Technology invades the modern world

Chapter 220 Six years? Half a year! (6k)

Lin Ran wants to go back to China.

I don't want to stay in America anymore.

I'm already eager to go home.

However, given the current situation, it is very difficult for someone in America to return home.

After all, China had finally managed to control the virus, and now America has started it again.

Secondly, what should I do when I go back?

Lin Ran chose to make a name for himself in the mathematics field first because he had many impressive achievements in this area, which would allow him to quickly gain fame.

Secondly, it's also because if they want to get involved in aerospace in 2020, they lack reputation and haven't proven themselves, so where to get funding is also a problem.

Before 1960, Lin Ran had completely abandoned the idea of ​​getting his first pot of gold from Bezos' Blue Origin.

It's very simple: helping Blue Origin is tantamount to tying one's own safety to Bezos's credit.

He was certain that if he revealed his desire to return to China, Bezos would betray him without hesitation.

He made a deal with himself, offering to help him get off the hook in exchange for making him work for him for the rest of his life.

Lin Ran didn't waste his years in America in the 60s.

Of course, if there's a door, you can go back.

But going back through the door would be a very troublesome thing to explain.

This is an era filled with cameras and ubiquitous information flow; the more obvious one's unusual behavior, the more comprehensive the investigation will be.

Just because we can't predict the future in 1960 doesn't mean we can't predict the future in 2020.

Therefore, Lin Ran no longer intends to take money from Bezos.

Instead, he found a new source of income to make his first fortune.

This is an idea that has been gradually refined over six years, spanning the past 60 years.

Information gaps don't only exist between the future and the past; they also exist between the past and the present.

In 1960, he was a powerful professor who held immense influence and was NASA's top figure, able to enter the White House and the Pentagon with ease.

Information asymmetry from the past can still be very useful today.

After Lin Ran finished speaking, Nilan Zhan was dumbfounded.

Because six months is too short a time.

With scientific research currently stalled, meetings suspended, and exchanges limited to online formats, group meetings can only be held online.

The students' progress is completely unknown.

Therefore, Lin Ran was able to solve the twin prime conjecture in six months.

Frankly, under the current circumstances, the time cost of verification is almost negligible for Nilanjan.

Because it's too short.

As a senior scholar in the field of artificial intelligence, Nilanzhan is able to learn about some major news in the mathematics community, whether actively or passively.

Similar to the progress made in the twin prime conjecture a few years ago.

Nilanjan knows this very well.

Because Zhang Yitang was the first to give an upper bound of 7000 million, the mathematics community then launched a project called Polymath8, which reduced the upper bound of the gap from 7000 million to 246.

This project, called Polymath8, was initiated by Terence Tao and incorporates computer-aided design.

That's roughly what they did.

It adopts an online collaborative model, with discussions conducted through blogs and wiki pages.

The project adopts a pipeline approach, dividing tasks into different groups, including theoretical analysis and computational optimization.

Polymath8a primarily optimizes Zhang Yitang's permissible k-tuples using the GPY sieve method (Goldston-Pintz-Yldrm sieve), type I, type II, and type III estimations, and performs numerical optimization.

The initial limit was 7000 million. Scott Morrison used computer assistance to lower the limit to 59470640, eventually stabilizing it at 4680 million.
It took three months and involved a lot of computational searching for permissible tuples, which was done with computer assistance.

James Maynard, the mathematician mentioned earlier who won the Fields Medal in 2022, proposed an improved GPY sieve that can prove that the difference between prime numbers does not exceed 600. His method is based on pure mathematical tools, with the core being the theory of analytical sieves, and does not require extensive calculations.

To reduce the value from 600 to 246, it is necessary to use mathematical tools, and no mathematician has yet achieved this using purely mathematical tools.

Nilanjan murmured, "Randolph, okay, no problem, I believe you can do it."

So what do you want?

If I were to train someone like Fields, even if they didn't contribute anything, I could still brag about it a lot.

Even if he didn't get a professorship at Stony Brook University, with his qualifications and student resume, he could easily get a professorship at a top 50 university in the US.

