As the vice dean of the School of Mathematics at the Xia Academy of Sciences, Zhang Ping was unquestionably an authority among authorities in the field of nonlinear partial differential equations within the country.
He had achieved remarkable success, particularly with the Navier-Stokes equations.
For example, regarding the well-posedness of the three-dimensional incompressible Navier-Stokes equations, he had introduced a novel class of negative-index B-S type function spaces and proven that when two components of the initial velocity in the three-dimensional anisotropic Navier-Stokes equations were sufficiently small, a unique global solution existed.
With numerous comparable achievements to his name, it was no exaggeration to call him the foremost scholar of the Navier-Stokes equations in the domestic mathematical community.
Yet precisely because of this, he understood better than anyone how far he remained from completely resolving the Navier-Stokes problem. It was an insurmountable chasm!
A chasm that no mortal could cross!
In his eyes, even if ten thousand brilliant mathematicians joined forces, they would still fail to crack this problem—unless Gauss were reincarnated...
Well, in truth, he was not even certain whether Gauss could solve the Navier-Stokes equations, but judged purely on mathematical talent, Gauss stood the highest chance.
In academia, a single morning's work by a genius could eclipse the lifelong research of countless mediocre scholars.
It was a sad reality, and he considered himself one of those mediocre scholars. At best, he was slightly more diligent and fortunate, allowing him to produce a few modest results.
"If this young man truly proved the Navier-Stokes equations..."
He suppressed the turbulent thoughts swirling in his mind. With one hand scrolling the mouse and the other holding a pen, he scribbled derivations across blank paper.
While he buried himself in the proof, scattered discussions about Huang Tian's new paper finally began to surface in the outside world.
At first, it was only a handful of scholars in the field of nonlinear partial differential equations reading and discussing it. Soon, however, the buzz spread across the broader communities of mathematics and physics. Eventually, independent media outlets caught wind of it and reposted the news online.
"Shocking! Huang Tian Claims to Have Solved Millennium Prize Problem, Could Win Million-Dollar Bounty!"
"Tackling the Problem of the Century: The Confidence of a Genius or the Hubris of Youth?"
"Brand-New Breakthrough by the Handsomest Mathematician in History!"
"Huang Tian Answers Century-Old Problem: Genuine Substance or Clout-Chasing?"
"Stunning! Huang Tian Publishes New Paper, One Step Away from a Million-Dollar Prize!"
"..."
Praise, skepticism, and wait-and-see neutrality all clashed as a swarm of media outlets jumped in to capitalize on the trending topic. Spurred on by their coverage, online debate grew even more intense. This was only natural; Huang Tian's previous wave of virality had only just subsided, and many still remembered him.
Seeing his name again naturally drew curious clicks, and the combination of a Millennium Prize Problem and a million-dollar reward was more than enough to capture the public eye.
"A million dollars! If that were me, I'd quit my job on the spot and go lie flat in my hometown!"
"It's way too early to talk about a million bucks. Nothing is set in stone yet. Over the decades, haven't tons of people claimed major breakthroughs? Just look at room-temperature superconductivity—it blows up every two years, only to be debunked shortly after."
"My advisor said that unless Gauss or Euler came back to life, solving the Navier-Stokes problem would still take decades or a century. In other words, practically nobody will prove it in this century."
"With such a massive fuss, if it ends up being a farce..."
"Farce or not, shouldn't daring to tackle such a daunting challenge be encouraged? Even if it turns out to be wrong in the end, can't people show a little tolerance?"
"..."
While the internet boiled with heated arguments, Huang Tian stayed comfortably in his hometown, accompanying his parents to visit relatives and sweeping the graves of deceased elders, entirely undisturbed by the outside world.
Yet just because he remained unaffected did not mean others did. Feng Zechun gave him a call.
"Professor Feng?"
"It's me." Feng Zechun chuckled warmly at first, before his tone turned somewhat somber. "Huang Tian, your paper has caused quite a stir online. Has it caused you any trouble over there?"
Huang Tian smiled. "I'm out in the countryside. How could it affect me?"
"That's good to hear." Feng Zechun breathed a faint sigh of relief. "Just keep your mind at ease and don't overthink it. There's no need to pay attention to those comments online. They're just following the crowd and chiming in for the spectacle."
"My mindset is fine."
"Haha, hearing you say that puts my mind at ease!"
Feng Zechun laughed heartily. After a few more casual remarks, he hung up.
Shortly afterward, Xu Kaizhi, dean of Changda's School of Mathematics, and Vice President Yang Dong also called, offering their words of comfort.
Later, Zong Wenjun initiated a video call. Rather than bringing up the online debates, she simply shared amusing anecdotes from the New Year holiday and grumbled about school starting before the Lantern Festival. After chatting for a while, she ended the call.
Setting his phone aside, Huang Tian returned to his cultivation and studies with single-minded focus, occasionally extending his awareness to check for any golden voice lines from the other world.
Time slipped quietly by until the Lantern Festival arrived.
By this point, many villagers had already left for work in the cities, leaving the village noticeably quieter. Fortunately, the festive cheer of the Lantern Festival softened the chill, and smiles still brightened everyone's face.
