Could That Person Be Him?

"System, oh system... can't you give me something simpler?"

A purple treasure chest! He had thought it would contain something good he could use right away, like a crash-course knowledge card for some subject. Instead, it had given him a proof of a major unsolved conjecture?

It was like opening a chest in a game and getting a max-level legendary weapon, your eyes lighting up with excitement, only to discover you had to be level 100 to equip it when you were only level 10.

What a rip-off.

"Can't you give me a simpler conjecture?"

"Like, say... something on the level of the S itapan Conjecture."

The S itapan Conjecture was a problem in the field of reverse mathematics.

Qi Hao knew the name because a piece of astonishing news had recently appeared online: a fourth-year undergraduate at Central South University had independently proved a reverse-mathematical proposition concerning the S itapan Conjecture.

An undergraduate!

Had proved an open conjecture in the international mathematics community!

After the news got out, the entire academic world erupted.

Central South University had not only awarded the student a million yuan but also hired him directly as a researcher at the rank of full professor.

Although the S itapan Conjecture was also an open problem, its standing and difficulty in the mathematics community were nowhere near those of the Jacobian Conjecture.

"If you gave me something on the level of the S itapan Conjecture, I might be able to learn just enough to use it on the spot. A million yuan and a tenured position-that'd be a win. But how am I supposed to fully understand the proof of the Jacobian Conjecture with my current foundation?"

If he could understand it, organize it into a paper, and publish it, the result would be enough to go down in the history of mathematics.

Unwilling to give up, Qi Hao opened the proof. A red warning box popped up on the panel, completely blocking everything that followed: [Your current academic level has been detected as insufficient. You cannot view the subsequent content.]

[Note: You must possess sufficient prerequisite knowledge to unlock access!]

[Suggestion: Go read some books first. Don't be illiterate. The Soviet Union doesn't support illiterates.]

Qi Hao: "..."

It was restricted, too!

Still, he didn't think the system was being unreasonable. It was right: he really couldn't understand it as he was now.

A first-year student who hadn't even gotten his foot in the door of abstract algebra wanted to tackle the proof of a century-old conjecture in algebraic geometry?

What was that if not a fool's dream?

He was about to close the panel when the system displayed another message.

[Since Comrade's foundation is so weak, the system hereby recommends the following prerequisite reading list. Please study the books in order. Once you have mastered the relevant knowledge, you may gradually unlock the proof:]

[Recommended Soviet reading list (Jacobian Conjecture: prerequisite knowledge path)]

[Stage one (algebra fundamentals):]

① Kostrikin, Introduction to Algebra

② van der Waerden, Modern Algebra

[Stage two (introduction to commutative algebra and algebraic geometry):]

③ Shafarevich, Basic Algebraic Geometry

④ Zariski & Samuel, Commutative Algebra

[Stage three (advanced topics):]

⑤ Vinogradov, Elements of Number Theory

⑥ Gelfand, Lectures on Linear Algebra and Multilinear Algebra

[Note: All the above textbooks receive an optimal learning-effect bonus. Using textbooks outside the list will greatly reduce efficiency.]

[Keep it up, Comrade. The distance from illiterate to academic master is only six books :)]

Qi Hao looked at the uniformly Russian author names on the list and couldn't help getting a headache.

Six books.

All Soviet textbooks.

The distance from illiterate to academic master was only six books? System, you must have some misunderstanding about the word "only."

He searched for them online.

Pick any one of the six, and it was a fighter jet among the hardcore.

Kostrikin's Introduction to Algebra was relatively manageable. It was said to have been written based on Kostrikin's teaching experience at Moscow State University and was currently a standard textbook in its mathematics department. It was anything but some cheap, cobbled-together work.

As for Shafarevich's Basic Algebraic Geometry, that was a bible-level work in the field. Countless graduate students had read until they went bald without finishing it.

But to see the complete proof of the Jacobian Conjecture...

Qi Hao gritted his teeth.

He was doing it.

Surely his situation was better than Yitang Zhang's when he was working at Subway?

Full of passion, Zhang had poured more than a decade of his most precious youth into it when he couldn't see a future. What did Qi Hao have to fear?

At least he had the answer. He just couldn't understand it yet.

Qi Hao made up his mind.

If he couldn't understand it, he'd study until he could.