Even at the City University of New York, a university in New York City, getting a professorship wouldn't be a problem at all.

Moreover, if Lin Ran wins the Fields Medal and he wins the Stony Brook University Board of Trustees Special Contribution Award, everyone will have a bright future.

After receiving the Board of Trustees' Contribution Award, it wasn't difficult to get the assistant professor's assistant position at Stony Brook University.

The Indian instincts took over, allowing Lin Ran to do as he pleased, waiting to boast about his achievements when giving a report to the leaders.

I knew at a glance that Randolph was a mathematical genius, so I gave him plenty of freedom to develop his skills. Although I didn't play a role in the field of mathematics, I did help him a great deal in terms of his growth and life.

I cleared the obstacles for Randolph's research life, allowing him to work without distractions.

Even before any results were achieved, Nilanjan was already thinking about how to report back.

Lin Ran said, "Nothing else. After I finish this, I want to graduate. I want to get my PhD from Stony Brook University and then go back to China."

Getting a doctorate would give me something to show for it when I return to China, and also so my mother wouldn't be too disappointed.

Otherwise, Lin Ran really wouldn't need a doctoral degree to prove himself.

And frankly, if he had a choice, Lin Ran would still prefer to get a PhD in Göttingen rather than at Stony Brook University.

I don't have much feeling about this.

Nilanjan nodded: "No problem, but you still need to have a paper in the field of artificial intelligence. You can choose which one to submit."

I'll arrange that for you. If you can really solve the twin prime conjecture, I think the university will be happy to help you too.

How would you evaluate Randolph Lin, a Chinese student studying abroad?

Lin Ran's story was first addressed by Terence Tao on MathOverflow, who then found the person and deleted the question.

Then the mathematicians attending the Zoom meeting started spreading the word.

Everyone knows Randolph Lin, a Chinese mathematician who holds a PhD in Artificial Intelligence from Stony Brook University. He proposed an elegant interdisciplinary approach to solve the weak form of Goldbach's Conjecture.

This whole thing is quite dramatic.

The journal Quantum published a special article titled "The Chinese Mathematician's Enthusiasm for Goldbach's Conjecture".

He wrote the following in the article:
"In the 20th century, Chinese mathematician Chen Jingrun made a landmark contribution to the study of Goldbach's Conjecture. Born in Min City, Fujian Province, Chen Jingrun grew up during the turbulent years of war. In 1949, he entered the Department of Mathematics at Xiamen University, where he studied under the renowned mathematician Hua Luogeng. Despite the difficult circumstances, he devoted himself to the study of number theory. In 1966, he published his famous Chen Theorem, proving that every sufficiently large even number can be expressed as the sum of a prime number and a number with at most two prime factors, for example, 100 = 23³ + 7 × 11."

This result was an important advance in the Strong Goldbach Conjecture, and although it did not completely solve the conjecture, it inspired later researchers.

Chen Jingrun's story was recorded in Xu Chi's biography "Goldbach's Conjecture," published in People's Literature in 1978, becoming a classic chapter in the history of Chinese mathematics.

Fifty-four years later, Chinese mathematician Randolph Lin decided to re-examine the weak Goldbach conjecture from a completely new perspective. Lin's method took a unique approach, combining algebraic geometry with number theory to construct an elegant proof based on elliptic curves.

Elliptic curves are a core object in algebraic geometry, usually defined by equations of the form y = x + ax + b, and have rich geometric and arithmetic structures.

Lin's proof begins with an intuitive observation: the problem of prime sums is essentially a Diophantine equation, and algebraic geometry excels at dealing with solutions to such equations.

He constructed En as an elaborately designed elliptic curve whose coefficients depend on n. By analyzing the rational points on En, Lin established a mapping that transforms these points into prime triples satisfying p1+p2+p3 = n.

In the introduction to Lin's paper, he describes in detail how to construct this algebraic variety and analyzes its structure using tools from algebraic geometry, such as the Mordell-Weil group and height theory.

