Technology invades the modern world

Chapter 217 This time it's a true god! (4k)

For Terence Tao, the biggest question right now is: who is Randolph?

Compared to top-tier universities like Princeton, Harvard, and Stanford, Stony Brook University certainly doesn't rank highly.

But that doesn't mean Stony Brook University is no good.

Ignoring other factors, if we only look at data reflecting hard power, such as publications in top journals and citation impact, Stony Brook University would rank 19th globally.

On average, they can publish 10 to 20 papers in the four top journals each year.

It's already considered the pinnacle of the pinnacle.

It's worth noting that the mathematics departments of these mid-tier 985 universities in China might only publish one paper in four major journals every three years.

Stony Brook University's specialty is differential geometry. Terence Tao had never heard of anyone at Stony Brook who was particularly good at number theory or algebraic geometry.

In his understanding, no one at Stony Brook University possessed the capability to achieve such a perfect combination of algebraic geometry and number theory.

What's even stranger is the paper itself.

After reading the paper, Terence Tao specifically researched the homepage of this person named Randolph Lin.

The homepage contains only this one article.

This article is also signed by only one person.

This suggests that the person is a complete newcomer, and it's highly likely that they secretly worked on this achievement.

He then searched on Google Scholar, but still couldn't find any papers published by Randolph Lin.

It's normal for Dr. Lin Ran not to have published any articles in his second year.

The problem is that the other party's paper is exceptionally well-written.

That’s right, maturity.

Terence Tao has read far too many academic papers over the years.

Mathematical papers are written in different styles by different people.

Even if a newcomer manages to create a big story, what they usually post on Arxiv for the first time is just a first draft.

The first drafts were all very rough, the ideas were not clear enough, the logic was somewhat chaotic, and some points that were easy to prove were actually not easy to prove.

Some things that could be simplified and explained in a few strokes are instead written in great detail.

These are common problems for newcomers.

It's like how a novice novelist likes to pile up fancy words, while a master only needs a few words to strike a chord with your soul.

Newcomers to the mathematics community, when they figure out a problem and make a big splash, become particularly proud of their thought process. They are afraid that others will not understand how brilliant their thinking is, so they insist on breaking it down and explaining it to you in detail.

Terence Tao understands this mentality all too well.

Let alone newcomers, even veterans have this mentality. After years of silence, Zhang Yitang's first draft of the twin prime conjecture paper was described by Quanta Magazine as "crystal clear".

"He nailed every detail down perfectly, leaving no room for ambiguity," said his colleague Andrew Granville.

Of course, Zhang Yitang was an old man who hadn't published any articles for a long time back then.

When Terence Tao was reading the paper, he felt like he was having a conversation with a master across time and space. There was not a single thing about him that made him seem like a newcomer, except that his name was indeed very new.

As a mathematician who enjoys improving upon others' work, this paper was not only the work of a master, but it also took him three whole days to find a way to improve it.

"If I were to do it myself, I'd probably only reach this level," Terence Tao thought to himself.

I've never felt such a strong urge to find Randolph Lin.

"Hey, Donaldson."

Even though it was already 10 p.m., he couldn't hide his excitement and immediately made a phone call to a good friend he knew at Stony Brook University.

"Has your department recently had a visiting scholar named Randolph Lin?"

Donaldson, still half-asleep on the other end of the phone, was a little taken aback: "Randolph?"

Terence Tao immediately realized that Donaldson was probably in London, not New York. He roughly calculated that, according to the time difference, it should be 6 a.m. in London: "That's right. Has a visiting scholar named Randolph Lin recently come to Stony Brook University?"

Mathematicians have many identities, especially famous mathematicians.

Simon Donaldson, whose full name is Simon Donaldson, is a researcher at the Geometry and Physics Centre at Stony Brook University and a professor at Imperial College London.

He and Terence Tao won the Breakthrough Prize in Mathematics together in 2014.

The two sides have some cooperation in the fields of harmonic analysis and partial differential equations.

Donaldson sat up in bed, thought for a while, and then told a lame joke: "No, we only have Joseph, not Randolph."

Terence Tao asked incredulously, "Do you have any PhDs named Randolph where you are?"

Donaldson thought for a moment, "Sorry, I don't think there's anyone with that name."

Terence Tao settled for second best: "Undergraduate?"

