Chapter 217: Truly A God This Time!
For Terence Tao, the biggest current doubt is who Randolph is.
Compared to top universities like Princeton, Harvard, and Stanford, Stony Brook University really can’t compare.
But that doesn’t mean Stony Brook University is no good.
Not considering other irrelevant things, just looking at data reflecting hard strength like top journal publications and paper citation impact, Stony Brook University ranks 19th globally.
On average, it publishes 10 to 20 papers in the four top journals every year.
That’s already among the top of the top.
You know, mathematics departments at those mid-tier 985s in China might only publish one paper in the four top journals every three years.
Stony Brook University’s specialty is differential geometry. Terence Tao hasn’t heard of anyone at Stony Brook University doing number theory exceptionally well, nor anyone doing algebraic geometry particularly well.
A perfect combination of algebraic geometry and number theory like this—in his understanding, no one at Stony Brook University has that strength.
What’s even stranger is the paper itself.
After reading and understanding this paper, Terence Tao specifically checked the homepage of this person named Randolph Lin.
The homepage only has this one article.
This article has only one author.
This shows it’s a pure newcomer, and this achievement was most likely produced secretly by himself.
He went to Google Scholar to search, and similarly found no papers published by Randolph Lin.
It’s normal for Dr. Lin Ran not to have published articles in his second year.
But the problem is, the other party’s paper is written very maturely.
Yes, mature.
Terence Tao has really read too many papers over these years.
Mathematics papers have different styles from different people.
Even if newcomers make a big splash, their first upload to Arxiv is usually just an initial draft.
Initial drafts are very rough, with unclear ideas, somewhat chaotic logic, and some seemingly easy proofs that are actually not easy.
Some things that can be simplified and explained in a few strokes are written verbosely at length.
These are common issues for newcomers.
Just like novice novel writers who like to pile on flowery rhetoric, while a master can strike straight to your heart in just a few words—it’s the same principle.
Newcomers in the mathematics community, during the process of thinking about a problem, if they figure it out and make a big splash, they are especially proud of their thinking process, afraid others won’t understand how awesome their ideas are, and insist on breaking it down and explaining it in exhaustive detail.
Terence Tao is too familiar with this mindset.
Not to mention newcomers—even veterans have this mindset. After years of silence, Zhang Yitang’s initial draft of the twin prime conjecture paper was described by Quanta Magazine as “crystalline clarity.”
Colleague Andrew Granville said: “Every detail of his is nailed down tight, with no ambiguity whatsoever.”
Of course, Zhang Yitang back then was a veteran who hadn’t published for a long time.
While Terence Tao, reading the paper, had the feeling of dialoguing across space with a master—there wasn’t even a tiny bit that felt like a newcomer, except the name was indeed very new.
As a mathematician who loves to improve on others’ achievements, this paper is not only a master’s handiwork, but even after spending a full three days on it, he couldn’t find even a tiny bit of room for improvement.
“If I did it myself, it’d probably be about this level,” Terence Tao thought.
The desire to find Randolph Lin has never been this strong.
“Hey, Donaldson.”
Even though it was already 10 p.m., he couldn’t suppress his excitement and called his good friend at Stony Brook University.
“Has your department recently had a visiting scholar named Randolph Lin?”
Donaldson, groggy on the other end of the phone, was still a bit slow to react: “Randolph?”
Terence Tao immediately realized that Donaldson was probably in London rather than New York right now. He roughly calculated the time difference—it should be 6 a.m. in London: “Yes, has Stony Brook University recently had a visiting scholar named Randolph? Randolph Lin.”
Mathematicians have many identities, especially famous ones.
Donaldson’s full name is Simon Donaldson—he is a researcher at Stony Brook University’s Center for Geometry and Physics and also a professor at Imperial College London.
He and Terence Tao won the Breakthrough Prize in Mathematics together in 2014.
The two have some cooperation in harmonic analysis and partial differential equations.
Donaldson sat up in bed, thought for a long time, and then made a cold joke: “No, we only have Joseph, no Randolph.”
Terence Tao was a bit incredulous: “Then do you have a PhD student named Randolph there?”
