned into Run Tu, huh.” Lin Ran immediately knew what meme Xu Xian was playing.
Xu Xian then remembered that there were roommates in the dorm.
Right now, some universities haven’t started classes yet, and those that have started are also calling on everyone not to leave campus.
Yenching University is a bit better, but not by much; most people are crammed in the library.
If you couldn’t grab a seat in the morning, you could only stay in the dorm.
Today there were two people in their dorm.
Unfortunately, neither had grabbed a seat and could only stay in the dorm.
Xu Xian said in a low voice: “No, Brother Ran, this is too exaggerated.
They all say the rich rely on technology, the poor rely on mutation.
Although I’ve always been unable to judge in my impression whether you’re rich or poor, did you use technology or mutation for this exactly?
You know, this problem is the big one my mentor left me to work on for five years of my PhD.
You calculated it all in half an hour, and even the numerical calculation needed in the process was done by hand directly.
Isn’t this a bit too perverted?
Although I still can’t judge if what you said is right or wrong right now, this is already very perverted.
At least I’ve thought about this problem for over half a year and can’t find any flaw in the method you described.
This problem is my mentor’s treasure; he said it’s a leveling up problem for young PhDs, and if I can solve it in five years, that’s already good enough to graduate smoothly from Yenching University.
You shouldn’t have known about it before.
If what you did is correct, it means for my PhD five years, I just need to do one small problem more to graduate from my mentor?
That would be graduating in less than three years. Brother Ran, I just said take me flying, and right after you helped me skip Qi Refining directly to Golden Core Stage. Are you a mutation or technology exactly?”
Generally speaking, when you go to study for a PhD in Mathematics, a good mentor will give you two problems: one big problem and one small problem. The big problem is the content to carry through your entire PhD stage, and ideally at the end you can publish a nice valuable paper in a qualified academic journal with enough value.
The small problem is for practice; once done, it can be published.
Then if you finish the small problem quickly, the mentor will give you one or two more small problems.
This way, even if you can’t finish the big problem and publish a nice paper before graduating with your PhD, you can still have a few small papers in hand, so you won’t be empty-handed when applying for postdoctoral or university young scholar positions.
However, such mentors are very scarce; they can guide you hand-in-hand, give you problems to feed you, let you grow slowly, and consider your development after graduation. This kind of mentor is an absolute scarce species in domestic universities.
Because this not only requires conscience but also sufficient ability; you need to judge the difficulty of problems.
Many mentors have easy-to-solve problems, huff and puff to attack them fiercely themselves, pick all the peaches, and leave the ones they can’t solve for students, then say this is a tough task, I’m entrusting it to you; it’s very difficult but I believe you can do it, a bunch of intense PUA.
Why PhDs in Mathematics are hard to graduate is because scarce species are few; many leave problems whose difficulty they don’t know, only that they can’t solve them, to students, and the students dive headfirst in.
They think for years, can’t figure it out, but want to graduate with no papers in hand.
And this is even considered good.
There are even more despicable ones: when the student has almost solved the problem and achieved a breakthrough, with only some minor cleanup left, he jumps out saying the problem is hard, let me think about it with you; then after thinking together, he wants to be named on the paper.
Yenching University is good; Xu Xian’s mentor is a top-tier scarce species. Xu Xian has always been very grateful, but he feels his mentor still isn’t scarce enough. How did his high school classmate from New York, far away across thousands of miles, become a mythical being.
“What technology, what mutation? Can’t it be the achievement of my hard study!” Lin Ran said righteously, thinking to himself that he could even hand-tear the NS equation, so what was this.
“Brother Ran, I already regret it.” After hearing this, Xu Xian got serious and said with a bitter smile.
Lin Ran asked: “Regret what?”
Xu Xian said: “No, you solved my problem; what do I do for my PhD stage?
At most I can verify your solution in a month; if it’s correct, spend another month writing the paper, a month for the mentor to review; revise if there are issues, or publish if not.
That means, ideally, I can finish this problem in three months.
But the problem is, plainly speaking, you did this problem; you take at least 90% of the merit, I only take 10%.
I really don’t feel good putting your achievement under my name; at most I can tag along for a second authorship.
That means I have to go back to my mentor for a new topic now; the past year plus was wasted directly, and if he doesn’t have a suitable problem, I’ll have to wait.
My Golden Core is indeed Golden Core Stage, but the Golden Core in my body is yours; you get it? This feeling is very strange.”
As a loyal web novel enthusiast, Xu Xian was used to such strange metaphors.
Lin Ran showed the expression of a subway elder: “Stop stop stop, what my yours. Your description is too weird; it sounds like I stuffed my thing into you.”
Xu Xian couldn’t take it either: “Stop it; what you said is way more disgusting than mine!”
Lin Ran said: “No no no, this is still your problem; I just gave you a little small help.
I don’t need to be credited.”
Xu Xian was still struggling: “No, Brother Ran, no, Ran Shen, this is called a little bit of help?
Isn’t this a bit too modest.
Low-key modest show off is indeed your Ran Shen style, but this really isn’t a little bit of help.”
Lin Ran said: “Alright, just put your name on it. For me, the paper on this problem really has no value.
If my approach is correct, I can solve it in an hour and a half. Would I value this paper?
If my approach is wrong, then you can think about it more.
Besides, if you can’t get over it in your heart, you can use this paper as a safety net. Ask your mentor for a big problem and take the remaining time to think slowly.
Take the thinking results from that big problem to muddle through the domestic universities’ up or out.
Achieve the up or out conditions in the first year inside, and mix to get associate professor.
