Awakening Elementary School System in University

Anyone with even a passing familiarity with contemporary academic mathematics knew one thing: ever since earning his doctorate, nearly all of Peter Schultz’s stunningly brilliant achievements were concentrated in a single field: arithmetic geometry.

It was an extremely abstruse field, a true test of a mathematician’s genius, primarily applying the tools and ideas of algebraic geometry to problems in number theory.

The profound and abstract nature of its theories was daunting to countless mathematicians, and its connection to other mainstream branches of mathematics was relatively limited.

And that was precisely why the manuscript on Differential Geometry that Schultz now produced was so exceptionally precious!

This was almost certainly a brand-new research result he had just achieved in the short time since reading Chen Lin’s paper!

At this thought, Annie’s heart couldn’t help but pound with excitement.

Mathematicians like Schultz, and the slightly older Terence Tao—those widely recognized as "super geniuses"—typically focused their energy on only a few core research areas. However, their terrifying mathematical talent was enough to let them thrive in almost any field of mathematics.

As long as they were willing to invest the time, their rate of progress in a new field was far beyond what an ordinary mathematician could hope to achieve.

’This is a golden opportunity!’

’A chance to witness firsthand what kind of astonishing flash of inspiration Schultz would produce in Differential Geometry, a field relatively unfamiliar to him!’

Annie was secretly delighted, feeling like she had hit the jackpot today.

Time ticked by. About five minutes later, under the breathless gaze of the two women beside him, Chen Lin slowly turned the manuscript from the second page to the third.

His mind, however, was far from the calm his expression suggested.

He was secretly stunned.

’Peter Schultz... He really is worthy of his reputation. No wonder some peers privately hail him as the man with a chance to become the next Mathematics Emperor after Grothendieck!’

According to the information Chen Lin had looked up before, this titan’s usual research focus couldn’t have been more unrelated to Differential Geometry.

And yet, the discussion of Differential Geometry presented in this manuscript contained not a single discernible error!

But that wasn’t what surprised Chen Lin the most.

What truly shocked him was the core idea Schultz proposed in the manuscript!

At the end of his own JAMS paper, Chen Lin had merely used rigorous mathematical proofs and calculations to demonstrate the existence of a new algorithm that could significantly reduce the hallucination rate of generative models.

But as for how to actually *find* this algorithm, he had only offered a vague general direction at the time.

Because at that point, even he hadn’t yet reached that stage in his research.

Only in the last two weeks, by dedicating three hours to intensive research every evening, had he finally worked out most of the details.

And this was precisely the core content he was preparing to share in his presentation the day after tomorrow.

Yet, here in this manuscript, Schultz had *also* proposed a concrete path to finding that algorithm!

Moreover, it was a path completely different from the one Chen Lin himself had discovered!

Schultz had ingeniously combined the modes of thinking and mathematical tools from his own most familiar field, arithmetic geometry, to construct an entirely new proof framework.

With the aid of [Little Mathematician], Chen Lin could tell at a glance that the method Schultz proposed, though still written in a very abbreviated form in the manuscript, was built on a core logic that was completely viable!

It was just that, compared to the "optimal solution" path that Chen Lin himself had devised with his [Little Mathematician] title, the route Schultz proposed was more circuitous and complex.

But it was still absolutely incredible!

A deep sense of admiration and heartfelt respect welled up in Chen Lin.

’Is this the true ceiling of human intellect?’

Time ticked by, second by second.

To make his performance appear within the bounds of a normal human genius, Chen Lin forced himself to be patient, staring at the few pages of the manuscript and deliberately dawdling for a full five minutes before turning to the last page.

After finishing, he didn’t speak immediately. Instead, putting on an Oscar-worthy performance, he furrowed his brow slightly and tapped his fingers on the armrest of the sofa, feigning deep thought and digestion of the material.

After another two minutes or so, judging that the time was right, he relaxed his brow and looked up at Schultz opposite him.

"Professor Schulz, I believe I understand your overall line of thought."

Chen Lin straightened the manuscript and said sincerely, "It’s incredibly insightful! Especially your approach to handling the Manifold boundaries by introducing tools from arithmetic geometry—that perspective is truly unique.

"However, for some of the specific details involved, I’ll probably need to take this back with me and spend some time mulling them over carefully."

"Wonderful!" A brilliant smile spread across Schultz’s face. "If it was helpful to you, then nothing could be better."

For him, providing valuable inspiration to a colleague was, in itself, a reason to be happy.

"Ah, speaking of which."

As he spoke, Chen Lin unzipped the black backpack he was carrying. "Regarding the questions you mentioned in the email you sent me last time, I recently found some time to pick one of them and do a little research."

Under Annie’s slightly surprised gaze, Chen Lin took a manila folder from his bag, pulled out three densely-written A4 draft sheets, and handed them to Schultz.

"These are some preliminary ideas I put together over about a week. They’re still quite rough, but you can take a look."

In reality, Chen Lin had only spent two evenings—a total of six hours—on it, but to avoid sounding too outrageous, he stated it more conservatively.

Hearing this, Schultz’s eyes instantly lit up.

He clearly hadn’t expected Chen Lin to be so efficient. He quickly sat up straight and took the three draft sheets with both hands, a gesture of respect.

His eyes quickly scanned the title at the top of the first page and the first few lines of definitions, and he couldn’t help but let out a gasp of amazement.

"The geometrization of the local Langlands Program for the FF Curve?"

Schultz jerked his head up, his blue eyes filled with incredible surprise and delight. "Mr. Chen Lin, you chose *this* problem? This is one of the points I currently find extremely thorny! I must take a good look at this!"

With that, he lowered his head, immersing his full attention in the draft papers in his hands.

Sitting beside them, Shen Yan didn’t have much of a reaction to the scene unfolding.

Chen Lin had mentioned to her before coming to the Imperial Capital that he was recently researching the problems from Schultz’s email.

Stemming from an almost blind faith in Chen Lin’s mathematical abilities, she felt that if he said he’d figured something out, there was no reason to be shocked.

Or rather, it would be strange if Chen Lin *couldn’t* figure something out. After all, ever since Shen Yan had known him, there had never been a math problem he couldn’t solve.