Technology invades the modern world

Chapter 219 Randolph Statue Siegel (4k)

"He has indeed achieved a great result recently."

Many experts have said that the weak form of Goldbach's conjecture is interesting.

But at most, this would only result in four major publications.

For us, the Four Great Masters are definitely the real gods, I don't deny that.

Each year, the School of Mathematical Sciences at Yenching University produces very few PhDs who are admitted to the Big Four accounting firms.

It wouldn't be an exaggeration for him to say that he is a true god.

But isn't it a bit too far to go from the Big Four to the Fields Medal?
After all, if we broaden the scope to the whole world, there are quite a few PhD students who can graduate from the Big Four accounting firms every year.

Fields Medals are awarded every four years.

Moreover, the selection is not limited to PhDs, but is expanded to include all scholars under the age of 40.

My personal understanding is that there is still a long way to go from the Big Four accounting firms to the Fields Medal.

From publishing one paper in the top four journals, to consistently publishing in the top four journals every two years, to giving a 45-minute or longer lecture at the main venue of the International Congress of Mathematicians, and finally to Fields.

In terms of levels, there are probably three more steps to take, right? Li Yiqing still felt that Xu Xian was exaggerating a bit.

Lin Ran was unaware of this. If he had heard it, he would have laughed out loud. If it were 1960, the International Congress of Mathematicians would have been dull without him giving an academic report.

When the mentors of the top mathematicians in the contemporary world listened to my academic reports, it was like listening to celestial music, and their ears were instantly enlightened.

After hearing Li Yiqing's doubts, Xu Xian hesitated for a moment, but after glancing at the formula he had saved as a screenshot, he shook his head again.
"No, Brother Ran is truly talented."

"Hello, Randolph? Can you hear me?" Terence Tao's voice rang out in the Zoom meeting room.

Lin Ran only found out after talking with Xu Xian that Tao Zhexuan had been looking for him for a long time.

For a newcomer to mathematics, it is still necessary to find a mentor to guide them.

After contacting Terence Tao via email and confirming Lin Ran's willingness to make a public appearance, Tao quickly called a Zoom meeting.

Many mathematicians currently confined to their homes want to talk to Lin Ran about combining algebraic geometry with prime numbers.

In addition, everyone wanted to see some excitement.

Let's find out who Randolph really is.

So after Tao Zhexuan invited Lin Ran, he gathered a group of friends, and there were as many as thirty or forty people in the Zoom meeting room.

As a newcomer, having this many people listen is already quite an achievement.

After all, time zone differences must be taken into account.

"Hello everyone, I am Randolph Lin, the author of 'Application of Algebraic Geometry Methods to the Proof of the Ternary Goldbach Conjecture'."

I am a PhD student at Stony Brook University, State University of New York, and I am delighted to have been invited by Terry to give a brief remote academic presentation.

Lin Ran appeared in the video.

Just as the outside world had speculated, he was indeed a young person of Chinese descent.

Simon Donaldson was puzzled. He asked, "Lin, I'm sorry, if you're a PhD student at Stony Brook, how come I've never seen you before?"
Let me introduce myself. I am a professor at Stony Brook University, specializing in harmonic analysis and partial differential equations.

Although my work is unrelated to algebraic geometry or prime number problems, I should have met you if you were at Stony Brook University.

Or perhaps our school's administrative secretary couldn't find your name on the student list.

Lin Ran explained, "Oh, Professor Donaldson, I'm sorry, I'm from the Computer Science Department. You'll have to look up the list in the Computer Science Department."

The voice chat room fell silent for a moment.

Your Computer Science Department.

Then the professors in the mathematics department at Stony Brook University don't know you.

What does this mean?
This shows that Lin Ran is self-taught.

Only those who are self-taught can publish in top journals.

Everyone was a little unsure what to say.

Fortunately, Simon Donaldson turned things around quickly:

"So, Randolph, would you be interested in transferring to the mathematics department?"

We desperately need a PhD like you.

Tao Zhexuan interrupted, "Simon, we'll discuss Randolph's change of major later."

Let's begin today's academic report.

We still have a lot to discuss.

Lin Ran began his introduction:
“My approach differs from traditional analytical methods. As you may be interested in, I use tools of algebraic geometry, specifically the properties of algebraic varieties and their zeta functions, to analyze the distribution of prime sums.”

