dognovel Chapter 9 Proof of the Collatz Conjecture: Outline of Required Core Mathematical Tools
Chapter 9 Proof of the Collatz Conjecture: Outline of Required Core Mathematical Tools
"You're asking for an exorbitant price!"
The girl, who was in advanced mathematics, stared wide-eyed, her face filled with regret at being extorted.
"Absolutely impossible, don't even think about it!"
"Which one... a complete one won't do, how about some fragments?"
With the mindset of "whether there are any good deals or not, I have to get something out of it," An Yi tried to bargain.
"Fragments?"
The girl, who was studying advanced mathematics, fell into deep thought.
"Yes, yes, it's just fragments. Anyway, I wouldn't understand it even if you gave me the complete one, so I'll just collect some fragments first. Maybe I'll be able to piece them together into a complete one later?" An Yi coaxed.
"Hmm...it's not that we can't consider it...but we can't specify, you know, it has to be random!"
As the calculus girl spoke, she glanced around nervously, as if worried that someone might overhear what she was saying.
"I'll secretly catch you once. Whatever I catch is what I get, no take-backs!"
Why does this girl give off the vibe of secretly taking things from home and siding with outsiders?
What? So I'm the one who took the benefits? Oh well, taking things from home is fine, and it's even better if you side with outsiders more!
"Okay, okay." An Yi smoothly chose to stop while she was ahead.
So he watched as the advanced mathematics began to operate—the girl continued to look around suspiciously for a long time, and then grabbed at the air with lightning speed!
There were no cool special effects or extraordinary phenomena in the whole process. It was as if the calculus grab simply grabbed the air. But when she handed her fist to An Yi, said "Here" and opened her palm with her palm facing up, An Yi found that there was a melon seed in her palm... a melon seed kernel.
Golden sunflower seeds!
"What is this, magic?" An Yi was stunned.
"Oh? Not bad luck, you actually got a gold one... Do you want some or not? If not, fine!" Gao Shu was a little surprised to see the gold melon seed kernel, and then glared at An Yi in annoyance.
There was no indication that he intended to pull his hand back.
"Eat, eat, eat..."
As An Yi spoke, she carefully picked up the golden melon seed and put it in her mouth.
There's no need to chew, because the golden melon seed, once it enters your mouth, transforms into a warm current that rushes straight to your brain!
In an instant, An Yi experienced for the first time what it meant to have his brain "shocked." Knowledge seemed to have a real presence as it flooded into his mind, even bringing a rather real impact!
The impact wasn't very strong, so it didn't cause any substantial damage to his brain, but it made him feel dizzy and disoriented, and he was about to lose his balance and fall to the ground.
Fortunately, a pair of warm hands pressed on his temples and gently massaged them. The massive amount of information was straightened, arranged, and neatly laid out like threads... Several seconds later, An Yi finally managed to recover.
He stared blankly at the girl rubbing his head, and the first thought that came to his mind was that he wished time could stand still at this moment.
"Don't bite off more than you can chew, now you know? It's not that I don't want to give you good things, it's that you can't handle them! Don't you understand the saying 'the weak can't absorb too much'? Be careful your head doesn't explode like a watermelon!"
Seeing that he had finally calmed down, the advanced calculus teacher let go of him, and even gave him a scare.
"I understand it perfectly!"
An Yi nodded repeatedly, even subconsciously controlling the amplitude of his nods to be very small, because he felt that his brain had become a well-smoothed mass, and it was just a matter of shaking it a little more...
"Try going through that information first; it will make you feel much better," the calculus instructor advised him.
An Yi followed the instructions and began to try.
The information flooding into his mind was so vast that even with the help of advanced mathematics, he still found it difficult to process for a while.
However, after much effort, he finally found the source of that massive amount of information, which was the title of the information contained in that "golden melon seed kernel".
[Outline of Core Mathematical Tools Required for the Proof of the Collatz Conjecture]
The Kolas conjecture? What kind of conjecture is this? I've never heard of it before.
When An Yi first saw the title, this was his thought. But when he saw the "Outline of Required Core Mathematical Tools" that followed, he couldn't hold back anymore.
You mean, a jumble of information that almost turned my brain into mush is just an outline of the mathematical tools needed to prove a conjecture? What's an outline? It's a table of contents plus a brief outline!
These things alone contain such a huge amount of information, so what exactly is this Kolas conjecture?
"In any case, it's definitely not some obscure 'wildcat conjecture.' It's just that I'm too ignorant about mathematics, so I haven't heard of it, right?"
With this in mind, An Yi continued reading.
The Kolatz conjecture, also known as the 3x1 conjecture, the hailstone conjecture, or the Kakutani conjecture, states that for any positive integer, if it is even, divide it by 2; if it is odd, multiply it by 3 and add 1. Repeating this process on the result will always return 1.
"It seems a bit simple?" An Yi thought to himself subconsciously.
This conjecture is renowned in the mathematical community for its simple formulation yet extreme difficulty in proving. The famous mathematician Paul Erdős once commented that "mathematics is not yet ready for this type of problem." The renowned scholar Guy, when introducing this problem, titled it "Don't Try to Solve These Problems."
An Yi honestly chose not to express his opinion any further.
Although he didn't know Paul or had never heard of Guy... it's clear that their assessment of this conjecture wasn't an exaggeration, but rather a realistic one.
This is like hearing that someone stole a 30-ton steel coil from a construction site. You ask, since it was discovered, why didn't anyone chase after them? Then someone releases the surveillance video, and you see, wow, that person just picked up the steel coil and ran away!
That's terrifying.
Composing himself with a sense of awe, An Yi cautiously chose to continue sorting through the information.
This outline does not provide a complete proof of the Collatz conjecture, but rather lists the new core mathematical tools necessary for proving the conjecture, divided into four parts: conceptual objects, theoretical framework, methodological techniques, and symbolic language.
[Before you begin reading this outline, please ensure that your ability meets the basic requirements (≥5), otherwise there is no need to waste your time.]
[Testing your [mathematical thinking ability] and [mathematical logic ability] to see if they meet the basic requirements...]
[Detection complete. Data temporarily archived. Please improve your skills before viewing.]
An Yi snapped out of her daze and realized what had happened.
In short, he passed a "sanity check," and then...
Failed.
Damn it, the essence of mathematics really is Cthulhu! My spiritual vision is insufficient; I can't even understand it!