149: Chapter 149: Speculation at the Beginning

In mid-August, the air in Beijing still retained the heaviness and stifling heat of midsummer.

Starting from 6:30 in the morning, the main traffic arteries near Wudaokou were already filled with all kinds of vehicles.

The traffic moved forward slowly, and the exhaust fumes mixed with the heat waves rising from the asphalt road surface.

School gates, orientation stations, volunteers, colorful banners printed with the names of various departments...

All these words were piecing together a bustling and vibrant picture in reality.

For the vast majority of eighteen-year-olds, these images would form their initial memories of university life.

Jiang Lin had breakfast, packed his luggage, checked out of the hotel room, and called a ride-hailing car to go to Tsinghua University.

However, the car was ultimately stuck on Zhongguancun North Street outside the West Gate of Tsinghua University.

Looking ahead, the traffic stretched for hundreds of meters, and the red brake lights connected in a string.

The sidewalks by the road were packed with people. The sound of suitcase wheels rolling, parents instructions, and childrens responses blended together, and that steaming-hot bustle could be felt even through the car windows.

"We'll have to wait a bit. It's always like this every year when new students register, and the West Gate can jam for half an hour." The driver smacked his lips. "How about I drop you off at the intersection ahead? It's only a few hundred meters if you walk over."

"Okay."

Jiang Lin got out of the car and stood on the sidewalk outside the West Gate with his suitcase.

Warmly welcome the Class of 2022 new students.

A huge red banner hung at the school gate. As the wind blew, the banner fluttered loudly.

Volunteers wearing purple vests stood at the entrance, holding signs for the Tsinghua University Orientation Reception Station, guiding new students and parents to take the dedicated passageway.

Walking inward, the branches and leaves of the sycamore trees on both sides of the main road intertwined, forming a natural tree-lined avenue.

Every few dozen meters, there was a department orientation station set up with a blue tent and a department sign.

School of Economics and Management, Department of Computer Science, Department of Mechanical Engineering, School of Architecture...

The tents were crowded with people. New students handed over their admission letters, volunteers smiled and handed over the new student gift packages, and parents stood aside holding cameras, constantly pressing the shutter.

There were the most people near the Second Gate.

In front of this stone archway engraved with the three characters "Tsinghua Garden", it was surrounded by people three stories deep inside and outside.

Every new student had to stop, stand right in the center of the archway, and let their parents take a photo.

Some stood stiffly, some made V-signs, and others went all out with their whole family, dragging their suitcases to squeeze into the frame.

Voices drifted far down the sycamore avenue, mixed with the guidance of volunteers, the laughter of children, and the accented conversations of parents, like a grand tide slowly washing into the entire campus.

Dragging his suitcase, Jiang Lin walked inward along the edge of the sidewalk.

Someone on the road recognized him.

First hesitation, then a low reminder to a companion.

"Is that Jiang Lin?"

"Looks like it."

"He's registering today too?"

"Duh, isn't he going to Tsinghua University?"

Some gazes chased after him.

Some also raised their phones, only to put them down quickly.

The further they walked toward the apartment area, the stronger the orientation atmosphere became.

Buildings 1 through 13 of Zijing are conventional undergraduate dormitories, and downstairs were full of people moving luggage.

Parents carried mattresses and quilts, children dragged suitcases, and long queues formed at the dormitory management office to collect keys...

By comparison, Building 17 was so quiet it felt like another world.

There were no orientation tents, nor clusters of parents, only the dorm auntie sitting in the duty room reading a newspaper.

Jiang Lin swiped his card to enter.

In the dormitory, he spent ten minutes sorting his luggage, then went downstairs to report to the Mathematical Sciences Center.

At the same time, a piece of news was fermenting at an astonishing speed within a few small circles on the Tsinghua University campus.

The news first spread in the faculty chat group of the Department of Mathematics.

[Notice: Today at 2:30 PM, on the first floor lecture hall of the Mathematical Sciences Center, a closed-door technical calibration meeting for PFR / Marton v1.0 will be held, with author Jiang Lin as the main speaker. Attendance is restricted to faculty and students of our university in the directions of Additive Combinatorics, probability, information theory, and formal verification, with attendance by name list. Interested teachers and students should report to the department office promptly.]

Another sentence was added afterwards.

[Rare opportunity, related directions get priority.]

The chat group was silent for a few seconds.

Immediately afterwards, avatars that had been lurking all year round popped up one after another.

[Is that the polynomial Freiman-Ruzsa conjecture?]

[Yes, that's the one. Version v1.0 was just sent to the core reviewers early yesterday morning.]

