The wall separating pure and applied mathematics—despite them both falling under the umbrella of "math"—is no thinner than the one between mathematics and physics.
For someone who studies the zeros of L-functions and someone who works with variational methods for partial differential equations to truly speak the same language, many concepts have to be translated and re-contextualized.
The technical terms Professor Levan just mentioned—things like the π phase difference in a three-basis expansion, the Gikhmanov regularization for ill-conditioned operators, and the inversion of a ligand field tensor.
Li Dong had heard of the first two but had never delved into them.
The last one was completely foreign to him.
In truth, the other titans of the field in the room were just as lost as he was.
Li Dong thought for a moment, then looked at Levan and said.
"Professor Levan, I haven’t studied the topics you’ve mentioned, so I can’t give you an answer to your question right now."
A flicker of disappointment crossed Levan’s eyes.
"However..."
He continued.
"I’m very interested. Give me a month, and I’ll have a response for you."
"Thank you, Mr. Li Dong."
Levan nodded, assuming Li Dong was just being polite.
After all, Li Dong clearly hadn’t understood a word he’d said, which confirmed that he wasn’t particularly skilled in applied mathematics.
’One month?’
’That’s nowhere near enough time.’
Meanwhile, Liu Ruochuan was the only one in the room internally cursing up a storm.
’One month?’
’This kid needs a month to answer those questions?’
’After all, Li Dong’s paper, *The Pair-Correlation Criterion for the Local-Global Compatibility of Automorphic Representations of GL(n)*, took him just a little over two months from start to finish.’
’And now he needs a whole month to figure this out?’
’Don’t tell me... Is this kid planning another major move?’
Liu Ruochuan shot him a deep look. ’Maybe... I should stick close to him for a while?’
To be honest, he was a little envious of Yang Shengguo and Penrose. He, Liu Ruochuan, wanted his name on a paper like that too!
The group discussed a few more mathematical problems before the meeting came to a close.
In total, it had lasted less than an hour.
Wiles still hadn’t fully digested what he and Li Dong had discussed the previous day. The old man needed time to process it all, so he arranged for another meeting.
For the remainder of his time at Yan University, aside from a public lecture he’d promised Principal Gong, Wiles planned to dedicate almost all his time to Li Dong.
Professor Penrose had barely spoken all day, but he had been constantly taking notes on what Li Dong said. As he left, he was muttering something under his breath, though Li Dong couldn’t make out the words.
After Li Dong agreed to give a lecture at Shuimu, Qiu Chengtong didn’t stay much longer either.
He didn’t want to run into certain people.
Professor Levan packed up his tablet, mentioning he was flying to Hecheng today and couldn’t stay.
In the end, only Liu Ruochuan and Li Dong were left, walking out of Jingchun Garden one after the other.
They walked in near silence.
Just as they emerged from the small grove of trees, Liu Ruochuan finally spoke.
"Kid, what’s next for you? Where will you go?"
Li Dong paused. "Where will I go?"
Liu Ruochuan gave him a look.
"With this, all the top universities in the world will be extending you an olive branch. And..."
"I’m not talking about as a student. Princeton IAS, MIT, Cambridge, Oxford, ETH—any one of them could offer you a tenured position directly. They might even waive the doctorate requirement for you."
Li Dong already knew, actually. He’d checked his email yesterday...
He glanced at Liu Ruochuan.
"Teacher Liu, what about Yan University?"
Li Dong’s question was an answer in itself. He wasn’t leaving.
Liu Ruochuan considered this for a long time before finally speaking.
"We have two proposed paths for you here."
"First, as soon as this semester ends, you’ll graduate with your bachelor’s degree. We’ll put you on a fast track and grant you the title of Research Fellow, equivalent to a full professor."
"Your compensation would be one tier below that of an academician. Teacher Tian and most of the other faculty feel this is the quickest route."
"The second option." Liu Ruochuan paused.
"This is my personal recommendation: you... go pursue your doctorate."
Li Dong blinked, taken aback.
"Huh? Then why not just make me a full professor?"
Liu Ruochuan sighed.
"Because with the first option, you wouldn’t have a doctorate."
"That might not seem important to you personally, but you have to understand, many institutions don’t recognize a full professor who was promoted unconventionally."
"Internationally, many collaboration agreements, directorships of joint labs, certain titles, and even academic committees like the one at the Clay Mathematics Institute have bylaws requiring specific degrees for their members."
"Of course, exceptions can be made, but making an exception always gives people something to talk about."
