My subject turned into a beautiful girl

"I see!"

An Yi suddenly realized.

So it's because of the mechanism? Then it's true that no matter how high the value is, it's useless.

No wonder the math expert thought something was wrong, no wonder I couldn't get the answer even after calculating until my head was spinning!

At the same time, he was also curious, "Brother, how did you determine that?"

"Generally speaking, for any polynomial equation of degree five or higher, it is solvable unless the corresponding Galois group is solvable..."

Xia Qing paused for a moment, as if realizing something, and changed her words.

"Well, unless the coefficients have special relationships, such as being able to be multiplied by cross or factored into fourth degree or lower, or like x^5-a=0, which can obviously be solved directly, they can all be considered as having no radical solution."

She tapped the equation An Yi had listed with the tip of her pen.

"If you break this equation down, it's at least an eighth degree. And the coefficients were just randomly chosen from the graph you looked at earlier, so there's basically no way there could be any special relationship between them. It completely meets the requirements."

"Did the teacher actually teach this kind of knowledge in class?"

An Yi scratched her head, feeling a little embarrassed, thinking that she had probably missed it again while reading a novel or sleeping.

"...Actually, it wasn't taught by the teacher."

Xia Qing thought about it and felt that she needed to clarify the matter to avoid any unnecessary misunderstandings.

"This is the Abel-Ruffini theorem, which is university-level mathematics. I came across it while browsing miscellaneous books out of boredom. It also includes the Galois group corresponding to the equation, which is also at the university level. It's a bit complicated to explain, and you won't encounter any problems beyond the syllabus, so I think you only need to have a basic understanding of it."

"..."

An Yi remained silent for a long time, then clutched his chest, took a deep breath, and said in a heavy tone, "Big brother."

"Um?"

"I looked at it from left to right, but I couldn't see the word 'leisure' anywhere. The entire text is filled with the character 'scroll'!"

An Yi asked with great distress.

"You didn't actually read and study the legendary 'Advanced Mathematics' textbook like a miscellaneous book, did you?"

"Advanced Mathematics" is the most difficult college mathematics textbook that An Yi knows of. After all, judging from the jokes he saw online, many college students' "first time" was with "Advanced Mathematics".

"How is that possible?"

It was clear that An Yi's emotional appeal was quite effective, but Xia Qing still smiled and waved her hand in denial.

"I've never even read the book 'Advanced Mathematics'! Okay, let's get back to the function graph. Hmm, your idea is pretty good; adding the arc makes it look more like an eyebrow..."

This attempt to forcefully change the subject is so obvious it couldn't be more obvious! An Yi thought to herself.

However, he wasn't too surprised. As the "always number one in the grade," Xia Qing's math was at the level where the teacher wouldn't care if she slept in class, but if she looked up, the teacher would start to wonder if they had made a mistake. Getting a failing grade was extremely rare, so it was quite normal for her to have self-studied material beyond the curriculum.

The only sad thing is probably that "how can this person be smarter than me and also more stubborn than me?"

An Yi looked at the semi-transparent light screen—

Seeing you make a fool of yourself in math made me laugh, and I immediately felt much less angry.

[Additionally, she noticed that the knot you just took out couldn't be untied using conventional methods; it could only be pried open little by little with a needle. But untying it this way would damage the rope, and no matter how carefully you did it, or how well you preserved the surface, it would still be different from the original rope.]

Tell her that you've discovered something: whenever a knot is tied five or more times, this will always happen. It can only be completely untied by deliberately tying a slip knot or tying a knot four or fewer times.

[The mathematics department is very curious about the phenomenon you shared.]

Even if you can't explain why right now, it's still fun to learn this new way of doing math.

[Mathematics' favorability towards you +10]

[She thinks you're genuinely trying to repair your relationship with her, and she was also a little embarrassed when she deliberately saw you make a fool of yourself. Since it's almost time for evening self-study and you don't have time to eat, she's giving you a bag of toast as compensation.]

You have received—[a bag of ordinary toast bread]

[Is it safe to eat?]

I will always be a loyal supporter of mathematics!

At this moment, An Yi had only one thought in his mind.