Donaldson said helplessly, "Tao, you should at least tell me who Randolph is."
What do you need him for?
I really don't know about undergraduates; I'd have to email the administrative secretary to answer you.

Terence Tao was genuinely shocked. It was unimaginable that an undergraduate could produce such a result. "Oh, okay, I saw a paper on Arxiv that combines number theory and algebraic geometry these past few days."

He combined algebraic geometry and number theory to optimize Helfgott's proof of the weak form of Goldbach's conjecture.

The optimized result is very elegant.

Starting with the four-color map, mathematicians have been introducing computer proofs into the field of pure numbers, but some conservative mathematicians consider this inelegant.

This contradicts the essence of mathematics.

Artificial intelligence plays the black box game, and now that we're in pure mathematics, you guys are still thinking about playing the black box game, huh?

If we, as mathematicians in the field of pure mathematics, have to play with the black box of artificial intelligence, then humans will be replaced by artificial intelligence sooner or later.

It is precisely because of this trend of thought that computer-aided mathematical papers are considered by some to be inelegant and not traditional enough.

This is somewhat similar to how handmade noodles are considered more authentic than machine-made ones.

Donaldson wondered if he was still dreaming: "Using algebraic geometry to solve the prime number problem?"

It seems our department doesn't work in this area.

To put it simply, this is a very new direction.

From Wiles, who first proved Fermat's Last Theorem, the techniques he used included algebraic geometry.

That was in 1994. From 1994 to 2014, for a long period of twenty years, many mathematicians tried to combine algebraic geometry with the problem of prime numbers.

Manjul Barghavajra studied the average rank of elliptic curves in Fields 2014.

Peter Schultz, who studied the cohomology of perfect spaces and prisms, won the Fields Medal in 2018.

James Maynard, who studies the distribution of prime numbers, won the Fields Medal in 2022.

The above content all includes a combination of algebraic geometry and the prime number problem. Simply put, almost everyone who has made a name for themselves in this field has received a Fields Medal.

After much deliberation, Donaldson couldn't think of anyone at Stony Brook University who had done this and achieved results.

“Okay, it seems you don’t know either. I’ll send you the Arxiv link on WhatsApp right now. Can you ask Randolph for me who he is and some details about his article? I want to talk to him.” The voice came through the phone line from across the ocean to Donaldson’s ears.

After Terence Tao hung up the phone, Donaldson still felt like he was in a dream.

It wasn't until he saw the link sent by Terence Tao and clicked on it that he realized it was real.

"I haven't heard of anyone at our school working in this area," Donaldson muttered to himself, looking at the paper title on his phone screen.

Terence Tao still refused to give up. He felt that if he didn't find a mathematician named Randolph, he would probably have trouble sleeping tonight.

"Does anyone know who Randolph Lin is? I saw an article he posted on Arxiv that I found very interesting. Some of the ideas in it are very insightful. I'd like to discuss with him how some of these ideas came about, as I think it would be very helpful for my work."

If you know the answer, please leave a comment below this question. If Randolph himself sees this and you'd like to chat with me, please feel free to email me. I will reply as soon as I see it.

Edited by Terry Tao on March 15, 2020

This even forced Terence Tao to post on MathOverflow to find someone.

mathoverflow is a forum similar to Zhihu, a math version of Zhihu.

As you can tell from the name, it's math.

A forum focused on asking and answering math questions.

Terence Tao is undoubtedly a big name on this forum. His earliest question was posted in 2010, which is ten years ago.

During the virus outbreak, almost everyone was confined to their homes.

Various online forums are exceptionally active.

The bigwig personally came out to find the person.

A large crowd of onlookers gathered immediately.

"I am not, but I can be."

"I took a look, and it's a very interesting title. Let me read it and then we can discuss it in more detail."

"Never heard of it. The name sounds like it belongs to a Chinese person, but I really haven't heard of it before."

"Stony Brook branch campus? I've never heard of it."

An hour later, there were already more than 100 replies, which is quite rare on such a professional forum.

No one knew Randolph; it was as if he had appeared out of nowhere.

Looking at the answers to the question, Terence Tao thought that things had already taken off, and the paper itself would probably soon attract the attention of mathematicians who could understand it, at which point Randolph would naturally emerge.

He thought to himself, "Finally, I've accomplished something."

During a virus outbreak, onlookers are everywhere.