He proved that for every odd number n > 5, En has at least one rational point, and this existence directly corresponds to the validity of the weak Goldbach conjecture.

Lin's method avoids the complex circle method and exponents and estimations in Helfgett's proof, and instead provides a more direct path through geometric intuition and algebraic tools.

"My goal was to find a more concise proof," Lin said in a telephone interview. "The rational points of elliptic curves provide a natural language that allows us to understand the problem of prime sums from a geometric perspective. This approach not only simplifies the proof but also reveals the underlying structure of the prime number distribution."

Helfgott's proof relies on the circle method, a classic technique in analytic number theory that estimates the number of prime sums by integrating over the unit circle. However, this method requires complex estimations of primary and secondary arcs and depends on computer verification for small values ​​of n. Lin's proof, on the other hand, is based entirely on pure mathematical tools, avoiding the need for analytical methods and computational verification.

"Lin's proof is a paradigm of combining algebraic geometry and number theory," commented the renowned Chinese-American mathematician Tretau. "His transformation of a problem traditionally dominated by analytical methods into a geometric one is an exciting example of interdisciplinary insight."

Lin's achievements are not only significant in the field of mathematics, but also carry on the long tradition of Chinese mathematicians in number theory research.

From Chen Jingrun to Lin, Chinese number theorists have left a profound mark on Goldbach's Conjecture. Chen Jingrun persevered in his research under difficult circumstances, and his story inspired a generation. Lin, in the modern academic environment, carried forward this tradition. His proof is not only a tribute to Chen Jingrun's work but also a completely new interpretation of the beauty of mathematics.

Lin's paper has been submitted to *Recent Advances in Mathematics*, and has passed peer review and is about to be published.

If it were just Lin Ran, the news wouldn't have reached China so quickly.

But the problem is Goldbach's Conjecture.

Goldbach's Conjecture is the mathematical and scientific enlightenment of countless Chinese people.

After Xu Chi finished writing "Goldbach's Conjecture", mathematical research institutions across the country, from universities to the Institute of Mathematics of the Chinese Academy of Sciences, received countless self-recommendation letters claiming to have solved Goldbach's Conjecture.

Countless Chinese people claim they have solved the 1+1 problem and want experts to take a look and tell them how to publish it in academic journals.

Lin Ran himself wasn't very famous, but Goldbach's Conjecture was incredibly well-known. The article in the Quantum Journal was immediately reposted on Weibo in China by independent media outlets, quickly sparking heated discussions.

From Weibo to Zhihu to Douyin, the news was almost explosive.

Anyone, human or dog, can come out and say a few words.

After all, there's nothing to do at home.

With activities in the real world almost at a standstill, activities in the virtual world will become unprecedentedly active.

"Thanks for the invitation. It's really impressive that an AI PhD can publish in a top-tier pure mathematics journal. That's absolutely amazing. Let me put it this way, there are only a handful of Chinese people who can publish in top-tier journals during their PhD studies."

You know Chen Gao, right? He graduated from the Huazhong University of Science and Technology's gifted youth program, and also from Stony Brook University.

Unlike Randolph, he holds a PhD in pure mathematics, studied under Professor Chen Xiuxiong, and solved the gravitational instanton problem proposed by Hawking in 1977. Later, in 2017, he went to Princeton for postdoctoral research. He has never published in the Big Four journals.

Randolph, a PhD candidate in the field of artificial intelligence, started directly with the Big Four accounting firms, making him a top expert.

But I think the online comments about Fields are a bit too optimistic.

First of all, his work is original and involves interdisciplinary fields. In recent years, Fields has tended to give credit to mathematicians who work on interdisciplinary problems.

But the work he did was something that others had already solved; he built upon the work of others.

Secondly, he only has one paper in the Big Four accounting firms, while other strong contenders for Fields Medal have far more.

Finally, since he doesn't have a mentor, he's on his own. It's hard to find enough problems to solve on his own, and he might only be able to publish one paper before it becomes very difficult to publish more.

If I were him, I would definitely find myself a mentor as soon as possible. Stony Brook University is a top school for mathematics, with plenty of Fields Medal winners. I should find a mentor quickly and do more while I'm still young.