Of course, he then added another sentence.

I will always be my brother's most loyal younger brother!

An Yi's earlier sadness vanished, replaced by joy.

It's a good thing that my older brother is both smart and cunning; the smarter and more cunning the better!

If it weren't for this, how could I possibly know about the Abel-Ruffini theorem now?

The fact that such a generous reward was given simply because the application conditions were known, without even understanding the underlying principles, demonstrates the immense significance of this theorem!

Of course, this also made An Yi realize that obtaining the full reward was impossible at this stage. It would require a lot of prior knowledge, much like how insufficient attributes such as [Strength] and [Agility] in a game prevent one from equipping a high-level weapon.

I'll investigate this privately later. It's better not to ask rashly now, lest my older brother misunderstand and think I'm being unrealistic... An Yi carefully considered his options.

Such caution is quite necessary.

Anyone who has gone to school can clearly understand how precious a teacher is who is highly skilled and can explain knowledge in an easy-to-understand way.

The eldest brother is undoubtedly such a person; even a casual remark can bring him great benefits.

This is an important person; they must be treated with the utmost respect!

At the same time, he also chose to consume the reward he had just received.

When playing games, An Yi is the type of player who hoards items, usually keeping them in the warehouse to gather dust rather than using them.

Right now, as long as you use the items, you can convert them into permanent combat power. As the saying goes, "Money doesn't leave, it just changes its way of being with you." In this situation, even if you hoard some items, you should go on a spending spree.

You consumed [a bag of ordinary toast bread]

Your memory ability has been greatly improved! Duration: Six hours.

Another exceptionally comfortable feeling flooded his mind. Unlike before, this feeling made An Yi's brain feel refreshed, as if "the top of his head had been opened to dissipate heat."

Calculate cookies, memorize bread?

He noted down the effects of these foods while listening to Xia Qing continue.

"...This equation is too high a degree. The PLOY mode on this type of Casio graphing calculator is a polynomial mode, which can only solve equations of degree six at most. So we need to switch to the SOLVE function to find an approximate solution using a numerical method..."

Upon hearing this, An Yi suddenly had a thought.

From the moment he realized his elder brother was a benefactor, he kept thinking about one question—

How can I get my older brother to teach me more good things?

Although An Yi verbally calls Xia Qing "Big Brother" and refers to himself as "Little Brother," in reality, they are just ordinary classmates.

Given this premise, occasionally helping with a few problems, teaching a study method, and even lending her an advanced graphing calculator is already more than enough. Helping with anything more… let alone whether Xia Qing would be willing, An Yi himself would feel embarrassed to waste her precious time and energy.

Being persistent and clingy doesn't look good, does it?

Therefore, the key to this problem is how to make the older brother feel that it is "worth it"!

money?

For An Yi, pocket money was something she had only ever heard of but never actually received.

There was no such thing as a secret stash of New Year's money. Every year, the red envelopes he received during the Lunar New Year would be confiscated under the pretext of "Mom will keep them for you." The money he spent on internet access was saved from his food expenses.

Besides, even if he had money, it wouldn't matter; her older brother had never been short of money. She didn't know if her parents gave her pocket money or not, but she couldn't possibly spend all the scholarships she received publicly!

people?

My older brother likes women but not men. Even if I went to Thailand now, not to mention where I would get the money for travel expenses, I wouldn't have enough time!

After thinking about it carefully for a while, An Yi still couldn't come up with a feasible answer.

It was only at this moment that he suddenly realized that he didn't necessarily have to make his older brother feel that it was "worth it," but he could also make his older brother "interested"!

Emotional value counts as value too!

Isn't your older brother just bored during evening self-study?

If they become interested, they might be willing to teach for a longer period of time!

As for how to get his older brother interested... he actually had a ready-made solution.

An Yi looked at the stuck equation.

At first, he used purely algebraic calculations to deduce the result. Based on the Abel-Ruffini theorem he had just learned, he knew that this was an attempt to make a non-existent brick fly by force, which was impossible.

If we switch to numerical methods... well, numerical methods, as the name suggests, are they simply about directly substituting numerical values ​​to find an approximate solution? An Yi guessed.