On Zhihu, an hour later, this question was reposted: "How would you evaluate Randolph Lin, whom Terence Tao is looking for? Is he a Chinese mathematician? Why did his research prompt Terence Tao to publicly seek him out?"

"I've taken a preliminary look, and the matter seems to be true, but I can't understand the paper, so I'll just skip it."

"They must be Chinese, as it seems very rare for foreigners to have the surname 'Lin'."

"After taking a quick look, it's quite rare for Terry to personally come out to look for someone."

I haven't had time to read the paper yet; I only glanced at the title and saw that it was being discussed enthusiastically on MathOverflow. I didn't expect to see anyone asking about it on Zhihu.

Let me briefly explain my understanding. Algebraic geometry mainly studies the solutions to polynomial equations, which usually involve affine or projective varieties and their regular function rings.

Traditionally, we consider Goldbach's conjecture to belong to additive number theory, which is closely related to the distribution of prime numbers, while algebraic geometry appears more often in number theory problems such as elliptic curves, modular forms, or L-functions.

I suspect that Randolph Lin was trying to extend the concepts of primes and primes from Goldbach's conjecture to the context of algebraic geometry, replacing integers with polynomials and primes with irreducible polynomials.

Any polynomial with at least two variables can be expressed as the sum of at most 2r irreducible polynomials, where r is the number of nonzero monomials of the polynomial.

This is similar to the concept in number theory of representing odd numbers as the sum of three prime numbers, but the object becomes an element in a polynomial ring.

By introducing classical number theory problems into the framework of algebraic geometry, I suspect that tools such as Newtonian polyhedra or forced algebra may also be involved.

In short, the author's work must have covered many aspects, demonstrating the profound connection between algebraic geometry and number theory, which is why it attracted Terence Tao.

I wonder if he's Chinese. If he is, it feels like another figure similar to Xu Chenyang or Yun Zhiwei in the field of Chinese mathematicians is about to emerge.

The answers to this question on Zhihu will be dug up and resurrected by netizens countless times in the future.

So much so that netizens later jokingly referred to it as Randolph's birthplace on the simplified Chinese internet.

The most frequent comments in the comment sections of various answers were: birthplace, checking in.

It wasn't until a week later that Lin Ran's high school classmate jokingly asked on WeChat, "Ran Shen, could it be you, Randolph Lin?"

Hours later, a screenshot appeared in the WeChat chat window.

It is a screenshot of the Arxiv user backend, and the username in it is Randolph·Lin.

"Holy crap!" Seohyun, who had been lying on the bed, sat up in almost a second. He slapped his face hard, wondering if he was dreaming.

Xu Xian was Lin Ran's high school classmate. He went to the School of Mathematics at Peking University, which was known as the top of the four major mental hospitals, for his undergraduate studies. After graduating, he stayed on at the university to pursue his doctorate in pure mathematics.

Because his name is Xu Xian, he is nicknamed Xu Xian, but he has always been single. He hasn't found anyone, not even Bai Suzhen or Xiaoqing.

He wasn't admitted to Yenching University through a special admission program; he got in solely based on his own entrance exams.

To be honest, as one of the 20% who got in purely through exams, Xu Xian has met countless big shots during his years in the mental hospital.

But this time it still shocked him.

"!!!!!!!" Seohyun only replied with a few exclamation marks.

The reason he asked was because Lin Ran's English name was Randolph when they were in high school.

No, buddy, I was just joking. I didn't expect you to actually be serious.

"Why are you suddenly asking this?" Lin Ran replied.

Seohyun never suspected that the photo was photoshopped, because there was no need to.

Lin Ran is not the type to joke about things like this.

“!!!!!”

Hey, the entire mathematics community has been discussing who Randolph is for a week now, and you're here asking why I'm suddenly asking this!
No wonder I could never reach Terry!
Who would have thought that someone who wrote the algebraic geometric solution to Goldbach's conjecture was studying artificial intelligence!
Holy crap! That's amazing!

Burning God!

No, Ran-ge, can you take me with you? Next time you publish an article, can you take me along as a helper and let me write one for you?

Xu Xian's fingers moved incredibly fast, displaying all her skills, determined to win over this powerful woman!
　I had so much fun writing this! I feel really excited writing about academic geniuses; even I enjoyed it! Haha.

　　Hope you enjoy watching!
　　
　
(End of this chapter)