He scrolled to a slide filled with equations, the cursor jumping between symbols. "Here, I defined a specific affine variety whose points correspond to the configuration of prime numbers. By studying its zeta function, I extracted statistical properties about these sums."

"Randolph, how exactly does the cluster you constructed encode prime numbers?" Terence Tao interrupted.

“Good question, Terry. The structure of this cluster is associated with certain polynomial constraints that reflect prime number patterns.”

Its zeta function, after decomposition, reveals information about the density of these points, which I then connect to the requirements of the conjecture.

As we all know, the zeta function is often used for point counting in algebraic geometry, but it is not common to associate it with the distribution of prime numbers.

We need to bridge this gap, which involves using the Euler product of the zeta function and relating it to the Dirichlet L-function to create a framework that mimics the analytic properties of prime numbers.

Compared to the paper, Lin Ran introduced his framework in a more in-depth way.

Lin Ran answered the mathematicians' questions flawlessly.

After such an academic conference, everyone had no further doubt that Lin Ran had written this paper himself.

Self-taught mathematicians are quite rare in this day and age.

One by one, people left the meeting room.

Only Simon Donaldson and Terence Tao remained in the Zoom conference room.

“No, Terry, don’t you think this is weird?” Simon Donaldson asked absentmindedly.

Terence Tao asked, puzzled, "I think Randolph's answer was quite good, wasn't it?"
The paper explained everything very well, and I need to think carefully about the depth of his thinking regarding how to combine different fields.

What's so strange about that?

Simon Donaldson shook his head and said, "No, I didn't mean his answer was bad."

The problem is that he spoke too well.

He doesn't seem like a PhD; he seems more like a top mathematician.

Moreover, he was already a top-tier mathematician with an established reputation.

Tao Zhexuan thought for a moment: "That's somewhat of a feeling."

I didn't see any of the hesitation or embarrassment that young scholars often exhibit.

Simon Donaldson rummaged through his long memories and finally found what he was looking for.

He said, "Not only that, I also see the shadow of the late mathematician Siegel in him."

His tone and way of explaining things reminded me of Siegel.

His answers to our questions weren't those of a novice; they were more like he was instructing us.

Tao Zhexuan asked in confusion, "Siegel?"

Simon Donaldson nodded: "Professor Carl Siegel. His last attendance at the International Congress of Mathematicians was in 1978, when the Congress awarded him the Wolf Prize in Mathematics, a lifetime achievement award."

At that time, I was pursuing my doctorate under Sir Atiyah and went with him to that mathematicians' conference.

Because Professor Siegel was already very old at the time, he said that this was his last time attending the International Congress of Mathematicians and giving a farewell speech at the congress.

Randolph reminds me of Professor Siegel.

Although he may not have been born when Professor Siegel passed away.

But the feeling is really similar.

If Lin Ran were still in the Zoom meeting room, he would definitely be amazed at how accurate Donaldson's intuition was.

"I am Siegel's successor, so isn't it normal that we're somewhat similar?" Lin Ran thought to himself.

The question of who Randolph was has finally been answered.

Lin Ran said at the academic conference that he was a doctoral candidate in computer science.

The news spread quickly.

First, there was the Stony Brook campus.

Lin Ran's mentor has a very long name: Nilanjan Balasubramaniam.

The institute they are at is officially called the AI ​​Innovation Institute.

Nilanjan is an assistant professor whose main research areas are algorithm design, data science, machine learning, and natural language processing.

Zhao Linran mainly wanted to do some work related to Graph AI.

Lin Ran, as a professional, has analyzed Nilanjan.

Although Niranjana is of Indian descent, it must be admitted that he is quite capable. After all, he has over four thousand citations on Google Scholar.

Although the most cited paper, with a total of 1641 citations, is from 2009, there have been top-tier conference papers published in recent years. While the citation count may not look impressive, at least it's not a low-quality paper.

According to Rate My Professors, its teaching evaluation is 3.8 out of 5.

The comments included the opinion that the course content was relevant, the lectures were of high quality, the assignments were interesting, and the course helped students apply what they had learned.

Some also felt the course was too challenging, with assignments that were difficult compared to the lecture content.

To put it another way, it means high standards.

In recent years, judging from the quality of his papers, his research level and energy have declined significantly, and he urgently needs fresh blood to help him make a difference.

