184: Chapter 184 Question

Chen Youhua remained standing in the center of the podium, waiting for the applause to subside. Next was the Q&A session. He spoke up.

"Next, we will move on to the Q&A session of this presentation."

"I will prioritize questions from the scholars present here, interspersed with a few pre-selected remote video questions from international colleagues."

"I ask that questioners please be concise and clear."

As soon as he finished speaking, arms shot up from the audience like bamboo shoots after rain.

Everywhere he looked, there were wise and sharp eyes, many of them familiar faces often seen in textbooks and top-tier journals.

The first person to get a chance to ask a question was a white-haired old European professor from the University of Cambridge, known for his extremely high standards regarding the rigor of partial differential equations.

He took the microphone, his voice slow yet powerful.

"Professor Chen, thank you for your amazing report. Your adaptive frequency projection operator framework is very ingenious, but I have a question regarding your core estimate 3.15."

He cited the number precisely, showing he had been following closely the entire time.

"When dealing with the coupling of high-frequency parts and low-frequency nonlinear terms, the damping coefficient γ(λ) you introduced relies heavily on an upper bound of the initial energy norm."

"How do you ensure that throughout the entire time evolution process, this upper bound remains uniformly controllable and does not grow exponentially over time, which would eventually invalidate your estimate?"

The question was extremely professional, pointing directly at a very technical key point in the proof.

The venue fell silent instantly; everyone who understood the subject held their breath.

This was a very sharp and incisive question.

Chen Youhua did not hesitate for a moment, as if he had already anticipated such a question.

He nodded slightly and calmly picked up the electronic pen, beginning to write on the blank space of the presentation screen.

"Thank you for your question; it's a very good one."

As he spoke, he fluently wrote down a string of complex symbols.

"The dependency you mentioned does indeed exist. However, the key point is that this upper bound does not come from external assumptions but originates from the information carried by the equation itself at the initial moment. Look, we can show through a proof by contradiction and an iterative compactness argument that..."

His explanation was clear and logical, leading the old professor step-by-step toward a deeper, self-consistent mechanism hidden within the fabric of the proof.

He didn't directly answer how to ensure it; instead, he demonstrated how this coefficient was ingeniously woven into the very fibers of the entire proof, making it automatically satisfy the required conditions.

Five minutes later, the old professor's furrowed brow relaxed. He slowly nodded, even showing a hint of an appreciative smile, and said simply.

"A brilliant construction, I understand now. Thank you."

Then he sat down.

A slight, relaxed sigh rippled through the venue, followed by a round of admiring applause.

The first challenge had been perfectly resolved.

Next was a young professor from the Institute for Advanced Study in Princeton via video link. His question focused on the potential connection between the proof and computer-aided verification, to which Chen Youhua gave an equally clear and affirmative response.

The third questioner was from the audience, a serious-looking Japanese mathematician whose English had an accent and who spoke very quickly.

"Professor Chen, you claim your proof is complete."

"But in your treatment of the Hausdorff dimension estimate for the singular set, you cited a lemma regarding geometric measure theory from your previous preprint."

"And that preprint has not yet undergone peer review. Does this mean the integrity of your entire proof depends on a result that has not been rigorously verified?"

This question was more aggressive, even carrying a hint of doubt.

A small commotion broke out in the audience.

Chen Youhua's expression remained as calm as water.

"The lemma you are referring to is one whose proof I reported in detail at the MIT Geometric Analysis Seminar last month; the relevant videos and notes are publicly available."

"To date, I have not received any substantive challenges regarding the proof process of that lemma."

"Of course, I welcome any peer review of it."

"However, logically, even if we set aside the review of that lemma for now, the main part of this paper—establishing global estimates—remains independent and complete."

"That lemma is only used to strengthen the final step of excluding singularities; it's the icing on the cake, not the cake itself."

"Even without it, we can still obtain the global smoothness of the solution through the main theorem of this paper."

His answer was neither humble nor arrogant, defending the integrity of his work while showing confidence in its foundations, and cleverly explaining that even in the worst-case scenario, the core of his work would still hold.

The Japanese scholar was silent for a moment, then nodded and didn't press further.

The Q&A session proceeded in a tense yet orderly fashion.

Questions flew in from all angles, some focusing on the rigor of mathematical details, some exploring potential links with other branches of mathematics, and some inquiring about the prospects for numerical applications.

Chen Youhua always responded calmly, his mind agile, addressing every question with precision and depth.

His eidetic memory was on full display at this moment, allowing him to recall any subtle step in the proof at any time and even cite papers from related fields from years ago to support his points.

He was like a peerless swordsman on the battlefield of academia, calmly parrying, dodging, and then accurately counterattacking, resolving all doubts one by one.

...

While Chen Youhua was dealing with the onslaught of the world's top scholars on-site, the online world was a different scene altogether.

For the vast majority of non-professional netizens, the mathematical clash on-site was like reading a book from heaven.

The style of the live stream comments gradually shifted.

"Here it comes! The big shots are starting to pick holes!"

"Even though I don't understand it, it feels so exciting! It's like watching masters fight!"

"God Chen's reaction speed is insane! It's like he knows what they're going to ask before they've even finished!"

"Requesting a class representative! Requesting a translation! What on earth are they talking about? I'm dying to know!"

"It feels like God Chen isn't just answering questions, but giving us a private tutoring session..."

Keen media outlets and science popularization platforms had long anticipated this situation.

Several large live-streaming platforms quickly switched modes, opening expert-led or simultaneous interpretation channels.

In the official Bilibili live room, the most popular science popularization uploader, 'Teacher Li Who Loves Science,' was invited again to provide a joint commentary with a specially invited domestic mathematics professor.

"Hello everyone! The one asking a question now is Sir James from Cambridge, an authority on fluid mathematics! This estimate he's asking about... wow, it's quite sharp!"

Teacher Li spoke rapidly, filled with excitement.

The mathematics professor beside him was relatively steady.

"Yes, this question is very deep, pointing straight at the core stability of Professor Chen's proof method."

"To put it simply, he's worried that the new mathematical method Professor Chen is using hasn't been tested by others, and whether this mathematical tool lacks universality—if it's just a formula Chen Youhua dreamed up himself."

"So how did Professor Chen answer?" Teacher Li asked at the right moment.

"Brilliant!" The professor couldn't help but exclaim in admiration.

"Professor Chen didn't answer his question directly. Instead, he broke down this mathematical tool and gave him a detailed explanation. I truly admire Professor Chen's magnanimity; that mathematician probably asked with that kind of mindset too."

"Professor Chen didn't hold back any details of his thought process at all. Instead, he taught everyone the detailed usage, universality, and various application scenarios of this mathematical tool. This might be the most valuable part of today's presentation."