"’A professor without a doctorate? Can you even call them a professor?’ We’ve had situations like that before in Huaxia."
"So, in my opinion..."
He glanced at Li Dong.
"You should remain a doctoral candidate for another year or two."
"It won’t hinder your research in any way during that time."
"Besides, after publishing in the *Annals* and proposing the Li Clan Conjecture, your path is all but guaranteed."
"By then, even as a PhD student, you’ll be able to enjoy perks and resources nearly on par with an academician."
"So why leave yourself with such a vulnerability?"
Liu Ruochuan chuckled. "Besides, I get the feeling you don’t just want to stick to this one path, do you, kid?"
Li Dong paused for a second, then smiled.
’This old guy really gets me.’
’He didn’t just want to do pure mathematics.’
’His attributes—Logic, Memory, Concentration.’
’Add his Memory Palace to the mix... if he really got stuck with the title of "unconventionally promoted full professor," he’d feel constrained.’
’The status of a doctoral candidate offered relative freedom.’
’He could attend other classes without his status being so lofty that it put pressure on the professors teaching them.’
’He could go to other departments and raid their "toolboxes," and it wouldn’t be seen as overstepping his bounds, but as a standard doctoral rotation.’
After thinking it over, Li Dong nodded. "Teacher Liu, I’ll take your advice."
Liu Ruochuan rolled his eyes so hard they nearly popped out of his head.
’Like hell you’re taking my advice! You wanted to do this all along, and now you’re just using me as an excuse so you can blame me for it later, aren’t you?’
’But he couldn’t be bothered to call him out on it.’
’Whatever. Let him pass the buck.’
’He still had to figure out how to report this to Tian Gang and Principal Gong.’
He then asked another question.
"What about your research direction? For your doctoral dissertation... are you still planning to work on the Langlands program?"
Li Dong smiled.
"Of course. I’ll definitely work on it. But I’m not going to focus only on Langlands."
He paused.
"During my PhD, I’d like to explore the intersection of four fields: the Langlands program, geometric representation theory, several complex variables, and mathematical physics."
"I’ll dip my toes in, get a feel for them, pick one, and then write my next paper on it."
Liu Ruochuan: ...
’Are you fucking kidding me? You plan to write your dissertation on a problem at the intersection of four Fields Medal-worthy fields?’
’Are you here to get a PhD, or to open a franchise?’
He said no more, simply walking ahead in silence.
「At that very moment.」
Mathematicians all over the world were studying Li Dong’s paper and his conjecture.
United States. Los Angeles. At UCLA, in Terence Tao’s office.
After finishing the last page of the paper, he leaned back in his chair, eyes closed, for a full hour.
Then, he opened his blog and began writing a long post:
*The Next Hundred Years of World Mathematics*
In the opening paragraph, he uncharacteristically eschewed his usual cautious, academic "cause-and-effect" style of writing and cut straight to the point.
"This morning, the *Annals of Mathematics* published a paper co-authored by Li Dong, Arthur Penrose, and Yang Shengguo."
"I have read it through twice..."
In his blog post, Terence Tao used four paragraphs to calmly summarize the paper’s contributions at the tool-making level.
Then came the fifth paragraph, which contained what he truly wanted to say.
"As a fellow mathematician, I would like to add a word about the conjecture at the end of this paper."
"It has already passed the first round of tests—that is, being checked for counterexamples—by several senior colleagues."
"It has repelled all the usual weapons: Galois conjugation, CAP representations, and bad place coupling."
"I don’t know when it will be proven."
"But I do know one thing."
"Until it is proven, a whole generation of mathematicians will use it as a beacon, guiding their voyages for the next ten, twenty, or even thirty years."
"It has been a long time since we have seen such a beacon."
Within two hours of the blog post going live, its view count shattered the records of all his previous long-form articles.
At almost the exact same time as Terence Tao’s blog post went up.
France. The IHÉS.
From his office, Wu Baozhu posted a tweet containing only a single, short line.
"Finally, someone has laid the foundation."
Oxford University. The Mathematical Institute.
Professor Wiles’s postdoctoral fellow—the one who had followed him all the way from Princeton to the United Kingdom—posted a single sentence to his social media.
"The old man might not be coming back."
The comment section below was filled with "Haha."
Princeton Institute for Advanced Study. Langlands’s office.
The old man sat by the window, his computer off, the paper unread.
He held a cup of long-cold coffee, his gaze fixed on the path outside the window—the same one Einstein used to walk.
After a long while, he finally whispered a single sentence.
"To the next generation... you’re the lucky ones."

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