42, It Will Explode

Feng Zechun was slightly taken aback when he saw the thick stack of manuscripts, taking them and glancing at the title.

"Research on the Blow-up Phenomenon of Supercritical Defocusing Nonlinear Wave Equations... You're still doing research after graduation?"

Feng Zechun said with surprise, "Looking at this stack of drafts, you've put in quite a lot of effort."

Huang Tian said: "It's out of interest. I quite liked mathematics during my undergraduate years and had planned to secure a recommendation for graduate school, study further, and root myself in research. Later, due to the economic pressure on my family, I had no choice but to find a job right after graduation.

That job wasn't exactly repulsive, just monotonous and repetitive. Of course, the frequent overtime also annoyed me. Over time, I started thinking about mathematics again, feeling that I couldn't let it go. If I didn't try to walk this path, I wouldn't be content..."

Hearing this, Feng Zechun was deeply moved, as if he were looking at the image of an inspiring, indomitable scholar. He nodded repeatedly, praising:

"This kind of drive for learning is rare in this day and age. It's good enough if today's students can honestly finish the tasks I assign them. Back in my day, everyone in my cohort was crazy, giving their all to learn and delve deep. If you didn't push yourself hard, you couldn't learn the real stuff..."

He recalled for a while, then suddenly patted his own forehead, saying embarrassedly: "When a person gets old, they just love to reminisce."

While taking a cleaning cloth from the glasses case on the glass table nearby to wipe his reading glasses, he asked: "Huang Tian, can you tell me what your thesis results and innovations are?"

Huang Tian replied without hesitation: "Based on my calculations, I reached a conclusion: the supercritical nonlinear defocusing wave equation will exhibit a blow-up phenomenon!"

If you throw a pebble into a calm lake, it will create ripples that spread outward. The energy spreads with them and eventually returns to calm. At this time, we can call the process of energy gathering 'focusing,' and the process of energy release 'defocusing.'

The mathematical equation studying the former is called a focusing equation. For this type of equation, its solution becomes infinite at a certain moment; we call this a "blow-up" because the energy is all gathered at one point, exploding with a bang.

However, the equation Huang Tian studied in this paper is a defocusing equation. Generally, the mathematical community accepts that defocusing equations do not blow up because they represent the release of energy in all directions. Since it is a release, intuition dictates it cannot blow up; its solution should exist forever and be well-behaved.

Yet, Huang Tian broke the academic consensus of several decades, using mathematical formulas to prove that it does blow up!

Sure enough, upon hearing Huang Tian's words, Feng Zechun was instantly shocked: "You mean, it will blow up?!"

Huang Tian nodded: "Yes, if mathematics hasn't deceived us."

Feng Zechun hurriedly asked: "What is your method, your tool?"

Huang Tian said calmly: "Usually, when people study defocusing equations, their focus is basically on real-valued solutions. After all, how could a force pushing outward possibly blow up?

But I tried complex-valued solutions, introducing special phases and oscillation modes, and discovered that when the phase and oscillation change, it leads to complex interactions between them, which in turn causes the energy to focus and blow up.

The most core part of the entire paper is introducing the relativistic Euler equations to turn the wave equation into a fluid dynamics problem."

Feng Zechun widened his eyes: "You introduced the relativistic Euler equations?"

"Yes. During the research process, I discovered a self-similar implosion solution in the relativistic Euler equations, and then I found a similar self-similar structure in the defocusing equation. So, I tried to perform a structural migration, mapping the former into the framework of the latter, and successfully turned the latter into a fluid dynamics problem."

Feng Zechun frowned deeply, muttering to himself: "Self-similarity, complex-valued solutions..."

At one moment, he suddenly raised his head, his cloudy eyes bursting with brilliance, staring at Huang Tian in surprise: "Although I haven't carefully read your paper yet and am not sure if your results are correct, your line of thinking alone is extremely novel! The migration of the relativistic Euler equations is simply a genius idea!"

Huang Tian smiled, neither arrogant nor overly humble.

Feng Zechun said excitedly: "I must take a good look at this paper of yours, but I have a major lecture in half an hour..."

He took his phone out of his pocket, found the number for Xu Kaizhi, the Dean of the School of Mathematics, and dialed it.

A few seconds later, the call was answered, and a mellow, resonant voice came through: "Hello, Old Feng, what's the matter that you're calling me so suddenly?"

Feng Zechun was concise: "I have something good here. Come over and take a look. I'm waiting for you in the lounge on the fifth floor of the Life Sciences Building. Also, help me find a substitute teacher; I won't be teaching the next class."

"Something good? Did you encounter a paper you're unsure about?" Xu Kaizhi reacted immediately.

"Yes, yes, you'll understand when you get here. It's hard to explain over the phone."

"Alright, give me a few minutes, I'll arrange a substitute teacher for you first."

After the call ended, Feng Zechun didn't rush to read the paper while waiting for Xu Kaizhi; instead, he chatted with Huang Tian, the kindness and warmth in his words practically overflowing.

Before long, Xu Kaizhi, wearing a gray jacket, appeared outside the lounge door. He was in his fifties, with hair that was still mostly black, a square face, a lean build, and a very spirited demeanor.

"Old Feng, what kind of good paper is it that made you call me over in such a rush?"

Xu Kaizhi walked into the room with a smile, then paused when he saw Huang Tian: "And this is?"

Feng Zechun introduced him proudly: "My former student, Huang Tian. The paper I want you to look at is what he wrote!"

"Dean," Huang Tian said. He knew Xu Kaizhi; Xu Kaizhi had been hired as the Dean of the School of Mathematics at Chang University during his junior year, and it had been several years since then.

Xu Kaizhi said with surprise: "Is he a student from our school? The young man looks very upright, like someone who does serious scholarship. What year of his PhD is he in now?"

Feng Zechun: "He graduated with his bachelor's degree last June."

Xu Kaizhi was astonished: "Undergraduate?"

Could an undergraduate write a paper that left Feng Zechun unsure?

Feng Zechun nodded: "Let me tell you, I really didn't recognize the talent back then. Huang Tian's mathematical intuition and insight are absolutely top-tier..."

He roughly explained the brand-new concept Huang Tian proposed in the paper. Xu Kaizhi's eyes grew brighter as he listened, and finally, he took a soft breath: "It is indeed a very genius idea. If it turns out there are no errors in the end, this is absolutely a 'Big Four' level paper..."

The four top journals in the mathematical world are Annals of Mathematics, Inventiones Mathematicae, Acta Mathematica, and Journal of the American Mathematical Society. Of course, the "Big Four" often have a fifth or even a sixth, but that is another matter entirely.

Being able to publish a paper in the Big Four is enough to walk sideways—to be untouchable—in most places in the academic world. At the very least, one could walk sideways at Chang University, because Chang University might not even publish one in ten years...