Wouldn’t that be great?”
Xu Xian opened his mouth wide, looking at Lin Ran on the screen, “No, Ran Shen, is studying PhD in America so effective?
Online it always says that pure mathematics PhD should go abroad, best America or France, next Russian, England, and only then stay domestic. Germany, Japan and staying domestic are similar, Japan might be a bit better than staying domestic.
Excluding the third language, isn’t it just America and England?
After you went to America, this change is too big.
Leaving mathematics aside, your strength I already can’t see through. I feel my mentor isn’t as strong as you.
How did you achieve this way of thinking about problems, becoming so comprehensive in just over a year in America.
America’s environment is so tempering, right.”
Lin Ran thought about it, and a bitter smile like Xu Xian’s appeared on his face. Indeed, America does temper people.
But not 2020’s America, but 1960’s America.
“Ran Shen, as a brother, rest assured, I won’t struggle anymore. You’re right, for you this problem is indeed negligible.
For me, it can help save a lot of time, maybe even directly mix a double first-class faculty position. No need to thank for great kindness. When you come to Yanjing, I’ll treat you to dinner.
Later on, anything like carrying me or putting my name on it, no need to think about it. I would feel embarrassed to accept.”
Lin Ran nodded: “No big deal.”
During the conversation with Xu Xian, he felt a sense of alienation from this spacetime slowly disappearing, gradually being pulled back to this era from a psychological level.
Because this feeling was really too wondrous.
He had gone to the 1960 spacetime for six years, and there from an obscure black household, became a professor known to everyone in the world, even playing the role of the omnipresent V Mister in conspiracy theories.
The even more absurd part was that after returning to 2020, on television stations, social media, Moments, everywhere were bad news.
On the road no cars, no pedestrians, of course no dogs.
It was as if because he went to 1960, returning to 2020 felt like a world apart, as if the end times had begun.
Talking with Xu Xian eliminated this sense of strangeness psychologically.
After ending the Zoom remote meeting.
Xu Xian took off his headphones.
The roommate next to him asked: “Chatting with which big shot?
Why again technology, then mutation?”
His roommate was also a mathematics department PhD, but not doing pure mathematics, but applied mathematics, named Li Yiqing.
“I met a god.” Xu Xian said.
Li Yiqing was also direct PhD.
To be precise, in Yenching University Mathematics Department, those who can get in are either undergraduate students; for graduate students, only finance and big data these two majors still recruit entrants.
“No, in the mathematics department, who isn’t a god?
Usually everyone isn’t god this god that, shouting back and forth?” Li Yiqing asked.
From undergraduate to PhD, everyone has been shouting like this all the way.
Li Shen, Yi Shen, Qing Shen, he had heard all these.
Xu Xian said: “No, those are fake, but the one I met today is real.
Damn! I met the real god!
I have a premonition that he has the opportunity to become the first Fields Medalist grown up in China.”
Xu Xian said.
Now it was Li Yiqing’s turn to be puzzled.
Shouting god this god that is very normal.
After all, in the mathematics department, the standard for shouting you god is only one: if you are human, someone will shout you like that.
But saying you can win the Fields Medal, he rarely hears that.
At most, during class, the professor says you have great talent. Even when mentioning the Fields Medal, it’s when talking about the history of mathematics, mentioning that there is no Fields Medalist who grew up locally in China yet, hoping everyone makes an effort.
Does Shing-Tung Yau count or not? Because he spent a long time in Hong Kong during his growth, and Hong Kong hadn’t returned yet at that time.
It’s in a kind of Schrödinger’s state.
“Really? So exaggerated?
You’re saying the one who just video called with you can surpass Xu Chenyang, Zhang Wei, Yun Zhiwei and these people to become the first Chinese Fields Medalist?” Li Yiqing asked doubtfully.
Wei Shen is very impressive, and he’s equally impressive in arguments on self-media, but compared to his research achievements and competition results, it’s quite a gap, and there’s still a considerable distance from the Fields standard.
The three people Li Yiqing mentioned all graduated from Yenching University, known as the golden generation of Yenching University Mathematics Department, all born between 1980 and 1982, considered the hope for Chinese people to win the Fields Medal.
Regrettably, the 2022 Fields Medal has to say goodbye to all three of them, because they are already over forty years old.
Xu Xian was still savoring: “Exactly, I think it’s very possible.
If the winning probability for those golden generation people you just mentioned is 30%, then for the one who just called me, the winning probability is at least 70%.
The feeling he gives me is even more awesome than Old Li.”
Old Li is Xu Xian’s mentor, and since Li Yiqing also has the surname Li, they call him Old Li privately.
Li Yiqing sat up straight: “No, Xu Xian, who is it, so awesome? Have I heard of him?”
Xu Xian nodded: “Of course you’ve heard of him. Recently, this person is known to everyone in the mathematics community.”
After thinking for a moment, Li Yiqing asked: “Randolph Lin?”
Known to everyone, and recently, isn’t it Randolph Lin who’s been making waves in the mathematics community because of Terence Tao?
After the paper was posted on arxiv, first Terence Tao posted looking for the person, then Helfgott came out saying Randolph’s achievement was too beautiful, much more elegant than his own, and then editors from the four top journals said Randolph should submit to them as soon as possible.
Plus many PhDs and professors from Stony Brook University Mathematics Department jumped out saying they don’t have a student, professor, or visiting scholar named Randolph Lin there.
Four top journals, Goldbach Conjecture, Terence Tao’s strong support, original author feeling inferior, mystery of Randolph’s true identity—these all heated up the topic even more.
“Exactly!”