Inside the Huang household, as they ate tangyuan, Huang Yusheng glanced at Huang Tian and hesitated. "Xiao Tian... I've been seeing things online these past few days saying you came up with some major research, and lots of people are talking about it...
"Well, whatever, I don't understand that stuff anyway. I just wanted to ask—what are your plans next? Are you going to look for a job, or keep studying at a university?"
"No rush," Huang Tian said, shaking his head. "Let's wait a little longer until academia reaches a consensus on my paper before deciding on future plans."
"Alright, you do whatever you think is best. If you need money for anything, just tell us. If you want to buy a car or an apartment, your mother and I can scrape some together. We can't promise much, but two or three hundred thousand yuan is doable."
Huang Yusheng knew nothing about academia and had little grasp of his son's current achievements, so he refrained from interfering in his decisions. Instead, he worried about securing an apartment for him.
In his mind, a scholar could hardly live in the countryside long-term. He would need a home in a big city—somewhere near Changda, for instance. But that would require a substantial sum of money.
Huang Tian could not help but laugh. "Don't worry about cars or apartments. In a little while, everything will fall into place..."
Huang Yusheng and Yang Guihua had an inkling of what he meant. Over the past few days, through popular science explainers posted by various bloggers, they had gained a rough idea of how monumental their son's paper was.
If the proof held without flaws, Huang Tian would ascend to the pinnacle of academia in an instant, looking down upon countless scholars from the heights of mathematics.
At that level, things like money, apartments, and cars lost their significance.
Even so, having watched those explanations, they also understood just how difficult it was. For nearly two centuries, countless elite mathematicians had thrown themselves at the problem, yet none had succeeded...
In the blink of an eye, two more days passed.
By then, online discussions surrounding Huang Tian and his paper had gradually quieted down. In a world where fresh news broke every minute, few lingered on a single topic for long.
Then, two announcements sparked a brand-new sensation!
First, during a media interview, French mathematician Pierre-Louis Lions was asked about Huang Tian's paper. He stated that he had read the paper and had not found any obvious errors or omissions for the time being, expressing hope that more peers would examine and debate it.
Lions had won the Fields Medal—the Nobel Prize of mathematics—in 1994 for his groundbreaking research in nonlinear partial differential equations and stochastic control theory.
As both a leading authority on partial differential equations and a Fields Medalist, his words carried immense weight and instantly drew widespread media attention.
The second announcement was that Professor Li Nuo, vice dean of Jingda's School of Mathematics, had reached out through various channels to invite Huang Tian to deliver a small-scale academic seminar at Jingda.
A Fields Medalist and a vice dean from Jingda's School of Mathematics speaking up at the same time instantly reignited the online frenzy.
In the Changda Tieba forum, eccentric posters quickly bubbled to the surface.
"Holy crap! Did our senior really conquer the Navier-Stokes equations? Can our school actually produce a godlike figure like this?"
"Has anyone here read the paper? Can someone explain it to the rest of us?"
"LMAO, how could we possibly understand it? Even prominent young mathematicians might not get it. Otherwise, Lions and Professor Li Nuo wouldn't be the only ones who've spoken up so far."
"By the way, if our senior's proof holds up, won't our school's math department jump several tiers? We'll stomp right over the Finance and Science universities, and maybe we can even reclaim the name Nanda!"
"Is good old Changda actually going to hit the big time?"
"Go get 'em, Senior! The underclassmen in the math department are counting on you! Please single-handedly elevate our entire major, we beg of you!!!"
"..."
Amid the clamor, Huang Tian received a phone call from Li Nuo, who had obtained his number from Feng Zechun after contacting Changda.
"Huang Tian? Hello, I'm Li Nuo from Jingda's School of Mathematics." The voice on the other end was very gentle.
"Hello, Professor Li."
"I apologize for intruding like this. It's regarding your paper. Several colleagues and I have studied and discussed it, and we believe the theoretical framework and methodology you constructed are profoundly groundbreaking. However, we still have many questions, so we would like to invite you to Jingda to give an academic seminar. Would that be convenient for you?"
Naturally, they could not verify a 120-page paper so quickly, but skimming through the broader structure was not difficult. And after reviewing it, they had found no obvious flaws in reasoning or logical lapses!
Deeply shaken, they had decided to invite Huang Tian to Jingda for an academic seminar so they could hear an explanation directly from the author.
"Certainly," Huang Tian agreed readily. This was already part of his plan.
"Wonderful!" Li Nuo replied with delight. "Around when can you set off? Jingda will cover all your travel expenses, and there will also be a consultation honorarium..."
Once he finished outlining the general arrangements, Huang Tian said, "Tomorrow works. I'll book the plane ticket today."
"Great. I'll arrange for a car to pick you up at the airport..."
"..."
After hanging up, Huang Tian went to his parents and told them about his upcoming seminar at Jingda. Both of them were stunned and overjoyed.
They were stunned because they had always regarded Jingda and Shuimu as hallowed grounds; for any child from their county or village to test into Jingda was a cause for monumental celebration, yet Huang Tian had been invited there to deliver an academic seminar!