There might be a glimmer of hope for the Fields Medal.

But it's still too difficult. In my memory, Stony Brook University isn't strong in number theory, let alone the combination of algebraic geometry and number theory. I estimate that even if I find a tutor, they won't be able to provide much guidance.

I think you should change schools, Princeton would be the best option. With a paper published in one of the top four universities, transferring to Princeton will be a breeze.

The highly-rated answer on Zhihu is as above.

The suggestions offered were all very pertinent.

(As an aside, Chen Gao's first paper in the top four journals was published in 2021 in New Advances in Mathematics, which was in March 2020.)
What they didn't know was that Lin Ran didn't need a master to find his problems at all, because he himself was a master, and a master among masters.

Showing the contents of your head to the outside world would be terrifying.

The general solution to the Navier-Stokes equations directly solved the problem of the US lacking large wind tunnels.

"Thank you for the invitation. Randolph Lin's Chinese name is Lin Ran. He was my high school classmate. I am Xu Xian. I have answered some questions on Zhihu before, and my resume is also on my homepage. I am currently a PhD candidate in theoretical mathematics at Yenching University."

Let me make a promise here: I'm 23 years old now, not even 24 yet, but I'll definitely get the Fields Medal before I turn 40! If I don't, I'll record a video on Bilibili of me doing a handstand while washing my hair.

Anyone want to bet with me? Leave a comment if you do. If I win, I'll make a video of myself washing my hair upside down.

Let me add a few more words. I've met many amazing people at Peking University, and all sorts of incredible talents have emerged, but Ran Ge is definitely the most awesome genius I've ever met. Everyone, stay tuned.

I'm really not trying to flatter Ran Ge to the point of ruining him. Ran Ge doesn't use social media at all. I'm just stating my own opinion, and Ran Ge should definitely take it.

Xu Xian's Zhihu name is "Mathematical Xu Xian," and he has five or six thousand followers on Zhihu. In this highly specialized and niche field of eccentricity, he is considered to be somewhat famous.

His answer received the second-highest number of upvotes.

The comments section is full of all sorts of things:

"A math PhD student at Nanjing University is just hanging around with someone; I bet he won't get the job."

"Jiangda's math PhD will also be included. I don't believe that an AI PhD can get the Fields Medal, let alone such a suddenly emerging genius. He's probably similar to Liu Lu, who solves a problem in his lifetime with a flash of inspiration, and then that's it."

"No, Xu Xian, shouldn't you advise Ran Shen to transfer schools as suggested in the top-voted answer? How can he get Fields if he doesn't go to Princeton?"
You'd at least have to switch to math, right? Otherwise, if you're a PhD in AI, and Fields Medal wins, what about pure mathematics? Even if you could get it, Fields Medal wouldn't give it to you.

"Can you stop washing your hair upside down? Can I come and freeload? I, Shuimu Laoba, can't wait any longer."

"If you don't want to gamble, then stop talking nonsense. He's not even 24 yet, which means the final verification of this bet will have to wait until the International Congress of Mathematicians in 2034. Only if he doesn't get it by then can the verdict be finalized."

This is taking way too long! Who can wait that long?!

Xu Xian, as Lin Ran's friend in the real world, appeared in person to give his account, which sparked heated discussions among onlookers.

Because the stakes weren't high—many people could do a headstand while washing their hair—and the verification happened many years later, plenty of people left comments in the comment section wanting to bet with him.

After reading it, Xu Xian forwarded the answer with the most likes and her own answer to Lin Ran, adding:

"No, Brother Ran, would you like to consider this suggestion?"
If you want to go to Princeton now, all you need to do is send an email, and an administrator will contact you. You can go in the second half of the year.

Finding a top-tier mentor like Pierre or Langlands might be difficult, as they are older and don't personally mentor students as much. However, finding a professor who is young and energetic shouldn't be a problem.

Find a professor with a similar research focus and collaborate on some major achievements; you'll definitely have a good chance at Fields University.
"You can ascend directly, and I won't need to wash my hair upside down!"

