Every Wednesday, Show Off
With the development of Yang- Mills theory, physicists have ambitiously attempted to use Non-Abelian Group Gauge Theory to unify Electromagnetic Force, Nuclear Force, and gravity, thereby accomplishing their long-cherished Grand Unification.
However, in Quantum Mechanics, each particle can be viewed as a special type of wave, thus the "massless" property becomes the crux of the Grand Unification theory.
Experiments, Computer Science simulations, and some theoretical calculations have led physicists to believe that there must be a "Mass Gap" for vacuum excitations, meaning that there are no massless particle waves.
This property of Mass Gap also explains why the Strong Force can only work over such a short distance.
This is the origin of the "Yang- Mills theory and the Mass gap hypothesis," but to this day, no one has been able to obtain a general solution to the Yang-Mills equations to rigorously prove the key property of the "Mass Gap."
Today, Wednesday, under a bright and sunny sky, Sebastian, a doctoral student in the Princeton Mathematics Department, announced that he has solved the "Yang- Mills theory and the Mass gap hypothesis".
Professor Witten laughed speechlessly, finding it comical.
Shen Qi thought to himself, "Yeah, even Professor Witten couldn't solve this problem, how could you, a doctoral student, possibly solve it? What a joke."
"What kind of mathematical problem best embodies the challenge to understanding Quantum Field Theory?" Witten asked several doctoral students.
Sebastian replied, "Occupying a central position in physics represents the difficulty of QFT."
Shen Qi added, "And it's important in mathematics."
Witten nodded and said, "For me, a significant problem involving the above points is proving the solvability of quantum Yang- Mills theories with a compact, simple non- Abel Lie group G as the gauge group for Re 4 and above, as well as the correctness of the Mass gap hypothesis."
"However, Sebastian, the symbols you wrote on the blackboard represent only one of thousands of mathematical methods and do not contribute to proving the Mass gap hypothesis. But then again, you have made an effort. I hope you can gain a deeper understanding of QFT, QED, and QCD before challenging the Mass gap hypothesis." Professor Witten criticized Sebastian a few times, but then offered encouragement.
It is acceptable to objectively and fairly reject students' research results, but it is unacceptable to devastate their academic enthusiasm. The balance between these two aspects is a skill that discipline leaders must master themselves.
QFT stands for Quantum Field Theory, QED for Quantum Electrodynamics, and QCD for Quantum Chromodynamics. All three Qs are quite difficult. Only with a deep understanding of the three Qs and exceptional mathematical skills can one possibly solve the "Yang- Mills theory and Mass gap hypothesis".
With the resolution of the Yang- Mills theory and the Mass gap hypothesis, the Grand Unification of physics has achieved theoretical success. As for what kind of applied breakthroughs it will bring, it is currently impossible to assess.
This is the significance of the Millennium Prize Problem: the "Yang- Mills Theory and the Mass gap hypothesis".
Sebastian was frustrated by Professor Witten's criticism, but he still held his head high with pride. "I will continue to work hard, and I will definitely solve the 'Yang- Mills theory and Mass gap hypothesis' within five years. Yes, I believe I can do it. Chris will work with me; he recently published a paper in the * Journal of Mathematics *. If I am 'Yang,' then Chris is 'Mills.'"
"It's my pleasure to do this for you, Sebastian," Chris said.
Sebastian shook his head. "Not me, it's us."
Every Wednesday is "Show-off Day"—life goes on, and so does showing off.
Sebastian and Chris had outmaneuvered him today, which made Shen Qi feel a sense of urgency.
Although Sebastian's research on the "Yang- Mills theory and the Mass gap hypothesis" is riddled with flaws, he has begun to attempt to tackle this significant Millennium Prize Problem, which requires courage.
Chris claims he's about to solve Goldbach Conjecture 1+1, but that's probably just a big lie.
However, being able to publish a paper in one of the four major journals, the Journal of Mathematics Sinica, demonstrates that Chris possesses strong mathematical abilities; at the very least, he has begun to tackle Goldbach Conjecture 1+1.
That's how basic theoretical research works; amidst countless wild and even absurd daydreams, you might just stumble upon the correct and fascinating answer.
Everyone around him was hardworking, ambitious, and driven. Shen Qi dared not underestimate Sebastian and Chris; who knew, maybe one day these two would strike it rich.
Many scientists who have gone down in history were unknown before they became famous. For example, Einstein was working at a patent office in Bern, Switzerland, in the year he published his Quantum Theory. He was just a regular technician who had recently been promoted. Several years later, the year Einstein turned 26 is known as the "Miracle Year of Einstein".
Sebastian and Chris took their coffee to another small table to continue their conversation. Witten came to Shen Qi's table and asked, "Qi, what have you been busy with lately?"
"Drafting a history of History of Number Theory and preparing for my doctoral dissertation defense." Shen Qi felt he hadn't put on a good show today; everyone else had already covered Yang-Mille equations and Goldbach Conjecture, while his research was unremarkable.
"Qi, among these doctoral students, you should be the first one to get a PhD." Witten looked at Jonas, then glanced at Sebastian and Chris not far away.
"I think so," Jonas said.
"Perhaps," Shen Qi said.
Witten asked, "What are your job plans after you graduate with your doctorate?"
Shen Qi laughed and said, "That depends on whether Princeton is willing to hire me."
Witten beckoned to Director Charles Feierman, who was sitting on the sofa, and Director Feierman came over and sat down.
Witten pointed at Shen Qi and said, "Charles, he needs a job at Princeton."
"Well, you'll have to start as a lecturer in the Mathematics Department," Feierman said.
"Of course, I know the rules." Shen Qi, who was already a teaching assistant, was familiar with the process. The promotion from lecturer to Associate Professor to professor required time and performance. Yun Wei, Terence Tao, and other record-breaking youngest professors had all gone through the lecturer and Associate Professor stages.
"To become a lecturer, you need to have the academic ability to teach a course independently. So, Qi, please tell me, in which course do you have the strongest ability?" Director Feierman asked casually.
Often, the interviews for personnel appointments and removals in the Mathematics Department are conducted over coffee. What may seem like casual conversation is actually a hidden test.
Shen Qi replied, "Actually, my studies are quite diverse. The ten papers I published during my undergraduate studies cover fields such Differential Calculus, integral Series Theory, series theory, Linear Algebra, Homological Algebra, and the Euler - Poisson Equation. They can be categorized into three branches of mathematics: Mathematical Analysis, algebra, and Mathematical Physics Methods."
"During my time at Princeton, I published four papers: a proof of the Wash Conjecture, two papers related to Group Theory, and the 'Muller -Shen theorem' in Bachmann Space, which involves three branches: number theory, Abstract Algebra, and Functional Analysis. Another paper on 'Shen Proximity Theorem' is currently under review, and it also falls under the broad category of Functional Analysis."
"Last semester, I taught a Non-Euclidean Geometry tutorial class for second-year students. Non-Euclidean Geometry is a branch of geometry, and I did a pretty good job tutoring them. The overall Non-Euclidean Geometry scores of the twelve students were the highest among the second-year students." Shen Qi stated the objective facts, which can be considered a summary of his professional expertise in the interview.
"So, Charles, Edward, I'm also troubled. The seven branches of mathematics listed above contain a total of thirty-two sub-courses, and I think I'm capable of teaching them all independently." Shen Qi shook his head helplessly. A jack-of-all-trades, master of none—he didn't know which to choose from the thirty-two.
Director Feierman fell into deep thought, "A versatile mathematics PhD candidate like Qi is indeed very rare. What do you think, Edward?"