[Holy crap, Jiang Lin, that undergraduate freshman, he actually made it?]

The news seeped out like water.

The teachers of the Department of Mathematics immediately forwarded it to the students they mentored.

In the Qiuzhen College Ph.D. student chat group, at 10:15, someone forwarded the notice in.

[Brothers, big news. This afternoon at the Mathematical Sciences Center, there is Jiang Lin's PFR closed-door meeting. Attendance is by name list, those in related directions hurry up and sign up with your advisors, slow hands miss out.]

The chat group, which originally only had a few orientation mutual-aid messages, exploded instantly.

[Isn't today the new student registration day? As an undergraduate freshman, shouldn't Jiang Lin be queuing up for registration at Zijing Playground?]

[That's why it's so outrageous! On the first day of school, other people are lining up to collect textbooks, while on his first day of school, he goes to do closed-door technical calibration for a bunch of doctoral supervisors at the Mathematical Sciences Center. Is there any reason left in this world?]

At 10:30, the news spread to the Institute for Interdisciplinary Information Sciences.

Lin Chuan, a young teacher doing formal verification, was originally holding a group meeting to discuss next week's Lean verification tasks with students. A message popped up on his phone, he glanced at it, and directly stopped his words.

"Group meeting is suspended for now."

The students were all stunned.

"At 2:30 this afternoon, there is a closed-door technical calibration meeting for PFR / Marton at the Mathematical Sciences Center, given by Jiang Lin." Lin Chuan put his phone on the table. "Everyone doing formal verification and theoretical computation, go sign up at the department office. Those who can get in should all go listen. The group meeting is postponed to tomorrow morning."

The students below looked at each other in dismay.

"Teacher, that PFR Conjecture? Did he really make it?"

"Version v1.0 just entered review today." Lin Chuan tapped the table. "If this proof holds, the underlying logic of several formal projects in our hands will have to change. All of you go listen, take notes carefully, and when you come back, we'll hold a special discussion."

By 11:00, the news had rushed out of Tsinghua University.

At the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences, Researcher Chen Zemin sat in his office, having just finished reviewing a student's first draft of a paper.

A message popped up from the same-school-alumni chat group on his phone, which was a notice sent by a classmate from Tsinghua University.

He stared at the screen for half a minute, picked up his phone, and called the three Ph.D. students he mentored.

"You three, go to the Tsinghua University Mathematical Sciences Center this afternoon to listen to a closed-door report."

"Ah, Professor Chen, what report? We were originally supposed to calculate the numerical simulation for that Additive Combinatorics this afternoon."

"Stop doing that, go listen to the report first. If the main chain of this proof is valid, the directions of those three projects in our hands will all need to be readjusted."

The other end of the phone was silent for a few seconds.

"Really or fake? Didn't he just make Jiangs Brick? It's only been a few days, and he's already settled PFR?"

"How many days he took to make it doesn't matter; what matters is the stuff itself," Chen Zemin explained. "If you can get in to listen, listen carefully and take good notes. If you can't get in, wait outside and see if there's a chance for post-meeting communication. For work of this level, managing to catch even a sliver of it is more useful than you guys burying your heads in work for three months."

At 11:20, the Department of Mathematics at Peking University.

Several Ph.D. students in the direction of Additive Combinatorics were gnawing on sandwiches in the discussion room while flipping through the latest papers.

One of them refreshed their Moments, posted by a classmate from Tsinghua University, with the caption that there was a heavy dish this afternoon, and the location was set at the Mathematical Sciences Center of Tsinghua University.

He clicked in to take a look and almost spat out his sandwich.

"Holy shit, brothers, Jiang Lin is holding a closed-door PFR meeting at Tsinghua University this afternoon!"

"Bullshit? Didn't they say just a while ago that there was only a prototype?"

"It's true, posted by my Tsinghua classmate. Attendance is by name list."

Several people immediately gathered around.

"Do they let people from outside the school in?"

"I don't know, let me ask my advisor."

One of the Ph.D. students immediately sent a message to his advisor.

In less than five minutes, the advisor replied.

[I've greeted the people at Tsinghua. You three go over, report my name, and you can get in. Hurry up, don't be late.]

The three looked at each other, instantly grabbed their schoolbags and notebooks, and ran outside.

"I originally thought it was an insider rumor, but it turns out our advisor is telling us to go attend it."

"This isn't attending, this is going on a pilgrimage."

"Seriously, I'm still a bit dazed up to now. PFR, when we were in our first year of Ph.D., we were still discussing how difficult this conjecture was, and as a result, people have directly made it out and are holding a closed-door meeting."