They were overjoyed because receiving an invitation from the vice dean of Jingda's School of Mathematics meant their son might have truly achieved remarkable progress on that century-old problem!
"Go attend to your business. I'll pack your bags right away," Yang Guihua said hurriedly.
Huang Yusheng nodded as well. "We don't understand your work. Just do as you see fit."
The next morning.
Huang Tian packed his laptop and belongings into a backpack, took a taxi to Chang City, and boarded a flight to Jingcheng.
After a flight of just over two hours, he landed at the Jingcheng airport. From there, he boarded a dedicated car sent by Jingda, arriving at the campus in roughly an hour.
Classes had only resumed a few days prior, and the campus brimmed with youthful vigor. Looking out the window, he could see students brimming with vitality walking along the pathways.
The car pulled up before a building. As Huang Tian stepped out, two people immediately came forward to welcome him.
The one leading was none other than Vice Dean Li Nuo of the School of Mathematics.
"Thank you for taking the time to come, Mr. Huang..."
Li Nuo smiled and shook Huang Tian's hand. After exchanging brief pleasantries, the staff member behind him led Huang Tian to the on-campus Shaoyuan Hotel to drop off his luggage and rest.
Meanwhile, Jingda published an announcement on its official campus website.
The notice stated that Huang Tian had been invited to the university to give an academic seminar in three days on the proof of global regularity for the Navier-Stokes equations, and scholars from domestic universities who wished to attend could submit their applications.
As soon as the announcement went live, numerous scholars in the field of nonlinear partial differential equations set off for Jingda, including Zhang Ping.
"Ten-odd days is simply too brief to judge whether his proof is complete..."
Zhang Ping rubbed his tired eyes. "Still, over these days, I genuinely haven't found any glaring errors. Besides, even if flaws remain in the end, the new theoretical framework he constructed is extraordinarily valuable. This seminar is the perfect opportunity to hear it firsthand..."
Three days passed in an instant.
Over twenty experts in relevant fields from various universities gathered on the Jingda campus.
It was not a large crowd, for a simple reason: many domestic scholars had not yet found time to read the paper Huang Tian uploaded to arXiv. Lacking familiarity, they naturally would not rush over. Others preferred to avoid the journey and wait for the seminar's outcome.
In addition to these scholars, several major media outlets were permitted entry onto campus: Renren Daily, New Xia Daily, Science and Technology Daily, and more.
Sunshine Hall, Yingjie Exchange Center, Jingda.
Over twenty professors and experts from various institutions, alongside dozens of professors from Jingda's School of Mathematics and School of Physics, gathered in the hall. A select number of Jingda doctoral students were also allowed inside.
Applause surged alongside the rapid clicks of cameras.
Huang Tian walked onto the stage with calm composure. Facing the assembly of scholars and journalists, he cleared his throat, opened his presentation, and spoke without the slightest hesitation:
"...We generally consider the perspective of traditional Euclidean space to be flat, which is insufficient for capturing the complex topology of vortices. Therefore, I attempted to construct a principal bundle... with the phase space serving as an associated bundle, defining the phase space of the Navier-Stokes equations as the associated vector bundle of this principal bundle..."
The seminar lasted three days. For the first two days, aside from Huang Tian, everyone in the audience looked either grim or bewildered.
Not until the morning of the third day did the brows of figures like Chen Yue, Li Nuo, and Zhang Ping gradually relax, their expressions turning pensive.
And when Huang Tian stood on the stage and announced that the entire proof was complete, the hall fell dead silent for a moment—before Zhang Ping took the lead in applauding, sparking a wave of applause like an incoming tide.
When the seminar concluded, the audience did not immediately disperse. Chen Yue and Li Nuo walked over to Huang Tian and spoke quietly with him. After pondering for a few seconds, Huang Tian gave a slight nod.
Chen Yue, the dean of Jingda's School of Mathematics, then stepped up to the podium and addressed the room:
"Over these three days, I expect many of you present have not fully absorbed every detail of the paper. In truth, I still have a few questions myself. Therefore, in twenty days, our university will host a much larger seminar, inviting experts and scholars from top universities around the world..."
This gathering had merely been a small-scale seminar intended for initial discussion and identifying potential gaps; its authority was limited. For one, among top scholars, only Zhang Ping, Li Nuo, and a handful of others were present. Mr. Qiu from Shuimu had not attended, nor had any Fields Medalists.
A reporter from Science and Technology Daily immediately raised a hand to ask, "Dean Chen, does your decision to hold a larger-scale seminar mean you believe Huang Tian's proof is correct?"
Chen Yue pondered for a moment before nodding slowly. "I believe so. Although a few minor questions remain, Academician Zhang, Professor Li Nuo, Professor Zhang Zhifei, and I generally consider his entire proof to be sound and complete.
"However, endorsement from just our group is not enough, because the significance of this paper is simply too immense!
"Therefore, we will extend invitations to more of our distinguished peers worldwide, inviting them to attend the seminar in twenty days to examine and witness what may well be the most important mathematical achievement of this century!"
Chapter 156