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Chapter 156: Chapter 154: Your Way of Thinking Is a Bit Like Those 19th-Century Masters

After parting ways with Li Yang, Li Dong walked back toward the East Suburb Hotel alone.

The January wind in Shanghai felt cold and biting against his face.

He took out his phone and dialed Liu Ruochuan’s number.

BEEP BEEP BEEP.

Still a busy signal.

”What is Old Liu up to?”

Li Dong muttered to himself, put his phone away, and continued on his way.

He soon arrived back at the hotel, swiped his card to access the executive suite area’s elevator, and went upstairs.

As Li Dong reached his room, he found someone standing in front of his door.

The person seemed to have just knocked. Realizing no one was inside, they were about to turn and leave.

The man was of average height and wore a pair of glasses.

Upon seeing Li Dong, the man’s expression first showed a flash of surprise, which was quickly followed by a gentle smile.

Li Dong took a look.

”Tao Zhexuan?”

The Fields Medalist, a mathematics professor at the University of California, Los Angeles, and a recognized genius among geniuses in the international analytic number theory community.

Winning the Fields Medal at 31 was a record that stood out even in the annals of history.

After all, the average age of a Fields Medal recipient is between 36 and 40. To have claimed the crown jewel of the mathematics world at 31—he was more than deserving of the title ”prodigy.”

”Mr. Li Dong!”

Tao Zhexuan took the initiative to walk over, greeting him with a smile.

”Perfect timing. I just knocked on your door. I thought you had gone out.”

”Professor Tao.” Li Dong also gave a slight nod.

”Did you need me for something?”

Tao Zhexuan’s tone was very casual.

”Yes, it’s about your paper.”

’My paper?’

Li Dong’s mind worked quickly, and he immediately guessed what this was about.

He didn’t ask any more questions, simply taking out his keycard and swiping the door open.

”Professor Tao, please come in. We can talk inside.”

The two of them entered the suite.

Li Dong poured a cup of hot water for Tao Zhexuan and sat down on the sofa across from him.

Tao Zhexuan accepted the cup and didn’t beat around the bush.

”You said during your presentation at the conference that you wanted the editors of the *Mathematical Annals* to reject your paper.”

He smiled.

”I’m afraid I’ll have to disappoint you.”

”I was assigned to review your manuscript.”

’Just as I thought...’

Tao Zhexuan was a long-term peer-review expert for the *Mathematical Annals*. In the field of analytic number theory, he was practically one of the *Annals*’ most trusted reviewers.

At this point, Tao Zhexuan lifted his cup and sighed softly.

”Everyone out there calls me a math prodigy.”

His tone was light.

”After reading your paper... I feel that you are the true prodigy.”

His words were sincere, and their meaning was obvious.

He believed Li Dong had the ability to stand on that awards stage at an even younger age than he had.

Hearing this, Li Dong quickly waved his hands in dismissal.

”Ah, you’re too kind, Professor Tao. You flatter me.”

Tao Zhexuan didn’t dwell on the pleasantries and cut straight to the chase.

”The reason I came to see you today is that there are a few things in your paper that I’m not entirely clear on.”

”I wanted to ask you about them in person.”

After all, Li Dong had already publicly admitted at the ICCM that he had submitted the paper, so discussing it now wasn’t a violation of protocol.

”Is now a good time for you?”

Tao Zhexuan’s tone was very respectful.

”If it’s not convenient, we can just follow the formal peer-review process, and I can list my questions in the reviewer comments.”

Li Dong had an unconcerned look on his face.

”It’s no problem at all. Please, go ahead and ask.”

Seeing this, Tao Zhexuan dropped the formalities. He pulled a stack of printed-out paper from his briefcase and flipped to a specific page.

”In step two, your proof for the interval |α|∈[1, 2], after separating the main term using the Riemann explicit formula, you perform a truncation on the summation of the contribution of prime numbers.”

Tao Zhexuan pointed to a formula on the paper.

”You cited the prime number theorem, Σ_{p≤X} log p ~ X, as the basis for the main term estimate. The problem is, when you perform the integral transform on x=T^α, you chose the truncation point at T instead of T^(1+ε).”

”Generally, when dealing with the mean value estimate of this type of Dirichlet polynomial, the choice of truncation point directly affects the order of the remainder term.”

”By choosing T as the truncation point, the bound on your remainder term seems to be tighter than if you had chosen T^(1+ε).”

”But I can’t see how you managed to do that without introducing additional error.”

Li Dong listened and nodded.

He took the hotel’s notepad and pen from the coffee table and casually wrote a few lines of formulas.

”Professor Tao, the key here isn’t actually the truncation point itself.”

”The method I used was to first convert the discrete sum over primes in the explicit formula into a continuous path integral passing through a saddle point, using contour integration.”

”On this integration path, the contribution from primes within the T^α range is naturally absorbed by the exponential decay factor near the saddle point. Therefore, I don’t need to manually set a truncation point.”

”The truncation is adaptive. The geometric structure of the integration path itself performs the truncation.”

Tao Zhexuan looked at the integration path Li Dong had drawn on the notepad, and his eyes lit up slightly.

”Adaptive truncation via contour integration...”

He chewed on this idea, falling into a brief, deep thought.

From the mainstream perspective of modern analytic number theory, this was a technique almost no one would use.

This was because contemporary mathematicians, when dealing with such problems, had grown accustomed to relying on computer-aided verification and large-scale numerical simulations to determine the optimal truncation parameters, and only then would they work backward to deduce the theoretical bounds.

But Li Dong had done the complete opposite.

He didn’t rely on any numerical trial-and-error. Instead, he started directly from the geometric-topological structure of the complex plane, allowing the mathematics itself to choose the optimal path.

This way of thinking was so... classical.