Feng Zechun was slightly taken aback when he saw the thick stack of papers. Taking it, he skimmed the title.
"On the Blow-Up Phenomenon of Supercritical Defocusing Nonlinear Wave Equations... You're still doing research after graduation?"
Feng Zechun asked in surprise, "Looking at this stack of manuscripts, you must have put in quite an effort."
Huang Tian said, "Driven by interest, I suppose. During my undergrad, I was quite fond of mathematics and hoped to pursue graduate studies—either through recommendation or the entrance exams—and devote myself to scientific research. Later, financial pressure at home mounted, leaving me no choice but to find a job right after graduation.
"That job wasn't particularly repulsive, just tedious and repetitive. Naturally, the frequent overtime also wore on me. Over time, mathematics crossed my mind again. I felt I just couldn't let it go, and if I didn't give this path a shot, I'd never truly be at peace with it..."
Hearing this, Feng Zechun was deeply moved. It was as if he saw the embodiment of an inspiring, indomitable scholar before him. Nodding repeatedly, he praised, "This kind of drive to study is rare nowadays. Today's students are doing well if they just dutifully finish the assignments I hand out. Back in my day, who among my cohort didn't study and delve into things like madmen, staking their lives on it? Without that relentless drive, you can never learn real substance..."
He reminisced for a bit, then suddenly slapped his forehead, smiling sheepishly. "When people get old, they just love to reminisce."
As he took a cleaning cloth from the glasses case on the glass table beside him to wipe his reading glasses, he asked, "Huang Tian, can you tell me about the findings and innovations in your paper?"
Without hesitation, Huang Tian replied, "Based on my calculations, I arrived at a conclusion: the supercritical defocusing nonlinear wave equation exhibits blow-up!"
If a stone were thrown into a calm lake, ripples would spread outward layer by layer. As the ripples dispersed, the energy would dissipate with them, eventually returning the water to tranquility. In this context, the process of energy gathering can be called focusing, while the process of energy releasing can be called defocusing.
Mathematical equations studying the former are called focusing equations. For these types of equations, their solutions can become infinite at a certain instant, which is termed a "blow-up," because the energy concentrates at a single point and erupts with a bang.
Huang Tian's paper, however, investigated defocusing equations. Generally, the mathematical community agreed that defocusing equations do not blow up, because they represent the dispersion of energy in all directions. Since energy is dispersing, intuition dictated that a blow-up was impossible, and its solutions ought to exist globally and remain well-behaved.
Yet Huang Tian had shattered decades of academic consensus, using mathematical formulas to prove that it would indeed blow up!
Sure enough, upon hearing Huang Tian's words, Feng Zechun was immediately startled. "You're saying it blows up?!"
Huang Tian nodded. "Yes—assuming mathematics hasn't lied to us."
Feng Zechun quickly asked, "What is your method? What tools did you use?"
Huang Tian said unhurriedly, "In the past, when people studied defocusing equations, their attention was almost entirely fixed on real-valued solutions. After all, how could an outward-pushing force ever lead to a blow-up?
"However, I experimented with complex-valued solutions, introducing special phases and oscillation patterns. Through this, I discovered that when the phase and oscillations change, complex interactions emerge between them, which in turn causes the energy to focus and trigger a blow-up.
"And the core of the entire paper lies in introducing the relativistic Euler equations, transforming the wave equation into a problem of fluid dynamics."
Feng Zechun's eyes widened. "You introduced the relativistic Euler equations?"
"Yes. During my research, I found a self-similar implosion solution within the relativistic Euler equations. Then I identified an analogous self-similar structure in the defocusing equation. So, I attempted a structural transference, mapping the former into the latter's framework, which smoothly transformed it into a fluid dynamics problem."
Feng Zechun knitted his brows deeply, muttering under his breath, "Self-similar, complex-valued solutions..."
At a certain moment, he suddenly looked up, his clouded eyes flashing with brilliance as he stared at Huang Tian in pleasant surprise. "Although I haven't read your paper thoroughly yet and can't be sure if your results hold up, your approach alone is extraordinarily novel! Transferring the relativistic Euler equations is an absolute stroke of genius!"
Huang Tian wore a faint smile, neither conceited nor falsely modest.
Feng Zechun said excitedly, "I need to take a good look at this paper of yours, but I have a lecture in half an hour..."
He fished his phone from his pocket, looked up the number of Xu Kaizhi, Dean of the School of Mathematics, and dialed.
A few seconds later, the call connected, and a rich, resonant voice came through. "Hello, Old Feng. What made you call me out of the blue?"
Feng Zechun was concise. "I've got something incredible here. Come take a look. I'm waiting for you in the fifth-floor lounge of the Life Sciences Building. Also, help me find a substitute teacher. I won't be teaching the next class."
"Something incredible? Did you run across a paper you can't be sure of?" Xu Kaizhi grasped the situation immediately.
"Yes, yes. Just come over, it's hard to explain over the phone."
"All right, give me a few minutes. Let me arrange a substitute for you first."
The call ended. Because Feng Zechun was waiting for Xu Kaizhi, he held off on diving into the paper and instead chatted with Huang Tian, his warmth and geniality practically brimming over in every word.
Before long, Xu Kaizhi, clad in a gray jacket, appeared outside the lounge doorway. In his fifties, most of his hair was still black. He had a square-jawed face, a slender build, and an energetic, spirited presence.
"Old Feng, what wonderful paper has you calling me over in such a rush?"
Xu Kaizhi entered the room with a smile, then froze slightly upon seeing Huang Tian. "And this is?"
Feng Zechun introduced him with pride. "A former student of mine, Huang Tian. The paper I want you to look at is his work!"
"Dean Xu," Huang Tian greeted him. He recognized Xu Kaizhi, who had been appointed Dean of the School of Mathematics at Changda during his junior year, several years ago now.
Xu Kaizhi said in surprise, "A graduate of our university? The young man looks very sharp and dignified—quite like an academic. What year of your doctorate are you in?"
Feng Zechun said, "He finished his bachelor's degree just last June."
Xu Kaizhi was astonished. "An undergrad?"
A fresh undergraduate writing a paper that even Feng Zechun couldn't immediately evaluate?
Feng Zechun nodded. "Let me tell you, we really failed to recognize talent back then. Huang Tian's mathematical intuition and insight are absolutely top-tier..."
He gave a broad overview of the innovative concepts in Huang Tian's paper. As Xu Kaizhi listened, his eyes shone brighter and brighter. Finally, he took a soft breath. "Truly a stroke of genius. If it turns out there are no errors in the proof, this is definitely a paper worthy of the Big Four..."
The Big Four top journals in mathematics: Annals of Mathematics, Inventiones Mathematicae, Acta Mathematica, and the Journal of the American Mathematical Society. Of course, people often argued about a fifth or even a sixth member among the top tier, but that was another matter entirely.
Publishing a single paper in the Big Four was enough to give anyone free rein in most academic circles—or at the very least within Changda, as the university couldn't reliably publish even one in an entire decade...
Chapter 42