When walking to the school gate to hail a cab, one of them suddenly remembered something and said, "Hey, do you guys think Teacher Wei will go?"

The steps of the other two paused.

"If he's interested, he'll definitely go."

...

At 12:10, the capital circle also caught wind of it.

In the tech investment chat group of Red Map Capital, Zhang Jing, the investment director in charge of the hard-tech track, sent a sentence.

[Confirmed, Jiang Lin is holding a closed-door PFR / Marton meeting at the Mathematical Sciences Center of Tsinghua University today. Basically everyone in the domestic Additive Combinatorics circle has arrived, and Terence Tao, Voss, and others are online too.]

The chat group, which was originally chatting about the exhibition projects of the World Robot Conference, instantly shifted direction.

[Director Zhang, what is PFR? Is it related to Low Entropy Workshop?]

[The founder of Low Entropy Workshop is Jiang Lin. Previously we thought he was an entrepreneur making robots, but now it seems he simply obtained top-tier results in the field of mathematics first before entering the field to do engineering.]

[Before, we wanted to schedule an appointment with Low Entropy Workshop to talk about Series A financing, but we never managed to book it. I thought the other party was deliberately putting on airs. Turns out they are not an ordinary hard-tech startup at all; the founder is genuinely doing world-class underlying theoretical research at the same time.]

[Then the previous valuation model has to be changed. Originally we thought the G-01 hexapod robot was the core asset, but now it seems that Jiang Lin's own mathematical ability is the most valuable thing about Low Entropy Workshop.]

The investors' discussion direction instantly shifted.

No one talked about the commercialization landing cycle of the robot company anymore. Everyone's focus turned to how much valuation premium the founder possessing world-class underlying mathematical capabilities actually means for a hard-tech company.

The chief partner in the chat group finally set the tone.

[Stop mentioning frivolous words like dropping by the booth during the robot exhibition. For us, the G-01 robot is merely a visible entry point; Jiang Lin himself is becoming the underlying asset of Low Entropy Workshop that is hardest to price and impossible for competitors to replicate.]

...

At 12:40 in the afternoon, the news was moved to Zhihu.

Under the mathematics section, a new question quietly popped up and then rushed upward at an astonishing speed.

[How to evaluate the closed-door technical report on PFR / Marton given by Jiang Lin today at the Mathematical Sciences Center of Tsinghua University?]

In less than half an hour, the answer section exploded.

The top upvoted answer was an anonymous user labeled as a Ph.D. student in the Department of Mathematical Sciences at Tsinghua University.

The number of upvotes surged to 1,200 in half an hour.

[People are in the corridor of the Mathematical Sciences Center, having just squeezed through the auditing crowd.]

Originally a core review and calibration meeting on the scale of eighteen people, it only invited a few core scholars in the directions of Additive Combinatorics, probability, information theory, and formal verification.

As a result, the news spread too fast; teachers from the Department of Mathematics, master's and doctoral students from Qiuzhen College, and people doing formalization and theoretical computation from the Cross-Information Institute all came over. In the end, Mr. Qiu made the final decision that teachers and students of the school in related directions could audit via a name list, and off-campus peers who had reported could also enter.

Adding a piece of trivia: Today is the official registration day for undergraduate freshmen of the class of 2022 at Tsinghua University.

Others registering: collecting campus cards, collecting bedding, getting to know roommates, and taking group photos.

His registration: doing PFR / Marton v1.0 technical calibration for a group of professors and doctoral supervisors at the Mathematical Sciences Center.

This legendary opening scene is probably unprecedented and unrepeatable.

The second post is from the verified account of an assistant professor in the Department of Mathematics at a certain 985 university, with a restrained tone, but full of amazement between the lines.

"The v1.0 distribution package only entered the first batch of reviewers' mailboxes early yesterday morning, and some people in the circle have already stayed up all night chewing on it. The core node calibration meeting is held immediately this afternoon, and the promotion speed is simply too fast."

"Participating online are Terence Tao, Tom Sanders, and Heinrich Voss, with Mr. Qiu presiding offline. Basically, half the country's experts in Additive Combinatorics and related directions are at the scene."

"This specification is no longer at the level of a young scholar's academic report, but close to the mid-term review of a domain-level work."

The comment section had long since erupted in arguments.

Someone asked—

"What on earth is PFR, and why is the entire mathematics circle so excited?"

Someone immediately added a popular explanation below.

"To put it crudely: What PFR asks is, if a set does not expand too drastically in an additive sense, does it actually hide a low-dimensional skeleton? And can this skeleton be captured at a polynomial cost rather than paying an exponentially exploding cost?"

