My Study Chat Group is Full of Real Big Shots

Chapter 237: Chapter 228: Göttingen Private Discussion Notes

Just as Li Dong closed his laptop, planning to rest for a bit before getting back to his paper, Wang Hao suddenly asked a question.

”Brother Dong, you finished the paper?”

”Not yet. I’m planning to review it again.”

”...Still for the *Mathematical Annals*?”

”That’s the plan.”

Wang Hao nodded.

After a moment, he asked again, as if offhandedly.

”It’ll be fine this time too, right?”

Li Dong suddenly turned his head to look at Wang Hao.

Wang Hao shifted uncomfortably under his gaze.

”I don’t mean anything by it, Brother Dong. Just... just asking.”

Li Dong just grunted and didn’t respond immediately.

He turned back to his screen. As he stared at the paper, his gaze gradually unfocused.

Before their meal, Liu Ruochuan had reminded him that for a paper of this caliber, the peer review process would be tough.

He hadn’t paid it much mind at the time.

But now Wang Hao had brought it up again.

A jolt went through him, and he suddenly felt tense.

’What makes me so sure of myself now?’

He’d never doubted his previous work, from the dimensionality reduction algorithm to his advancement on Montgomery’s Conjecture on Association. The reason for his confidence was simple: every time he finished, he was rewarded with a red packet from the group.

Receiving a red packet was essentially a seal of approval from the titans in the group, which was why he was always so sure his papers were flawless.

’But this paper is different.’

For this one, Riemann had only given him a small hint at the start, and had been pretty much offline ever since.

The entire paper, from start to finish, had been the work of just three people: himself, Penrose, and Old Yang.

And it hadn’t received the red packet seal of approval from the Cyan Dragon Study Group.

’Damn it, he actually got me worried.’

He then opened the Cyan Dragon Study Group.

The file transfer counter was still at zero.

’I can’t use that function.’

His only option was to try dragging the paper’s PDF into the dialogue box and sending it.

And it didn’t fail to send.

He had developed the paper’s main framework, chosen its core tools, and derived the proof’s entire outline step-by-step on the seminar room whiteboard.

Penrose and Old Yang had made significant contributions, but many of the crucial creative leaps and key choices of tools had come from him.

In other words, he understood this work inside and out.

He could even glimpse the grand theoretical edifice that might one day be built upon the foundation of this paper.

Under these circumstances, it made sense that the file could be sent.

Li Dong immediately tagged Riemann.

[AcademicInProgress]: @Your Excellency Bernhard Riemann, that thing my nephew and his friends were tinkering with... I helped them work through some of it.

Then he stared at the group chat, not daring to blink.

Ten seconds.

Thirty seconds.

One minute.

There was no reply at all.

”...That Riemann,” Li Dong muttered.

”He’s so elusive. I practically threw the file in his face, and he’s still ignoring me.”

It wasn’t that he actually wanted to keep getting handouts from Riemann.

He just wanted the confirmation that came with a red packet.

But Riemann just wouldn’t bite.

Just as he was starting to fidget anxiously,

Someone spoke up in the group.

[Felix Klein]: AcademicInProgress.

Li Dong froze...

’How did I flush him out?’

Felix Klein.

One of the most important mathematicians from the late 19th to the early 20th century.

He was appointed to a professorship at the University of Erlangen-Nuremberg at the age of 23.

That was the same year he wrote his *Erlangen Program*, a work that no modern textbook on mathematical history can afford to ignore.

It used the concept of transformation groups to unify the various branches of geometry, which at the time were a complete mess.

From that day forward, geometry was no longer a collection of disconnected islands; he had integrated it into a single, vast continent.

He was also the one who conceived of the famous Klein Bottle in 1882.

Of course, he was also Einstein’s academic ancestor—a total badass.

He was definitely one of the top-tier titans in the group.

[Felix Klein]: Why... do I feel as though my own blood runs through this work?

[Felix Klein]: What exactly is it?

Huh?

Li Dong paused for a second, then it hit him.

The Langlands Program grew from the old tree of the Erlangen Program.

The core of the Erlangen Program could be summarized in a single sentence: Geometry is the study of the invariants of a space under the action of a transformation group.

And at its core, the Langlands Program was doing the very same thing.

It connects objects from number theory (representations of the absolute Galois group) with objects from analysis (automorphic forms) via the representation theory of groups.

Li Dong blinked.

He first opened the group’s member list and scanned it.

Just as Li Dong expected, Langlands was not in the group.

In that case, Li Dong couldn’t be blamed for inventing a friend out of thin air.

[AcademicInProgress]: You are not mistaken, Sir Klein.

[AcademicInProgress]: This is a path a friend of mine is pursuing. We are currently calling it the ”Langlands Program.”

[AcademicInProgress]: Before this, all thought on ”geometry as the invariants under group action” had reached the limits of commutativity and progressed no further.

[AcademicInProgress]: But now, what some of my associates and I have been pondering is how to take that map you drew back then and redraw it on non-commutative coordinate paper.

[AcademicInProgress]: So the reason you feel your blood in it is because its very backbone was borrowed from your work in Erlangen.

Li Dong didn’t try to take sole credit for Langlands’s work, but he did insert himself as a driving force. After all, what if there was a red packet in it for him?

After he sent the messages,

The group fell silent for over ten seconds.

Then...

[Felix Klein]: I see. So that is how it is.

[Felix Klein]: Sir, would it be possible for you to explain this Langlands Program to me in detail?

[Felix Klein]: From the ideas you just conveyed, I can sense that this is but a single branch. Behind it lies an entire, unseen mountain.

[Felix Klein]: I wish to see that mountain.

Li Dong was dumbfounded.

’I haven’t fully grasped the entire program!’

’I can’t send it through the group chat.’

’And my file transfer count is zero.’

So he could only bite the bullet and reply.

[AcademicInProgress]: Sir Klein, my sincerest apologies. There are still several core structures within this program that my friend and I have yet to fully organize.

[AcademicInProgress]: Once I’ve sorted them out, I will inform you at the first possible opportunity.

[Felix Klein]: Thank you.

Then the group went quiet.

Li Dong sat numbly in front of his computer, watching as a potentially massive red packet reward floated away right before his eyes.

”Sigh...”

Just as he sighed in disappointment,

A red packet suddenly appeared.

[Klein has sent you an exclusive red packet.]

”Huh?”

Li Dong’s face immediately broke into a wide grin.

’Hehehe, what a generous titan.’

Li Dong immediately clicked open the red packet.

[You have received Klein’s gift.]

[Obtained: *Symmetry and Natural Law—Göttingen Private Discussion Notes* (Original Lost Version)]

[Description: The original records of the closed-door discussions held by the core Göttingen trio (Klein, Noether, and Weyl) from 1915–1925. Later textbooks inherited only its conclusions, discarding its soul. This is a legacy of global symmetry from an invariant-first perspective, one that was completely lost in the second half of the twentieth century.]

[These notes will be integrated into your Memory Palace from the ”original perspective” rather than as a ”retelling of conclusions.”]