It dawned on them.
This little game, which looked like an elementary school math problem,
was a 19th-century mathematician using the simplest of methods to touch the foot of the 20th century’s most colossal mountain.
And a new peak on this very mountain had just been named by the young man standing before them.
Li Dong drew a simple arrow between the two formulas on the blackboard.
Then he looked out at the audience.
"I said this lecture wouldn’t be about Langlands."
"I didn’t lie to you."
"I didn’t talk about it."
He smiled.
"But every word you just heard was, in fact, about it."
"The question hasn’t changed."
"a2 + b2 = n. How many pairs of solutions are there?"
"The answers have."
"The algebraic perspective tells you to change the number system."
"The geometric perspective tells you the average order is π."
"The analytic perspective tells you that π comes from an L-function."
"They are all, in fact, the same thing."
"The same thing, just said three times by different people in different languages."
The hall was utterly silent.
At this, Li Dong’s tone softened, and he slowed his pace.
"I once had a high school teacher."
"My math teacher."
"He once said something to me."
"Of course, I don’t remember his exact words, but I’ll give you the gist."
"Whether it’s geometry, algebra, analysis, number theory, or combinatorics..."
"They all seem to be in different rooms."
"But that’s only because the people who built the house put up walls."
"The walls aren’t the knowledge."
"The walls are there for the convenience of teaching."
"When you need the knowledge from another room, you just tear down the wall."
"Once it’s down, the house becomes one big, open space."
"This lecture today was about how to tear down those walls."
The classroom was so quiet you could hear someone in the back row swallow.
Li Dong looked up.
His gaze swept across the audience.
"Fifty years from now, when one of you is standing where I am now, explaining this problem to the next generation..."
"I hope you won’t just tell them how Jacobi wrote that formula,"
"or how Gauss counted those integer points."
"Tell them one single sentence."
He paused.
"Mathematics... there has only ever been one kind of mathematics."
"It passes through different windows, casting different shadows."
"Those of us who do math have only one task in our entire lives—"
He looked up.
"To pass through those shadows and find that single beam of light."
For half a second, the classroom was dead silent.
Then, one person began to clap.
Immediately after, everyone else rose to their feet and joined in.
More than five hundred pairs of hands.
The resulting applause was so thunderous it felt like it would blow the roof right off the Guanghua Building.
Unceasing.
Li Dong stood at the lectern.
He didn’t move.
Below, the audience’s eyes were fixed on him.
They couldn’t put a name to the feeling.
They just felt that this young man at the front of the stage...
...had so much more behind him.
The place he wanted to lead them was a place they couldn’t see.
They didn’t know where it was.
Perhaps it was the very end of mathematics.
Perhaps it was a star that would only become visible a hundred years from now.
But they just felt...
...that they wanted to follow him.
「After the lecture ended, in a small reception room in the Guanghua Building East Main Building.」
The moment Li Dong walked in, Shen Wei stood up.
He didn’t say a word.
He simply extended a hand toward Li Dong.
Li Dong paused for a second, then quickly shook it.
"Academician Shen."
"My lecture today was a bit subpar. I’m afraid I made a poor showing."
Shen Wei shook his head.
"I was sitting in the front row."
"Halfway through, I couldn’t help but start working through the derivations on my own scratch paper."
He chuckled.
"If you call that a ’poor showing,’ then no one else can give a good lecture."
Wu Jianguo, who was beside them, also chimed in.
"Li Dong."
"I came to this lecture today mainly to show my support."
"As someone in surface physics, there’s not much I can usually understand in a specialized math seminar."
He paused.
"But after your lecture today, something suddenly occurred to me."
"In my work on surface physics, there’s a long-standing issue with an energy-level splitting that I could never account for."
"I had always been trying to solve it from the perspective of crystal symmetry."
"But when I was sitting out there and heard you say ’change the number system,’ I had a sudden thought."
"Maybe that problem isn’t meant to be solved from the angle of symmetry at all."
"Maybe it needs to be viewed from within a ’number system’ I’ve never used before."
He looked up at Li Dong.
"So, I have to thank you. Your lecture gave me this insight."
Li Dong quickly waved his hands in dismissal.
"You’re too kind, Teacher Wu."
"It was just a small lecture."
Wu Jianguo smiled.
"For you, this may have been a ’small lecture.’"
"But for those of us sitting in the audience, it might have been something more."
Shen Wei nodded.
"I suspect word of this will reach Shuimu in a few days."
He gave Li Dong a peculiar look.
"Mr. Qiu over there is probably going to be calling you again."
"I heard he asked you to lecture at Shuimu, but you haven’t gone yet. Instead, you came to our Fudan University first."
Li Dong: ...

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