Cheers That Shook the Dome, a Sacred Hymn!

After a brief opening remark, Huang Tian got straight down to business. He did not jump directly into his proof. Instead, he began by walking through the new theoretical framework he had developed. His subsequent arguments rested entirely upon the foundation of this new theory; if this part was not made clear, there would be no point in continuing. "...Regarding the Navier-Stokes problem, existing mathematical tools have clear limitations, making a direct and intuitive resolution difficult. I have therefore attempted to introduce geometric analysis, topological constraints, and infinite-dimensional dynamical systems into partial differential equations, thereby constructing a new mathematical apparatus..." His voice was calm and steady, echoing through the auditorium. Down in the center aisle, the reporter from Science and Technology Daily looked completely baffled. Beside him, the cameraman scratched his head, feeling as though his brain were straining just to sprout a new wrinkle. "It’s only been two minutes, and I’m already completely lost. Is this what mathematics is really like?" The reporter shivered, privately rejoicing that he had never chosen a math major. The cameraman simply emptied his mind and focused on framing the shot, doing his best to record every detail. If Huang Tian’s proof of the Navier-Stokes problem proved correct today, this recorded footage would become an invaluable historical document, and excerpts from it would certainly lead the evening news. Beside Science and Technology Daily, several other major media outlets were filming throughout the hall. "It’s getting harder and harder to follow..." a master's student in mathematics from Jingda murmured under his breath. The person next to him glanced his way and whispered, "You didn't actually expect to understand it, did you? We’re just here for the spectacle, to witness a miracle. The real audience are those titans sitting in the front rows!" "Sigh... I thought getting into Jingda made me one genius in ten thousand. Only after arriving did I realize geniuses here are a dime a dozen. And today, looking at him... it’s truly a mountain to revere, an exemplary path to follow..." "A one-in-ten-thousand genius? Xia alone can scrape together a hundred and forty thousand of those!" "..." Many students could still grasp the early parts of Huang Tian’s presentation. But as time went on, and more concepts were introduced and explored at greater depth, they grew increasingly dazed. Eventually, they felt utterly blind, their eyes glazed over as they stared blankly at the figure on stage, his mouth opening and closing as if speaking some incomprehensible tongue of the gods. Compared to the students, the invited experts and scholars were naturally far better equipped. Not only did they possess immense academic depth, but they had also studied the paper in detail prior to the conference, and several had already engaged in face-to-face discussions with Huang Tian. Consequently, following along was relatively manageable for them. Around two hours in, even some physics professors began to feel the strain. While no physicist could go without studying mathematics, their work rarely required the esoteric depth demanded of pure mathematicians. In particular, although the Navier-Stokes problem was a classic problem of mathematical physics, it leaned heavily toward pure mathematics. Grappling with it was profoundly taxing, making their heads throb. In truth, even among the mathematicians present, only thirty to forty percent were fully keeping pace with Huang Tian’s train of thought. This was hardly surprising: fields differed vastly, and within mathematics, the divide between separate subfields was like an insurmountable mountain range. A scholar steeped in algebraic geometry would be just as baffled when confronted with deep branches of topology. Not everyone possessed the extraordinary gift of someone like Terence Tao, capable of diving into a dozen mathematical disciplines simultaneously and producing groundbreaking results in every one. The morning session began at 8:50 AM and continued until 11:50 AM. Over the course of three full hours, Huang Tian finally concluded his exposition of the new theoretical framework. With that, the morning session came to an end. As he stepped down from the lectern, many students in the audience finally snapped out of their stupor, eagerly pulling out their phones to snap photos and take videos. The experts and scholars crowded around Huang Tian, guided toward the Faculty House by Chen Yue, dean of Jingda's School of Mathematics, and Vice Dean Li Nuo. The Faculty House was not a staff dormitory, but an upscale restaurant on campus. Originally restricted to faculty and staff, it had later opened its dinner service to all students and teachers. Situated beside Weiming Lake and under the shadow of the Boya Pagoda, it bordered an expansive lawn. Stepping inside, one was greeted by a semicircular vaulted ceiling. Warm sunlight poured through massive floor-to-ceiling windows, bathing the sofas and chairs in a gentle glow. Near the spiral staircase, someone was playing a piano, filling the air with melodious notes that lent the room