He had no classes the next afternoon, so he slung on his backpack and headed straight for the library.

He arrived at the mathematics shelves.

He scanned row after row: Qiu Weisheng's Higher Algebra, the Peking University mathematics department's Higher Algebra, Xiong Quanyan's Modern Algebra...

The selection of domestically published algebra textbooks was quite complete.

But he searched the entire foreign-language book section and found plenty of imported English textbooks, yet not a single Soviet textbook-not even a translation.

Qi Hao sighed and decided to settle for the next best thing. Since he couldn't find the books the system recommended, he'd make do with a similar textbook for now.

Math was universal, after all. Whether a Soviet or a Chinese person wrote the book, the mathematical theorems themselves wouldn't change.

He pulled an immensely thick classic Western textbook from the shelf, one widely used at universities in China and even Europe and America: David Dummit's Abstract Algebra, in translation.

"I choose you!" Qi Hao hugged the book, which was as thick and solid as a brick, and found an out-of-the-way seat by a window.

For the first ten minutes, Qi Hao read smoothly. But when he turned to chapter three and encountered concepts like quotient groups and isomorphism theorems, which truly began to test abstract thinking, his normally quick-running brain gradually felt as though it had been stuffed with a waterlogged sponge. It couldn't keep up.

The Western textbook's pages were full of dry definitions and derivations of lemmas. It was dull in the extreme.

After reading for over an hour, Qi Hao's brows were nearly twisted into a knot. He felt he recognized every word on the page, but put together, they became an indecipherable string of Martian text. Not only had he failed to build an algebraic structure in his mind, but the reading had also left him drowsy and yawning repeatedly.

Just as his head was about to crash down onto the book, something suddenly changed before his eyes.

[Comrade has been detected reading Abstract Algebra, a textbook not specified on the reading list (capitalist watered-down revised edition).]

[System analysis: This capitalist scholar's organizational logic, emphasis, and exercise design differ significantly from those of Soviet scholars. Studying with a non-recommended textbook is expected to reduce knowledge absorption efficiency by approximately 70%.]

He didn't understand why the system kept praising Soviet textbooks.

As far as he could see, there didn't seem to be much difference between textbooks.

Never mind. Since the system was talking them up so much, he'd better find one and take a look.

Qi Hao checked online. Kostrikin's Introduction to Algebra cost over thirty yuan, and buying all six books would cost over two hundred. That was a little expensive for him.

In the end, he decided to look for them at the provincial library on Saturday after tutoring Fang Jiaze. Its collection was more comprehensive.

On Friday, Qi Hao received a call from Fang Jiaxue. He learned that her whole family had to go out together on Saturday to take care of something, so the tutoring session was off for the time being. She asked whether they could arrange it for the following week.

Qi Hao agreed.

On Saturday, he went straight to the provincial library.

He found Kostrikin's Introduction to Algebra without any trouble.

How should he put it?

If the Western textbook he had read the night before was like an aloof math teacher who immediately threw a pile of definitions at you and said, "Read them if you want; get lost if you don't. If you can't understand them, that's your problem," then Kostrikin's book was like a patient but rigorous old Soviet professor.

He didn't start by telling you the axiomatic definition of a group.

He first told you why humanity needed the concept of a group.

The first example Qi Hao read concerned symmetry transformations of a square.

Rotate a square by 90, 180, 270, or 360 degrees, and add reflections across its diagonals and midlines. Together, these give you eight transformations. The eight transformations form a closed system of operations: perform any two in succession, and the result is always one of those same eight transformations.

That was a group.

Reading this, Qi Hao suddenly understood.

A group wasn't some abstract monster that had popped out of thin air. It grew out of concrete geometric operations!

He eagerly turned the pages.

What struck him even more was that Kostrikin's organizational logic was completely different from that of the Western textbook.

The Western textbook used a top-down deductive structure: definition → lemma → theorem → corollary. It was as though it were telling you, "This is how the world is. Just remember it."

Kostrikin's logic, on the other hand, used a bottom-up inductive structure.

He would first give you a concrete example, then guide you to observe the patterns hidden within it.

Next, he would ask whether the pattern could be generalized. How far could it be generalized? Where were its limits?

Finally, after following his train of thought all the way around, you would find that the abstract definition had naturally taken root in your mind.