In this way, his improved "numerical power" will finally have a place to be used!

For him, simple substitution and calculation were incredibly easy. Even with such complex equations, the difficulty was no different from solving 1+1=2.

Moreover, by using the patterns on the CASIO graphing calculator, he was able to estimate the approximate value of y when the center of the circle tangent to the two quadratic functions is x=2, saving him a lot of effort.

After determining the equations and calculation methods, An Yi simply left the calculations to his "instinct," just as before.

Substituting numbers, verifying, eliminating, moving on to the next number... the whole process was actually proceeding in an orderly manner, but because the calculation speed was so fast, there was no chance to display it. Therefore, what appeared in his mind was only the corresponding answer!

-0.8412362…

A string of numbers appeared in An Yi's mind, the digits after the decimal point kept jumping and extending, soon exceeding a hundred digits.

But writing it down directly would be too exaggerated, so he hesitated for a moment before putting pen to paper.

b≈-0.84124

"Huh?" Xia Qing was taken aback.

"An approximate value of b".

An Yi carefully considered her words, "I've looked at it, and I think this should be it. Is this level of precision sufficient?"

"If it's correct, then it's more than enough, after all, it's just drawing a diagram."

Xia Qing was somewhat confused; it was rare for her to experience such emotions.

"But... how did you figure that out?"

"That's how I figured it out."

An Yi offered the excuse she had prepared while he hesitated: "Sometimes, I'm more sensitive to numbers when it comes to calculations."

"You have... extremely sensitive skin? It's sensitive to a level of 10^-5!"

Xia Qing complained as she picked up the graphing calculator and started calculating. It took her quite a while just to input the data.

An Yi didn't understand what she was calculating, but she knew that after the results came out, the way she looked at her changed for the first time.

"Brother, please watch your eyes..."

An Yi's eye twitched slightly.

"You remind me of a monkey showing signs of evolving into a human, so it's quite amazing!"

"You really only glanced at it?" Xia Qing ignored An Yi's sarcasm.

"Um……"

"You sensed it?"

"right!"

With things having come to this point, An Yi had no choice but to stand firm to the end.

"What's your English name?" Xia Qing suddenly asked.

"Huh?"

Which argument is this based on?

An Yi was caught off guard, but still chose to answer honestly.

I don't have an English name yet.

"How about we name him Ramanujan An?"

The girl's bright eyes sparkled with a light that seemed to say, "That's interesting."

"With your talent, if you develop it further, you might one day be able to sit at the same table as Ramanujan!"

①: Niels Henrik Abel, if all mathematicians were ranked by their level of misfortune, he would certainly be in the top three.

After correctly proving at the age of 22 that a general quintic equation in one variable has no radical solution, he paid for the printing of his paper out of his own pocket. Because he was too poor, in order to reduce printing costs, he condensed the proof into a booklet of only six pages and sent it to Gauss.

As a result, because the booklet was so sparse, Gauss thought it impossible to prove a world-famous problem in such a short space (equivalent to someone handing you six A4 sheets of paper claiming to have proven Goldbach's Conjecture; anyone would think it was amateurish harassment), so he didn't even bother to open it and threw it into a pile of books. Others who saw the paper couldn't understand it because of its excessive brevity, so he didn't receive the recognition he deserved immediately.

At the age of 24, he proved a theory about algebraic functions, now known as Abel's theorem. His paper was sent to the French Academy of Sciences, where the secretary, Fourier, read the introduction and then entrusted Legendre and Cauchy with its review. However, Cauchy took the manuscript home and casually set it aside, forgetting to review it, and later completely forgetting about it until two years later when Abel died of tuberculosis, at which point the paper was rediscovered. The paper's value was then recognized and formally published, a full twelve years later.

②: Srinivasa Ramanujan, one of the most legendary mathematicians. He often claimed that the goddess Namakar gave him revelations in his dreams, enabling him to write down numerous mathematical formulas and propositions every morning upon waking. Many of these he himself never proved, but were later verified as correct by numerous mathematicians. His mathematical intuition is therefore considered one of the most mysterious and powerful in human history.