Donaldson thought again: “Sorry, doesn’t seem to be anyone with that name either.”
Terence Tao settled for the next best: “Undergraduate?”
Donaldson said helplessly: “Tao, at least tell me who Randolph is?
What do you want with him?
I really don’t know about undergraduate students—I’d have to send an email to the administrative secretary to answer you.”
Terence Tao was truly shocked; if an undergraduate produced such an achievement, it was unimaginable. “Oh, okay. These past few days I saw a paper on Arxiv combining number theory and algebraic geometry.
He combined algebraic geometry and number theory to optimize Helffgott’s proof of the weak form of the Goldbach Conjecture.
The optimized result is extremely elegant.”
Starting from the four color map theorem, mathematicians have continuously introduced computer proofs into pure mathematics, but to some conservative mathematicians, this is inelegant.
This goes against the essence of mathematics.
Artificial intelligence plays black box, and now you people in pure mathematics still want to play black box?
If we mathematicians in pure mathematics all play artificial intelligence black box, humanity will eventually be replaced by artificial intelligence.
Precisely because of this trend of thought, mathematics papers assisted by computers are considered inelegant and not traditional enough by some.
This is similar to how handmade ramen is considered more authentic than machine-made.
Donaldson suspected he was still dreaming: “Using algebraic geometry for prime number problems?
Our department doesn’t seem to do this direction.”
To put it this way, 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, over those long twenty years, many mathematicians tried to combine algebraic geometry with prime number problems.
Manjul Bhargava, who studies average ranks of elliptic curves, won the 2014 Fields.
Peter Scholze, who studies perfectoid spaces and prismatic cohomology, won the 2018 Fields.
James Maynard, who studies prime distribution, won the 2022 Fields.
The above all involve combinations of algebraic geometry and prime number problems.
Simply put, almost anyone who makes a name in this field has won the Fields.
After much left-and-right thinking, Donaldson really couldn’t think of anyone at Stony Brook University who had achieved results in this.
“Okay, looks like you don’t know either. I’m sending you the Arxiv link on WhatsApp right now—help me ask who Randolph is, and some details about his article. I want to chat with him.” The voice came through the phone line from across the ocean into Donaldson’s ear.
After Terence Tao hung up, Donaldson still felt like he was in a dream.
Until he saw the link Terence Tao sent, clicked it, took a look, and realized it was real.
“No one at our school is known to work in this direction.” Donaldson muttered to himself, looking at the paper title on his mobile phone screen.
Terence Tao wasn’t ready to give up; he felt that if he didn’t find this mathematician named Randolph, he might be sleepless tonight.
“Does anyone know who Randolph Lin is? I saw an article he posted on Arxiv, I think it’s very interesting, some ideas in it are very reference-worthy, I want to discuss with him how some ideas were generated, I think it would be very helpful to my work.
If you know, please leave a comment below. If Randolph himself sees this, if you’re willing to chat with me, welcome to email me, and I will reply as soon as I see it.
Terry Tao edited on March 15, 2020″
Terence Tao was forced to post directly on MathOverflow to find the person.
MathOverflow is a forum similar to Zhihu, the mathematics version of Zhihu.
You can tell from the name: math.
A forum focused on asking and answering mathematics problems.
Terence Tao is an absolute big shot on this forum; his earliest question was posted in 2010, ten years ago.
During the virus outbreak, everyone was almost locked at home.
Various online forums were exceptionally active.
A big shot personally coming out to find someone.
For a time, onlookers gathered.
“I’m not, but I can be.”
“Took a look, interesting title, let me read it and come back to discuss in detail.”
“Never heard of him, this name sounds like Chinese people, but I really haven’t heard of him.”
“Stony Brook University? How come I haven’t heard of it.”
An hour later, the answers below had exceeded 100, which is rare on such a professional forum.
No one knew Randolph, as if this person popped out of thin air.
Terence Tao looked at the answers under the question, thinking the matter had fermented; the paper itself would soon be noticed by mathematicians who could understand it, and then Randolph would naturally emerge.
