Li Dong’s words made Zhou Qifeng recall what happened after he sent the PDF to Gao Yuanlin that day.
Gao Yuanlin had called him back that same evening.
"Old Zhou."
"I want you to go talk to Li Dong."
"These three lines of reasoning of his... it seems they’re not just for solving this one problem."
"He’s secretly building bridges to somewhere else."
"Go and probe a little. See where he’s building them."
"Probe if you can. If you hit a wall, come back and tell me."
"I’ll go myself."
Why didn’t Gao Yuanlin just go himself?
It was simple.
He had a bad temper.
If the conversation went south, it would be difficult to salvage.
He was sending Zhou Qifeng in first to test the waters.
If the talk went well, everyone would be happy.
If it didn’t, he would step in personally.
So, Zhou Qifeng had blurted out the question unconsciously.
"Are you... building bridges to other places?"
Of course, Li Dong didn’t know about all the maneuvering behind the scenes.
He just thought it was terrifyingly perceptive of Professor Zhou to see right through him!
So he reined in his arrogance and said humbly.
"Teacher Zhou, you could tell?"
"That’s amazing."
Zhou Qifeng: ...
’Like hell I could tell.’
’I’m just the errand boy.’
’It was Dean Gao who figured it out.’
But he still put on an inscrutable smile.
"Mm."
"I noticed a few things."
"Go on."
Li Dong nodded.
Since he’d been found out, there was no point in hiding anything.
Li Dong placed the stack of PDFs in front of him and flipped to the page with the third line of reasoning.
"Teacher Zhou, look here."
"In my third line of reasoning, I didn’t actually do anything new."
"Fujikawa already told us back in 1979 that the origin of the chiral anomaly isn’t in the dynamics."
"I just followed Fujikawa’s path and pushed it one small step further."
Zhou Qifeng nodded.
He had read this part and understood it.
And when he read it, he’d thought, ’That’s a pretty neat move.’
Li Dong continued.
"While reviewing this Jacobi determinant, I had a vague feeling that..."
"Its structure wasn’t just describing ’how a Fermi field undergoes a chiral transformation in a gauge background.’"
"It’s describing something more universal."
"It’s about how a discrete, combinatorial object leaves a topological imprint on a continuous, geometric base. An imprint that can be captured by analytical tools."
"The chiral anomaly is just a special case of this."
"Mm... a very beautiful special case."
Zhou Qifeng’s eyebrows twitched slightly.
’Just a special case.’
’Does this kid even know the weight of those words?’
The chiral anomaly—from when Adler and his group first wrote about it in 1969, to when Fujikawa used path integral measures to unearth its geometric roots in 1979, and then to 1984 when the Atiyah-Singer group completely welded it to the index theorem.
It took a full fifteen years to explain the whole thing clearly.
And now, a nineteen-year-old freshman was casually telling him: it’s just a special case.
The two words "special case" implied there was something even grander, a layer above it.
’And you’ve seen that layer?’
But Zhou Qifeng didn’t let any of this show on his face.
He simply gestured for Li Dong to continue.
Li Dong, completely unaware of how audacious he sounded, continued.
"This made me think of a field that’s been quite active in recent years: geometric deep learning, and the application of message passing neural networks in Quantum Chemistry."
"Gilmer’s group had a really nice paper in ’17, and Bronstein wrote a long review last year."
"What they’re doing, in essence, is constructing a differentiable, symmetry-preserving map between discrete molecular graph structures and continuous physical fields, all while satisfying constraints like rotational, translational, and permutational symmetries."
"This approach has already produced some very useful tools."
"They can predict physical quantities like a molecule’s energy, force, and dipole moment, and they’re several orders of magnitude faster than traditional density functional theory."
Zhou Qifeng nodded slowly.
He’d heard of Gilmer’s paper and had skimmed through Bronstein’s review.
He was aware of this field.
But he still didn’t understand why Li Dong had suddenly jumped from the "topological imprint of the discrete on the continuous" to this topic.
On the surface, the two seemed completely unrelated.
As if reading his mind, Li Dong continued to explain.
"But all these methods currently share a common problem..."
"They’re all empirical."
"They use neural networks to approximate that map. Whether the approximation is good or not depends on the amount of data, the architectural design, and the training techniques."
"There’s no rigorous mathematical foundation to tell you why the map should have this particular form, what its error bound is, or when it will fail."
"I think the structure hidden behind the chiral anomaly might be the first brick for this foundation."
"Because the Jacobi determinant in the chiral anomaly has already shown us that a strict mathematical correspondence between a discrete topological quantity and a continuous geometric field does exist."
"And it can be captured by a very clean set of analytical tools."
"If this toolkit could be taken out of Quantum Field Theory and generalized to the molecular context..."
"Then this entire path of geometric deep learning could transform from approximation to deduction."
"From an engineering problem into a mathematical one."
Zhou Qifeng’s hand, holding his teacup, tightened.
From approximation to deduction.
From an engineering problem into a mathematical one.
’This kid has some serious nerve.’
’Across the entire academic world, you could count on one hand the number of people who could say that in a conference presentation without being laughed out of the room.’
’And every single one of them is an old monster at the level of an academician.’
Li Dong, seemingly oblivious to his expression, pushed his point one step further.
"And it’s not just about molecules."
"The correspondence between discrete lattices and continuous elementary excitations in condensed matter physics, the correspondence between discrete defect structures and continuous elastic fields in materials science, and even going a step further, the chasm between lattice field theory and continuous field theory..."
"Fundamentally, they’re all the same thing."
"They’re all a Dialogue between discrete topology and continuous analysis."
"The chiral anomaly is just the first sentence in this Dialogue that humanity managed to hear clearly."
"There are many more sentences after it that we haven’t heard yet."
At this, Li Dong smiled again, as if afraid Teacher Zhou would misunderstand him.
"Of course, this is all just speculation on my part."
"I haven’t completely figured out how to build this bridge myself, to be honest."
"I need to build a solid foundation in chemistry and biology first. Otherwise, even if I have some great ideas, I won’t be able to put them into practice."
"That’s why I said that after I finish my current math project, I need to go and catch up on those two subjects."
"After that, coming back to mathematical physics should be much smoother."
"Because by then, I won’t just have two legs to stand on—math and physics."
"I’ll have chemistry and biology too."
"Walking on four legs is bound to be more stable than walking on two."
Li Dong felt he was absolutely right.
Beasts of burden are tougher than humans, after all.
The seminar room fell silent for about ten seconds.
After he finished speaking, Li Dong picked up the glass of water on the table and took a sip.
Zhou Qifeng sat motionless.
He stared down at the third page of the PDF on the table, his expression complex, even a little dazed...
Professor Penrose, who had been waiting patiently on the side, now also sensed that the atmosphere was a bit off.
He tilted his head, looking at the two Chinese men speaking in their native tongue with an innocent expression.
"Dong?"
"Are you... discussing something very important?"
Li Dong turned his head and smiled at Penrose.
"Nothing major, Professor."
"Teacher Zhou was asking me what field I want to pursue in the future."
The old Professor Penrose said, "Oh."
He didn’t ask any more questions.
But Zhou Qifeng’s mind was in turmoil.
’Dean Gao.’
’The situation is far more serious than you thought.’
’This kid isn’t just planning to "switch" to mathematical physics.’
’I have no fucking idea where he’s planning to switch to!’

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