an aura of warmth and refined elegance. Taking into account that the invited scholars hailed from countries all over the world with diverse tastes, lunch was served buffet-style, offering a wide array of cuisines and pastries for guests to choose at their leisure. Huang Tian did not feel particularly hungry and merely took a few symbolic bites. Professor Gerd Faltings, tall and gaunt, swallowed a few pieces of bread in quick succession before walking over to Huang Tian with a glass of warm milk to discuss questions lingering in his mind. Several people soon gathered around them, chatting and debating in lively spirits. After a while, Professor Srinivasan walked over and said, "Huang, if I recall correctly, you don’t hold a faculty position at any Xia university yet. Would you consider coming to NYU? We can offer you the finest terms..." As the dean of NYU Tandon School of Engineering and vice provost for engineering and applied sciences, Srinivasan had plenty of leverage behind his offer. However, before he could finish, another voice cut him off. "Going to NYU pales in comparison to Princeton. For a mathematician, what institution could hold more allure than the sacred sanctuary of Princeton?" Srinivasan frowned, annoyed, and turned toward the voice, only to find Edward Witten smiling amiably. His lips twitched, and Srinivasan let out a soft huff. "In the end, it all depends on what he wants." Whether measured by overall institutional ranking or strength in mathematics, NYU indeed fell far short of Princeton. Still, with sufficient compensation and resources, anyone could be swayed. On the other side, Vladimir Drinfeld chimed in with a genial smile. "Huang, if you're willing, UChicago would be delighted to welcome you as well." In rapid succession, several others extended invitations for Huang Tian to join their respective institutions. Regardless of whether his proof of the Navier-Stokes equations held completely true, these days of interaction had revealed an astounding breadth and depth to his mathematical mastery. No matter the branch, he possessed profound insights, and his perspectives on cutting-edge problems across disciplines were consistently refreshing and original. An all-around polymath of this caliber possessed boundless potential! Moreover, after their discussions over the past few days, their instincts told them that his paper contained no flaws. For mathematicians, intuition was often remarkably acute, and most were now inclined to believe that Huang Tian had genuinely conquered a challenge that had perplexed the world for over a century! If they didn't try to recruit such an extraordinary, once-in-a-generation talent right now, when would they? Watching Huang Tian surrounded by the crowd, Li Nuo felt utterly helpless. Compared to premier global powerhouses like Princeton and UChicago, Jingda still lagged behind. The chances of Huang Tian choosing to remain at Jingda were slim indeed... While Huang Tian and the others enjoyed their lunch, many outside were closely monitoring the situation on campus. "The whole morning is over! Does anyone know how it went in there?" "The conference is supposed to last three or four days, isn't it? How could there be a final verdict already?" "It might span three or four days, but the later days are mostly for Q&A. The first day should be enough to reach a preliminary conclusion." "Let me weigh in! I sat through the whole morning in Centenary Memorial Hall, completely dizzy. I didn't understand ninety percent of it, but I noticed the big shots in the first few rows nodding constantly with barely any skepticism on their faces. So my guess is that, up to this point, Huang Tian's arguments have been accepted. Now it all comes down to the afternoon." "Those luminaries definitely read Huang Tian's paper thoroughly before flying to Jingda. If they didn't believe it was essentially sound, they wouldn't have traveled thousands of miles across the globe." "Can't wait for the final outcome!" "Brother up there, keep us updated! Ping me the moment you hear something concrete!" "+1, ping me too!" "..." At two o'clock sharp in the afternoon, back in the Centenary Memorial Hall auditorium. Once everyone was seated, Huang Tian returned to the lectern to resume his presentation. This time, he would deploy the theoretical framework introduced that morning to prove the Navier-Stokes equations. "...First, we carry out a geometric reformulation of the Navier-Stokes equations, lifting them onto an infinite-dimensional fiber bundle..." "Under the aforementioned gauge-theoretic framework, the L^2 norm of the vorticity field can be associated with a Chern-Simons action. This action represents the variation of a topological invariant and, under appropriate boundary conditions, remains conserved for smooth solutions. "If a solution were to blow up in finite time, the corresponding Chern-Simons form would necessarily undergo a topological phase transition..." He advanced the slides, pointing out key details on the screen with a laser pointer while occasionally writing out intermediate steps on the whiteboards to his left and right so the audience could follow along. "...The aforementioned scaling transformation can be regarded as a