"The Marton entropy form is a completely different set of languages: instead of talking about compression using set size and additive structure, it keeps accounts using entropy, degrees of freedom, conditioning, and probability space."

"The real hell-level difficulty lies in the fact that these two sets of languages are not simple translations. Rather, someone must pay the bill in the end for every loss generated by compression and every probability space changed by conditioning. If the accounts do not close, the proof will blow up."

Scrolling further down, the tone gradually turns into an emotional breakdown.

"Competition geeks, assemble. I used to watch him score 749 on the Gaokao and thought it was a routine genius script, but it turns out he also has the Jiangs Brick, and now he is directly charging at PFR / Marton. I am still chewing on GTM introductions, and he is already building new tools."

"Asking out of ignorance, what level is the PFR Conjecture? High-voted reply below: It's roughly equivalent to a freshman on the first day of registration going to the Fifth Academy of Aerospace to lecture academicians on a new rocket engine they designed themselves, but also demanding that the academicians find faults on the spot."

"Does anyone know if we can still get into the venue? Is it too late to take a taxi over now?"

"Forget about it, it's a name-list system, even the air in the corridor is rationed."

The discussion slowly spread from the mathematics section, and people in the Gaokao, competition, and science and technology sections all began to repost.

Gaokao top scorer, ICCM Gold Award, eighteen years old, undergraduate freshman, world-class conjecture...

These labels stacked together naturally carry an impact.

Everyone is curious about what kind of thing this young man who has just turned eighteen has brought out that can mobilize the entire Additive Combinatorics field with such fanfare.

At 1:40 PM, outside the lecture hall on the first floor of the Mathematical Sciences Center.

The name list verification officially began.

A long table was placed beside the glass door, and two master's student volunteers from the Department of Mathematics sat behind it, clutching printed name lists in their hands.

The name list was originally only two thin pages, consisting of the initial core reviewers. Later, people kept coming to the department office and advisors to apply, and names were hand-written and added one by one. The edges of the paper were curled from being flipped through, soaked slightly with sweat from palms.

"Student, please state your name and affiliation."

"Wang Baisong, second-year PhD student in the Department of Mathematics."

"Alright, sign your name here and collect a copy of the auditing guidelines."

"Understood."

The queue stretched from the entrance of the lecture hall all the way to the water dispenser, numbering at least seventy or eighty people.

Almost no one in the queue was chatting idly.

Some lowered their heads, clutching a thin de-sensitized abstract in their hands, their brows slightly furrowed, reading carefully line by line.

Some wrote down a few keywords on the first page of their notebooks, all of which were directions they prepared to follow up on.

Others simply leaned against the wall with their eyes closed, running through the basic definitions and classical conclusions of the PFR Conjecture in their minds.

Simply put, no one was here just to join the fun.

Those who could appear here were either researchers in related directions or students desperately trying to squeeze into the frontier. Everyone was well aware of how heavy the weight of this report was.

The conference organizing committee temporarily printed an extra fifty copies of the auditing guidelines, which were handed out in less than ten minutes.

Someone from the back row brought over a bar stool from the laboratory, and some simply sat on the steps, spreading their notebooks on their knees and turning to a blank page in advance.

No one complained about bad seats, nor did anyone care whether there was a desk.

Being able to get in was already a win.

Liang Chen stood at the very back of the queue, his palms sweating slightly.

He was a second-year master's student at Qiuzhen College this year. Hearing from a senior fellow apprentice at noon that there was this report, he sent a message to his advisor with a try-it-out mentality, not expecting his advisor to immediately sign him up and tell him to rush over.

He had long since heard the name Jiang Lin.

But those were legendary names in the news.

Until today, standing in the corridor of the Mathematical Sciences Center waiting to listen to a closed-door report on a world-class conjecture delivered by this person, did he truly feel for the first time the almost suffocating gap between peers.

"Student, name and affiliation?"

"Liang Chen, second-year master's student at Qiuzhen College."

"Sign your name, and when you go in, try to stand as far back as possible. There aren't enough seats in the front."

"Okay, thank you."

Taking the auditing guidelines, Liang Chen walked into the lecture hall.

As soon as he stepped through the door, he was stunned for a moment.

The lecture hall was not large; its original one hundred and twenty seats were already fully occupied long ago.

Two rows of folding chairs were added to the middle aisle, and they were also packed full.

Quite a few people were standing along the walls on both sides, and the gaps in the back row were also crammed with people, leaving almost no room to set foot.

The front row was reserved expert seating, and the nameplates had already been set up.

Shing-Tung Yau, Professor Han Yanshan, Ding Jian...