It felt like burying a seed in the soil with your own hands, watering and fertilizing it, giving it sunlight, then watching it slowly sprout, put out branches, and blossom. When the flower opened, you wouldn't be surprised, because you had taken part in every step and could understand each one.

The Western textbook's approach was to put a plastic flower directly in front of you and say, "Look, this is a flower. Remember what it looks like."

You remembered it, all right, but you didn't know where its roots were, why it looked that way, or, even less, how it would change if its environment changed.

Besides the organizational logic, the exercise design also opened Qi Hao's eyes.

Kostrikin's exercises weren't mechanical problems you could solve by plugging in formulas. They were exploratory problems with graduated difficulty, guidance, and ideas behind them.

The exercises in each chapter were divided into several levels. Qi Hao even suspected that when Kostrikin wrote the book, he had asked himself: if a student had only this book and no teacher, could they learn on their own?

In other words, Kostrikin wanted students to be able to understand the book even while studying on their own.

What a grand vision!

It seemed the system really hadn't lied to him!

Qi Hao found two more books in one go and headed for the checkout desk.

"Excuse me, I'd like to borrow these three."

The librarian was a middle-aged woman wearing reading glasses. She glanced at the titles, then gave Qi Hao a surprised look.

"Kostrikin? Hardly anyone borrows this book. Don't you young people all read Artin these days?"

"Yeah, I read Artin before, but I didn't think it suited me," Qi Hao answered honestly.

The librarian shook her head. "Ah, hardly anyone reads Soviet textbooks. You'll come back and exchange it later."

Qi Hao didn't think there was any need to argue with her, so he nodded in agreement.

After checking out the books, Qi Hao stuffed the three thick bricks into his backpack and walked out of the library with the heavy bag on his back.

Heavy as it was, his steps were surprisingly light.

It was already past three in the afternoon when he got back to campus.

Qi Hao planned to go straight back to his dorm and dig in, using the mind-clearing, brain-strengthening pills to grind through his studies. But just as he reached the entrance to the mathematics school's teaching building, an excessively enthusiastic voice stopped him.

"Hey! Qi Hao!"

Qi Hao stopped and looked at the man.

He wore a plaid shirt washed slightly pale, its sleeves rolled up to his forearms. A stack of printed papers was tucked under his left arm, and he waved enthusiastically with his right hand.

"Long time no see! I haven't seen you since last time!"

Qi Hao looked at him in confusion and realized he apparently couldn't remember him.

Lately, his mind had been occupied entirely by mathematical derivations of all kinds. As for functions like facial recognition, those had deteriorated considerably.

Seeing how enthusiastic the man was, Qi Hao quickly made a mature adult judgment: pretend first.

"Long time no see!" Qi Hao greeted him with a smile, matching his enthusiasm without losing an inch. "What have you been busy with lately?"

That question was an all-purpose social remedy: it expressed concern, tossed the conversation back to the other person, and let him infer the man's identity from the answer.

"That project Old Wang gave me, what else? He's really pushing me to hurry." Liang Wenhao hadn't noticed that Qi Hao didn't recognize him.

"But speaking of which, I really have you to thank for last time. You said my approach was headed in the right direction, and I followed it through afterward. Sure enough, it worked! Although Old Wang still tore into me at the group meeting, saying my derivation in the middle wasn't rigorous enough, the final result was right, so he didn't say anything more."

Liang Tianhao then changed the subject, his expression turning a little subtle. "Oh, right. There's something I think I should tell you."

"What is it?"

"Aren't you writing a paper? Be careful."

"Hm?" Qi Hao was taken aback.

"Today on the mathematics Tieba-you know Tieba?"

Of course he did. He sometimes browsed the mathematics Tieba himself. How could he not know it?

When Qi Hao nodded, Liang Tianhao continued, "Someone posted there today, claiming that an undergraduate math major was suspected of academic misconduct in a paper."

"What kind of academic misconduct?" Qi Hao grew curious.

"They said the undergraduate cited some references in his mathematics paper, and an academic fraud exposer came forward and said he'd checked the references one by one and couldn't find them at all."

"Come to think of it, I think this undergraduate is from our university."

The more Qi Hao listened, the more he felt something was wrong.

Wait.

This person...

Could it be him?