renormalization group flow defined on the function space. We prove that all possible singularity limits must lie on the stable manifold of a hyperbolic fixed point of this renormalization group flow..." Time slipped by quietly. Huang Tian maintained his steady, measured pace, while the students below had long since abandoned any hope of following the math. They simply sat wide-eyed, listening blankly, with an occasional student raising a phone to film. Others kept their eyes glued to the luminaries in the front row, trying to deduce whether Huang Tian’s arguments were holding up from their expressions. "It’s five-ten..." The Science and Technology Daily reporter pushed up his left sleeve and glanced down at his watch. "The afternoon session should be wrapping up soon." Looking up at the projection screen, the slides appeared to have reached their end. Within the hall, an indescribable atmosphere gathered. The students struggled to contain their mounting excitement, their eyes sparkling, while the experts and scholars instinctively held their breath. In the front row, Terence Tao seemed caught up in the mood. He unconsciously gripped his own hands, fingers interlaced, his lips pressed thin. Peter Scholze, seated to his right, noticed the subtle gesture and whispered, "It's almost over. Have you reached a conclusion?" Tao paused for a moment, tilting his head to reply in a low voice, "To be honest, before coming to Jingda, when I finished reading his paper, I was already fairly certain he had truly solved the Navier-Stokes problem. My discussions with him over the past few days only deepened that conviction. And today, hearing him walk through the entire structure once more... I can say with certainty, he did it!" *He did it!* Scholze fell silent. Though a Fields Medalist himself, his work did not center on the Navier-Stokes equations, so he had hesitated to pass judgment prematurely. Tao was different. He had dedicated years of research to this century-old challenge and produced numerous breakthroughs of his own. If he endorsed Huang Tian's work, there was little room for doubt. Scholze glanced a few seats down at Mr. Yau and Srinivasan. The former had his brow furrowed, seemingly lost in deep thought, while the latter nodded repeatedly with a faint smile. He then looked toward Faltings, Witten, and Drinfeld. Their expressions varied, but all kept their eyes fixed on the massive projection screen, their postures taut with anticipation. "He is so remarkably young." A soft murmur of admiration drifted into his ear. Scholze turned; it was Tao again. Known as the Mozart of mathematics, Tao had won the Fields Medal at thirty-one—a recognized genius among geniuses—and was now fifty-one years old. He was no longer young, and his energy was no longer boundless. Seeing the twenty-four-year-old Huang Tian standing there, Tao felt a fleeting daze, as though catching a glimpse of his own youth when his spirits had soared highest. While Scholze also marveled at Huang Tian’s youth, he felt less sentimental. After all, he was only thirty-nine, still in the absolute prime of his energy and intellect. Even so, he couldn't help sighing inward: *A once-in-a-century genius has been born...* Gauss, Euler, Riemann... a handful of immortal names flashed across his mind. On stage. With a click of the laser pointer, Huang Tian brought up the final slide. This page bore no intricate numbers or symbols, only a single, simple statement. Huang Tian read it aloud, his voice resonant and powerful. "We therefore conclude with certainty— "Solutions to the three-dimensional incompressible Navier-Stokes equations do not develop finite-time singularities! "That is to say, their solutions possess global regularity!" The hall froze in absolute silence for a split second. *Boom!* As if a volcano dormant for centuries had erupted all at once, Edward Witten and Terence Tao in the front row were the first to leap to their feet, clapping their hands with fervent intensity. The second row, the third row... like a sweep of wind through a field of wheat, nearly three thousand people across the entire auditorium rose in unison. *Whoosh—!* Applause crashed down like a torrential storm, fusing in an instant into a deafening roar of thunder. The sound carried physical force, shaking the air until even the bright chandeliers overhead seemed to quiver! The young students, their faces flushed red, clapped with all their might and cheered at the top of their lungs, their eyes gleaming with pure reverence. Scholars and experts applauded with total abandon, some with eyes welling with tears. They clapped relentlessly while shouting excitedly to their colleagues, and though their voices were drowned out by the roaring tempest of cheers, they continued to speak with uncontainable fervor. A sea of camera flashes shimmered like a galaxy of stars, capturing this moment destined for the annals of history. Wave after wave of sound crested higher and higher, crashing against the ceiling of the auditorium as though ready to rip off the very roof! This was not merely celebration for the conquering of a century-old enigma—it was a sacred hymn to yet another triumphant venture into the farthest frontiers of human intellect!