And several other professors whose names he had only seen in papers and textbooks.

The whiteboard at the very front was clean and completely blank.

The display screen next to it was black, and the remote connection had not yet been turned on.

The air conditioner was turned down very low, but because there were too many people, it was still a bit stuffy.

Yet no one cared; everyone's gaze more or less fell on that blank whiteboard, waiting for what was about to be written on it.

Liang Chen squeezed into the corner of the back row, found a spot where he could clearly see the whiteboard, stood still, and took out his notebook.

At 2:02 PM, the remote window opened.

The account names of overseas scholars appeared on the screen one after another.

Terry Tao.

Tom Sanders.

Heinrich Voss.

Ben Green.

Freddie Manners.

...

Every single one of these names was a pillar in the fields of Additive Combinatorics and probability.

Many people had pursued PhDs for five or six years, citing their papers countless times, yet this was the first time they saw them in person.

Even if it was just an online account avatar.

The staff repeatedly tested the audio, confirming that every channel was clear.

At 2:15 PM, the experts in the front row entered the venue one after another.

Shing-Tung Yau walked at the very front, wearing a dark shirt and holding a notebook in his hand.

He walked to the center position and sat down, whispered a few words to Professor Han Yanshan beside him, and his gaze fell on the whiteboard in front.

Professor Han Yanshan and Ding Jian sat on his left and right sides respectively.

In the subsequent rows, senior professors in the directions of Additive Combinatorics, probability, and information theory domestically took their seats one after another. Some nodded and greeted each other, while others opened the full manuscript in their hands and turned directly to the position of node No. 38.

The middle area was filled with young teachers, postdoctoral researchers, and doctoral students.

Standing in the back row and aisles were mostly junior doctoral students and master's students.

Many people just held a pen and a notebook, preparing to tough out the listening.

The sound in the lecture hall grew lower and lower.

The rustling sound of turning paper rose and fell in succession, and occasionally someone conversed in a low voice for a sentence or two, which was also quickly reined in.

Everyone was waiting.

Waiting for the person who advanced PFR / Marton to v1.0 to walk to the front of that whiteboard.

At 2:24 PM.

Footsteps came from the stairwell at the rear side of the lecture hall.

The conversation sounds, which had been suppressed very low, stopped instantly.

Everyone's gaze turned toward that direction.

Jiang Lin came down from the second-floor office.

He wore a clean white shirt with sleeves rolled up to his forearms, dark trousers, and a pair of ordinary black sneakers on his feet.

In his hand was only a black soft-leather notebook and three whiteboard markers clutched in his hand.

Many gazes fell upon him.

Some were seeing him for the first time—curious, scrutinizing, and carrying a hint of disbelief.

Some had seen him at ICCM in Nanjing and knew how steady this young man was standing on stage.

And even more people had repeatedly seen this name in papers, emails, and news, and today they saw him in person for the first time.

Eighteen years old.

Undergraduate freshman of the class of 2022 at Tsinghua University.

Winner of the ICCM Gold Award.

Author of the Jiangs Brick.

Author of the PFR / Marton v1.0 manuscript.

These identity labels were all stacked on this young figure at this moment.

But soon, everyone temporarily forgot about these labels.

Because in the academic lecture hall, identity is not important, titles are not important, and age is even less important.

The only thing that matters is what is about to be written on the whiteboard.

It is the proof.

Jiang Lin placed his notebook on the corner of the podium, unscrewed the cap of the black whiteboard marker, and test-wrote in the corner of the whiteboard to confirm that the ink flowed smoothly.

The action was very natural, without the slightest tension, nor any deliberate calmness.

Just as if he had deduced in front of this whiteboard hundreds of times before.

At 2:29 PM.

Shing-Tung Yau raised his hand to adjust his glasses and turned his head to give a slight signal.

Professor Zhou Wendao, who was sitting slightly to the front, nodded, stood up, walked to the front of the stage, and gently tapped the microphone.

Zhou Wendao was the teacher responsible for the coordination work of this closed-door technical calibration meeting at the Mathematical Sciences Center of Tsinghua University.

"Good afternoon, teachers and students."

"Today's session is the PFR / Marton v1.0 closed-door technical calibration meeting."

"Thank you, teachers and students, for coming to the Mathematical Sciences Center on the freshman registration day, and thank you to all overseas peers attending online for taking time out of your busy schedules to participate."

"The content of this report is very heavy and time is very tight, so I won't take up much more time."

He turned sideways, looked at Jiang Lin standing at the side of the whiteboard, and made a gesture of invitation.

"Now, please let Jiang Lin begin."