Scholar's Advanced Technological System
chapter-609

Chapter 609: Proof of the Existence of a Solution

It was in the afternoon.

Lu Zhou stepped into the classroom in the midst of the bell ringing. He looked at the crowded classroom and smiled while making some simple opening remarks. He then began to give the first-ever computational materials science lecture in his life.

Actually, strictly speaking, computational materials science wasn’t part of the core applied chemistry classes. The mathematics knowledge and the programming knowledge that were needed were a bit too advanced for undergraduate students.

However, due to the development of computer technology, the field of computational materials science was becoming stronger and stronger. Also, because Lu Zhou was the founding father of this emerging discipline, this course had been classified as a core class, which was compulsory for all applied chemistry students.

After all, Jin Ling University had been around for many years, but there had only been one Nobel Prize alumnus.

However, classifying it as a core was unnecessary.

Even if the class wasn’t compulsory, Lu Zhou didn’t have to worry about people not coming to his class.

Not only were there Jin Ling University students sitting in the classroom, but there were also genius students from Dong University that took the subway to come here, and even professors in fields like theoretical chemistry, nanomaterials, etc. After the class, most of the people would talk about how “difficult” it was, but in fact, most of the people were taking notes seriously…

Lu Zhou used a hundred and twenty percent of his energy to lecture, and after the lecture, he left the classroom in the midst of a round of applause.

He looked at his phone in the hallway and saw that it was still early, so he went to his mathematics building office.

When he arrived at his office, his students and assistants were all here.

Even though he hadn’t been at the office for the past few days, all of his students had been clocking in every day.

Lu Zhou sat down at his desk and looked at his tidy desk. He reached out and flipped through his document folder. When he couldn’t find what he was looking for, he asked casually, “Where are the draft papers that I put on my desk?”

Assistant Zhao stood up and quickly said, “I put it in your drawer when I was organizing your desk.”

Lu Zhou: “Oh, thanks… But in the future, you don’t have to organize my desk, just keep it the same.”

Zhao Huan said, “Okay, Professor, I’ll take note.”

Lu Zhou found the draft papers from his drawer and placed it on his desk. He looked at the lines of equations he wrote a week ago and thought for a moment. He then began to continue where he left off.

Feng Jin, who was writing at his desk, hesitated for a bit. He then finally made up his mind and stood up before walking toward Lu Zhou.

“Professor.”

Lu Zhou looked at his student standing next to his desk. Since he was in a pretty good mood, he said, “What?”

“That question… Did you solve it?”

Lu Zhou smiled and asked, “You read my draft papers?”

Feng Jin awkwardly scratched his head and said, “I accidentally saw it…”

Lu Zhou looked at him and didn’t say anything.

He didn’t really care that Feng Jin secretly read his draft papers.

After all, he wouldn’t put anything important on the table. If he wanted to hide it, he would at least put it in his drawer.

“Then what? You researched the problem for an entire week?”

“Yeah.” Feng Jin saw that Lu Zhou didn’t seem to care, so he sighed and scratched his head as he muttered, “I tried thinking about it for a week, but I don’t have a single clue.”

“It’s normal. If you can solve that problem, forget about a master’s degree, you can become a professor right now.”

Feng Jin smiled awkwardly.

It was true, challenging the Yang-Mills equation was a bit ridiculous for him.

Lu Zhou looked at his expression and knew what he was thinking, so he smiled and said, “Tell me about your thoughts over the past week.”

Feng Jin said, “Thoughts?”

Lu Zhou: “That’s right. Since you’ve been thinking about it for a week, regardless of whether or not you found the solution, surely you have thought of something? Don’t tell me you just looked at the draft papers and wrote down some nonsense.”

Feng Jin blushed and said, “It’s not nonsense, I thought about it seriously.”

Lu Zhou raised his eyebrows and asked, “Like?”

“Like…” Feng Jin thought that Lu Zhou would laugh at him again, so he hesitated for a bit before clenching his teeth and bravely speaking his opinions.

“According to my understanding of quantum mechanics, the Yang-Mills field is mass-less, yet the strong interaction mediated meson has mass. In this case, if we introduce a scalar-field on top of the space-time manifold, it would simplify this problem.”

Lu Zhou nodded with approval and said, “Correct.”

Surprised, Feng Jin looked at Lu Zhou. He didn’t expect him to actually compliment himself.

Lu Zhou: “You’ve studied quantum mechanics before?”

Feng Jin, who was a little surprised, suddenly felt a little depressed.

I guess Professor Lu isn’t complimenting my thoughts, but rather my attitude toward studying extracurricular knowledge…

Feng Jin nodded. Lu Zhou smiled as he said, “You remind me of someone.”

Feng Jin paused for a second before asking, “Who?”

“One of my students at Princeton. He studied under Witten and was in the mathematical physics field. You guys have similar personalities, both competitive types.”

Speaking of which, time really flew by. It had been a year since he left Princeton.

Lu Zhou didn’t know how his students were doing.

Qin Yue was probably lecturing at Princeton, and they had talked about number theory problems some time ago.

Vera…

Lu Zhou’s expression was somewhat unnatural, and he coughed and diverted the conversation.

“Anyway, back to what we’re talking about. In a sense, there aren’t huge problems with your idea.”

Feng Jin asked excitedly, “Really?”

“Don’t be too happy just yet. Like I said, there aren’t huge problems.” Lu Zhou looked at Feng Jin’s excited expression and said, “However, in terms of physics, having no problems doesn’t mean it is correct.”

“Doesn’t mean it is… correct?”

“That’s right.” Lu Zhou looked at Feng Jin and nodded with approval. He said, “When you can really understand the meaning behind this sentence, then you’ll be closer to the truth than ever.”

…

Lu Zhou stayed on campus until 6 o’clock in the evening.

When Lu Zhou returned home from school, it was already dark outside.

He went straight into his clean and tidy study room and sat down on his chair. He quietly picked up a pen and began to finish the incomplete proof from this morning.

Sometimes, mathematics problems were almost magical.

After a proof idea appeared in his mind, Lu Zhou already knew the proof process would work. All he had to do was to write down the proof in a rigorous mathematical form.

After Lu Zhou wrote down the last line of equations, he looked at the stacks of draft papers and smiled.

Even though this wasn’t a decisive result, it could be considered an in-progress result.

Which was, he used mathematical methods to prove the existence of a solution to the Yang-Mills equations.

This was the first half of a Millennium Prize Problems, and this part wasn’t challenging for him at all.

Even though he used some advanced mathematical techniques to solve this problem, it was nothing novel.

Actually, the core of the whole proof was built around the L-manifold that he invented when he was solving the Navier–Stokes equations.

Regardless, the problem was finally solved.

The next step was to find the actual solution to the Yang-Mills equations…

Compared to the proof of the existence of a solution, this part was undoubtedly more challenging…