He thought, finally accomplished one thing.
During the virus outbreak, onlookers were everywhere.
On Zhihu, an hour later, this question was ported to Zhihu: “How to evaluate Randolph Lin whom Terence Tao is looking for—is he a Chinese mathematician? Why did his achievement cause Terence Tao to publicly seek him?”
“Flooding: Took a preliminary look, the matter is real, but can’t understand the paper, just passing by.”
“Should be Chinese people; foreigners rarely have the surname Lin.”
“Roughly took a look; Terry personally coming out to find someone is indeed very rare.
Haven’t had time to read the paper yet, just glanced at the title, saw everyone discussing hotly on MathOverflow, didn’t expect to see someone asking on Zhihu too.
Let me briefly share my understanding: algebraic geometry mainly studies solutions to polynomial equations, usually involving affine or projective varieties and rings of regular functions on them.
Traditionally, we think the Goldbach Conjecture belongs to additive number theory, closely related to prime distribution, while algebraic geometry more appears in number theory problems like elliptic curves, modular forms, or L-functions.
I guess Randolph Lin is attempting to extend the prime sum concept of the Goldbach Conjecture to the context of algebraic geometry, replacing integers with polynomials and primes with irreducible polynomials.
Any polynomial in at least two variables can be expressed as the sum of at most 2r absolutely irreducible polynomials, where r is the number of nonzero monomials in the polynomial.
This is similar to the number theory concept of expressing odd numbers as the sum of three primes, but with elements in polynomial rings.
By introducing classic number theory problems into the framework of algebraic geometry, I guess it may also involve tools like Newton polyhedra or toric algebra.
In short, the author’s work should involve many aspects, demonstrating the profound connection between algebraic geometry and number theory, which is why it attracted Terence Tao.
Just don’t know if he’s Chinese people; if so, it feels like Chinese mathematicians are about to have another character like Xu Chenyang or Yun Zhiwei.”
The answers under this question on Zhihu were later dug up countless times by netizens.
So much so that later netizens jokingly called it Randolph’s birthplace on the Chinese Internet.
The most common comment in the comment sections of various answers was: Birthplace, check-in.
The news didn’t reach until a week later, when Lin Ran’s high school classmate asked in a joking tone on WeChat: “Ran Shen, Randolph Lin couldn’t be you, right?”
Hours later, a screenshot appeared in the WeChat chat box.
It was precisely the Arxiv user backend screenshot, and the username inside was Randolph Lin.
“Holy crap!” Xu Xian, who had been sprawled on the bed, sat straight up in less than a second, slapped his own face hard, doubting if he was dreaming.
Xu Xian is Lin Ran’s high school classmate; he went to the Faculty of Mathematics at Yenching University, the top of the four asylums, for undergraduate, and after graduation directly stayed on for PhD in pure mathematics.
Because his name is Xu Xian, he’s nicknamed Xu Xian, but he’s always been single—no Madam White Snake, not even Xiao Qing.
He got into Yenching University not by recommendation, but purely by exam.
Honestly, as one of the 20% who got in purely by exam, Xu Xian has seen countless big shots in the asylum over these years.
But this time he was still shocked.
“!!!!!!” Xu Xian only replied with a few exclamation marks.
The reason he asked was that back in high school, Lin Ran’s English name was Randolph.
Bro, I was just joking, didn’t expect you really are.
“Why suddenly ask this?” Lin Ran replied.
Xu Xian never suspected it was photoshopped, because no need.
Lin Ran isn’t the type to joke about this kind of thing either.
“!!!
Ran Shen, the entire mathematics community has been discussing who Randolph is for a week, and you’re here asking why suddenly ask this!
No wonder Terry couldn’t find the person!
Who would think that someone who wrote algebraic geometry solving the Goldbach Conjecture is studying artificial intelligence!
Holy crap! This time it’s really godlike!
Ran Shen!
No, Brother Ran, can you take me flying? Next time you publish an article, let me do odd jobs, rub one off together?”
Xu Xian’s fingers flew, unleashing his lifelong mastery, determined to hug this golden thigh hard!