Due to the time difference, Lin Ran didn't see it until early the next morning.

Upon seeing this, he smiled faintly and said, "Langlands? At the 1962 Mathematicians' Congress, he was only 26 years old and a teaching assistant at Princeton, not even an assistant professor, so he could only stand."

The Pierre that Seohyun is referring to is not Jean Pierre, but Pierre Deligne.

I also had a very pleasant conversation with his mentor, Grothendieck. Grothendieck even said that he was willing to help me think of ideas that I didn't want to consider.

Even if I start from scratch, I don't need to go to the younger generation.

In Lin Ran's eyes, these masters were really just juniors.

"Need not

Just wait and see.

2034? Let's take Fields as an example for 2022.

You've got this in the bag!

Lin Ran simply replied with one sentence.

Then he found Li Xiaoman's WeChat. A faint smile appeared on his face, followed by a sense of sadness, because he really didn't know how to persuade Li Xiaoman to give up her studies and return to China with him.

If he doesn't return, then when he becomes famous worldwide in China, any interaction with him will be Li Xiaoman's biggest risk.

Lin Ran sighed and then sent a WeChat message:

"Sister Xiaoman, when you're betting on the 2022 Fields Medal winners on Polymarket, if Randolph Lin appears as an option, you can blindly bet on my choice."

Finally, he dialed Mikhail Lyubich's number:
"Hello, Professor Lyubich, I am Randolph, Randolph Lin."

Mikhail Lyubich, of Jewish descent, is the chair of the mathematics department at Stony Brook University and a leading figure in numerical computation.

However, he is already sixty years old, and his academic career is almost over.

“Randolph, it’s great to hear from you. It’s wonderful to see another outstanding student emerging from Stony Brook. It’s such good news right now,” Mikhail Lyubich said. “I emailed you hoping you could transfer to the mathematics department so you can fully utilize your talents.”

I couldn't quite understand your paper, I apologize for the time constraints, but I asked some colleagues who could.

They all gave it extremely high praise.

Stony Brook University is always like this, starting with Sing-Shen Chern, then Hsiu-Hsiung Chern, and Gao Chen. Well, it's a bit of a shame you don't have the surname Chern.

If your surname is also Chen, that would be perfect.

In short, Stony Brook University has produced outstanding Chinese mathematicians in every era.

In the 20s, there was also Randolph, an outstanding young Chinese mathematician.

Come to the mathematics department and let your talent shine!

As people get older, they tend to ramble on and on about all sorts of random things.

Especially lately, with everyone at home, no group meetings, and the young administrative secretary not saying a word, Mikhail Lyubich is going crazy from being cooped up at home.

He always likes to talk a lot when he's on the phone with someone.

"Professor Lyubich, of course, I would be happy to receive both a PhD in mathematics from you and a PhD in artificial intelligence from the AI ​​Innovation Institute when I graduate."

So I need your little bit of help.

I believe that the Stony Brook University Mathematics Department will be incredibly proud of me in the future.

Mikhail Lyubich laughed: "Randolph, I admit you could be an excellent mathematician."

But if you want the Stony Brook University Mathematics Department to be incredibly proud of you, do you think you can become the Grothendieck of this era?

This century has indeed not produced a figure like Grothendieck, but I don't know who could be, and you, I think, are probably quite far off.

Randolph, the distance between good and excellent is great, but the distance between excellent and Grothendieck is even greater than the distance between good and excellent.

It's good for young people to be ambitious, but being too ambitious can often be a burden.

Even if you can actually do it, do it first, and then talk about it later.

I think if you want to become Grothendieck, you should probably start with Fields.

He won the Fields Medal at 28, your time is running out.

Six years from now, you'll have to get the Fields Medal.

"Six years? Half a year!"

Even with just a phone call, even with just a voice, Mikhail Lyubich could sense unparalleled confidence.

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　　I'm asking for monthly votes! Anyway, the modern storyline is sure to be a treat for everyone!
　　
　
(End of this chapter)