Before going, Lin Ran thought he was such a talented person.

After going there, Lin Ran realized that Graph AI was a mountain he couldn't support.

Lin Ran was thinking, "Let whoever wants to go, go ahead. I'm not going to put up with it anymore."

When Nilanjan received the call from Steven, the director of the AI ​​Innovation Institute, he was completely stunned.

I haven't met the student recently and can only contact him via email and Zoom to inquire about his progress. It turns out that Randolph Lin is the same Randolph Lin who has been making waves in the mathematics world recently, and his article has even been pre-accepted by New Advances in Mathematics, one of the four major mathematics journals.

No, I haven't seen you for three months. How did you suddenly turn from a shared bike into a giant bumblebee, into something I can't understand?

Most importantly, why isn't my name listed as an author on the paper? I should at least be listed as a second author.

For people of Indian descent, not gaining an advantage is considered a loss.

“Lin, no, Randolph, is there some communication gap between us?” Nilanjan’s tone was more polite than ever before.

He used to be very polite.

To say something extremely pushy while being polite.

The politeness now even carries a hint of flattery.

"No, our communication has been excellent, and I've been working on the tasks you assigned me," Lin Ran said.

From a mentor's perspective, Nilanjan is quite good.

Lin Ran chose the other party largely because the other party's research involved the application of machine learning in information retrieval, mainly optimizing the efficiency of search and information extraction.

It's good to learn this.

Learning this skill can lead to a job at a major company in America, whether it's Google, Amazon, or Facebook, they all need talent in this area.

Optimizing search efficiency is such a promising area.

Lin Ran just didn't expect that after arriving, Nilan Zhan suddenly had a whimsical idea to do something called Graph AI.

“Randolph, I heard you’re going to publish a paper at the new mathematics conference,” Nilanjan said.

He's been stuck in the assistant professor position for years, so if he can get it this time...

Dr. Lin Ran has at least three more years. If he publishes a few more papers in top mathematics journals, it's not impossible for him to become a professor himself.

“Yes.” Lin Ran said directly, “Professor, I know what you mean, but the problem is that my thesis is on number theory and algebraic geometry.”

I really wanted to sign my name too, but the problem is you probably can't even understand the question, so it wouldn't make any difference if you signed it.

I know your achievements in mathematics, don't you think the math professors at Stony Brook University know that? Won't they report you then?

Nilan Zhan fell silent, knowing that Lin Ran's words made a lot of sense.

Lin Ran continued, "Professor, if you can make things convenient for me, I can continue to stay at the AI ​​Innovation Institute. The institutions where I publish papers are also the AI ​​Innovation Institute."

For you, simply having trained a student like me is enough to earn you this year's Stony Brook University Board of Trustees Award.

While we can't add your name to the credits, that doesn't mean you won't benefit from it.

Nilanjan felt like he'd been fooled: "No, you're saying I can get the Stony Brook University Board of Trustees Award based on a single article in a top mathematics journal?"

"Don't even mention just one top-tier journal article; even if I were given first authorship in that journal, I probably wouldn't win."

Nilan Zhan understood perfectly what Lin Ran was talking about; the Board of Trustees Award was the highest honor within Stony Brook University.

The mathematics department produces about ten papers in the top four journals every year.

With your achievement, and me merely your mentor, isn't that a bit of an exaggeration?

Lin Ran said, "What if it's not just one of the Four Big Four accounting firms?"

Nilanjan immediately became curious: "If it's not one of the Big Four, then what is it?"

Lin Ran said, "Fields."

Nilanjan was speechless: "Fields? I'm not a math major, but I know very well that Fields is two years from now."

Lin Ran said, "No, no, no, it's an undeniable job."

Once this paper is published, I will reserve a Fields Medal two years from now.

Regardless of how many mathematicians participate or what results they achieve, I have reserved a seat in advance.

In short, you just wait and see.

Nilan Zhan was skeptical, mainly because Lin Ran already had an article in the Four Great Classical Novels that was in the process of being prepared for publication: "What achievement?"

Lin Ran said calmly, "To completely solve the twin prime conjecture."

Niranjan naturally knew what the twin prime conjecture was, and he also knew the significance of this problem.

"real or fake?"

“Of course it’s true, six months, I only need six months,” Lin Ran said.

(End of this chapter)