After taking the advice, I became a top student.

At 8 p.m. on Saturday, Chen Mo turned on his phone on time and logged into the video conference link sent by Zheng Mingyang.

This is their agreed-upon weekly online discussion time.

The screen lit up, and Zheng Mingyang's face appeared on the screen.

He wore reading glasses, and the bookshelf behind him was densely packed with mathematical classics.

Sitting next to him was Zhao Yiming, holding a cup of tea and smiling at the camera.

"Chen Mo, how's the abstract algebra assignment coming along this week?" Zheng Mingyang asked directly.

Chen Mo opened his notebook, which was filled with densely written derivations.

"I've gotten to the group theory section," he said. "I basically understand the definitions and examples, but..."

"But what?"

"I'm thinking about a question."

Chen Mo paused for a moment, then said, "The fundamental theorem of homomorphisms for groups states that G/kerφ ≅ imφ. Can this theorem be generalized to rings?"

If φ is a cyclic isomorphism, then is R/kerφ ≅ imφ a cyclic isomorphism?

Zheng Mingyang and Zhao Yiming were both stunned.

"You've only been looking at it for a week, and you're already thinking about ring homomorphisms?" Zhao Yiming almost spat out his tea.

"Uh... I saw that the book mentioned rings later on, so I flipped back to the beginning."

Chen Mo scratched his head. "If it's not right, then pretend I didn't ask."

No, that's a very good question.

Zheng Mingyang took a deep breath. "This generalization is correct. As long as kerφ is an ideal of the ring, then the quotient ring and the image ring are isomorphic."

He paused, then couldn't help asking, "You really haven't studied abstract algebra before?"

"Really, no."

Chen Mo said sincerely, "I only started reading it after you gave me the book last week. When I got to the third chapter, I felt that the structures of groups and rings were very similar, so I tried to push them forward a bit."

Zheng Mingyang and Zhao Yiming exchanged a glance across the screen.

This intuition, this ability to draw inferences from one instance to another, is not taught; it is innate and ingrained in one's mind.

"Okay, then we'll deviate from our plan today."

Zheng Mingyang made a quick decision: "Tell me everything you've read this week, from beginning to end. I want to hear your understanding."

Chen Mo was not intimidated. He opened his notebook and began to speak.

"A group is a set plus an operation that satisfies closure, associativity, identity, and inverse."

"The simplest example is the addition group of integers, where the identity element is 0, and the inverse of each number is its opposite."

"The symmetric group S_n is the set of all n-ary permutations. It is not a commutative group because the order of permutations is not necessarily the same as the order of permutations."

He spoke clearly and logically, occasionally even giving his own examples.

Zheng Mingyang became increasingly alarmed as he listened.

It's not because the content is particularly advanced; it's all first-year undergraduate material.

It's because Chen Mo's way of understanding is not rote memorization at all, but rather something that grows from his very bones.

When he talks about groups, he starts from the concept of symmetry, rather than from the definition.

He blended abstract structures with concrete examples, making his presentation vivid and engaging.

"I have a question."

Chen Mo suddenly stopped. "The book says that if a group G acts on a set X, then the size of the orbit is divisible by the order of the group. I understand that, but I don't know what the use of this conclusion is?"

"This is so useful."

Zheng Mingyang laughed, "Do you know Burnside's lemma? It's used for counting."

For example, if you use n colors to color the six faces of a cube, how many different ways are there to color them?

If rotations are ignored, the result is n^6, but if you consider rotations as group actions, you can use Burnside's lemma to calculate a completely different coloring.

"I see."

Chen Mo's eyes lit up. "So a group is a mathematical language of symmetric operations."

"Yes! You've grasped the essence."

Zheng Mingyang was somewhat excited, "Many students study the entire textbook but still can't grasp this sentence, but you will understand it in just one week."

Zhao Yiming silently took a sip of tea.

He recalled how he spent a whole month learning group theory to understand that a group is a symmetrical language, while Chen Mo figured it out on his own in a week.

People are more mad than people.

The discussion continues.

Chen Mo asked a few more questions, each one hitting the nail on the head and making Zheng Mingyang even more convinced of his judgment.

"Professor Zheng, I have another question."

"you say."

"In the book you gave me last week, you mentioned Galois theory. I flipped through it but didn't quite understand it. However, I roughly know that it talks about the relationship between field extensions and groups."

"Yes, Galois theory is one of the greatest theories in the history of mathematics. It transforms the question of whether a higher-degree equation has radical solutions into a group theory problem."

I have a guess.

Chen Mo's voice came through the screen, tinged with uncertainty: "If the Galois group of the domain extension is a solvable group, then the corresponding equation has radical solutions."

Conversely, if the Galois group is not solvable, such as a symmetric group of degree five or higher, then the equation has no radical solution, is that what you mean?

On the other end of the screen, Zheng Mingyang's pen fell to the table with a thud.

"you……"

His voice trembled slightly, "You've read this far in the book?"

"I only flipped through it, I didn't fully understand it."

Chen Mo frankly said, "But when you were talking about Burnside's lemma, it suddenly occurred to me that the correspondence is somewhat similar to the group acting on a field, and the invariant being the intermediate field?"

"Yes! Absolutely!"

Zheng Mingyang slammed his hand on the table. "The Galois correspondence means that there is a one-to-one correspondence between the intermediate field and the subgroup!"

Zhao Yiming leaned closer to the screen, his voice filled with disbelief, "Chen Mo, are you sure you haven't learned any of this before?"

"No." Chen Mo shook his head.

Zhao Yiming fell silent.

Zheng Mingyang was also deeply shocked. It took him a while to remember, "By the way, did you do the exercises I assigned this week?"

"I did it."

Chen Mo held the laptop up to the camera.

It's a full twenty pages long, with detailed steps for each question, and some questions even include two solutions.

Zheng Mingyang glanced at it, his brows gradually relaxed, then turned to shock, and finally to an emotion he hadn't experienced in a long time: ecstasy!

"These questions were selected from graduate-level problem sets."

He murmured, "He got them all right, and some of his solutions were even simpler than the reference answers."

Zhao Yiming added from the side, "He also managed to deduce the theorem of ring homomorphisms."

The two exchanged a glance, both seeing the same message in each other's eyes: this student must be accepted!

"Chen Mo," Zheng Mingyang said seriously, "I'll ask you one last question."

"Please speak."

Have you ever considered becoming a mathematician in the future?

There was a moment of silence on the other end of the screen.

Then, Chen Mo said something that surprised both professors: "I don't know."

"At first, I just didn't want to disappoint my parents and wanted to get into a good university. But as I learned more, I discovered that mathematics is really beautiful. Every time I understand a theorem, it's like seeing a ray of light in the darkness."

"So I won't limit myself now. Whether it's being a mathematician or an engineer, as long as it involves exploring the unknown, I'll enjoy it."

Zheng Mingyang was stunned.

He has taught many students, some for a good job, some for bringing honor to their families, and some for a genuine love of mathematics, but few can be as unrestricted as Chen Mo, simply following their curiosity.

Chen Mo has great ambitions, but can he control them?

Zheng Mingyang didn't know, but Chen Mo was still young and had plenty of room for trial and error.

"Very good." Zheng Mingyang smiled. "Then we'll teach you according to your curiosity. We'll answer whatever you ask, without following any system or order, just what you want to know."

"Really?" Chen Mo's eyes lit up.

"Really." Zhao Yiming laughed as well. "Anyway, with your speed, you can learn very quickly on your own. We're just here to offer some encouragement."

On the screen, the boy showed a bright smile.

The two professors smiled in front of the screen.