I Kidnapped An Alien Civilization

2021-07-07

Chapter 5 Thesis

Keep going! Li Mo clicked on the new task release.

New missions released! The horse-riding generals reappeared on the screen.

Task: A scholar who can’t write a paper is not a good scholar. Let’s publish a paper. juvenile!

Task Description: Please publish an academic paper in any academic journal or newspaper.

Quest reward: 3000 points, lottery once.

Assignment time limit: ten days

Write a math paper? Li Mo looked at the set of math problems on his desk and asked if he could write a paper by solving a math problem that no one has solved.

But where is it published? Li Mo turned on the phone to dial, and asked if he didn’t understand it was Li Mo’s consciousness as a scumbag in the past.

“Hello Zhang teacher, I’m your student Li Mo. I want to ask, I want to write a mathematics paper, I don’t know where to publish it.”

Li Mo called his math teacher. He had heard other teachers say that Zhang teacher had a very high level of mathematics, but he was assigned to teach in their school because of his unsophistication.

“Hello, Li Mo, what do you want to publish?” Zhang teacher thought he had heard it wrong. In his impression, Li Mo’s grades were mediocre, so how could he publish a paper?

“I would like to ask the teacher, where is the best place to publish a mathematical paper.” Li Mo repeated.

“Mathematics papers, generally speaking, “Mathematics Monthly” has more readers and is more credible. But it is very difficult to submit papers. I think it is better for you to publish it in “Mathematics for Middle School Students”, which is popular science. There are more classes, and the difficulty of submission is lower.” Zhang teacher explained in detail.

“By the way, what kind of math paper did you write?”

“Oh, I haven’t written it yet, I haven’t submitted a manuscript, so I’ll ask the teacher. “Li Mo obediently and honestly answered.

“No?? Li Mo! Are you playing Truth or Dare? Teacher’s time is also very precious!”

Beep.Beep.Beep.

Li Mo was a little confused when he saw the call that Zhang teacher hung up directly. He didn’t know how he made Zhang teacher angry.

It’s easy to know where to post. It is the most difficult question for a scholar to do and the most difficult to publish. The goal is set! Mathematical Monthly.

Li Mo took out the book of world puzzles. This book is a collection of all the puzzles in the world, including solved and unsolved ones. This book was written by Li Mo mother when he was in elementary school. Bought it for him at some point, and then shelved it.

Opening the title page, there is a passage from Einstein in the preface—one reason why mathematics is respected over all other sciences is because his propositions are absolutely reliable and indisputable, while other The science of is often in danger of being overturned by newly discovered facts. …Another reason why mathematics has a high reputation is that mathematics makes the natural sciences theorized and gives them a certain degree of reliability.

The fundamental reason why mathematics can be the foundation of other disciplines is that the results of mathematics are absolutely reliable and indisputable. No wonder the learning machine system needs me to upgrade the math level to Level 6 first.

The categories are lined with unsolved problems in the history of mathematics.

1.NP complete problem

Example: On a Saturday night, you attended a big party. Feeling cramped, you wonder if there is anyone you already know in this hall. The host of the banquet proposes to you that you must know the lady Rose in the corner near the dessert plate. It doesn’t take a second for you to glance over there and see that the host of the banquet is correct. However, without such a hint, you’ll have to look around the hall, looking at everyone one by one, to see if there is anyone you know.

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Generating a solution to a problem is usually much more time consuming than validating a given solution. This is an example of this general phenomenon. Similarly, if someone tells you that the number 13717421 can be written as the product of two smaller numbers, you may not know whether to believe him, but if he tells you that it can be factored into 3607 times 3803, then you This can be easily verified with a pocket calculator.

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It has been found that all complete polynomial nondeterministic problems can be transformed into a class of logical operation problems called satisfaction problems. Since all possible answers to this kind of problem can be calculated in polynomial time, people then wonder if there is a deterministic algorithm for this kind of problem, which can directly calculate or search for the correct answer in polynomial time? This is the famous NP=P? conjecture. Determining whether an answer can be quickly verified using internal knowledge, or whether it takes a lot of time to solve without such prompts, is seen as one of the most salient problems in logic and computer science, regardless of our dexterity in programming. It was stated by Steven Cocker in 1971.

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Programming? logic operation? computer science? ?

Li Mo is a little confused. Most of the mathematical knowledge used here has not been mastered.

Forget it, go to the next question.

BSD conjecture

2. Poincaré conjecture, any closed three-dimensional space, as long as all closed curves in it can be contracted into a point, this space must be a three-dimensional space Sphere

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The title of this question is incomprehensible. . next.

3. The Hodge conjecture asserts that, for a particularly perfect Space Type called a projective algebraic variety, the parts called Hodge closed chains are actually geometric parts called algebraic closed chains. (rational linear) combinations.

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He knows all the Chinese characters in the title, why can’t they understand them when they are connected together?

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This question does not know, this question does not understand, what does the title of this question mean? ?

Li Mo’s face is ugly, remembering that he is only Level 2 in mathematics, it is really too difficult to use high school knowledge to try to solve an unsolved problem.

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Those questions that cannot understand the name will be given up directly, and only those within the scope of high school mathematics will be selected. Li Mo speeds up the “page turning” speed.

Finally, he found a question that fits perfectly within the scope of high school knowledge.

Koraz conjecture, also known as 3n+1 conjecture, Kakutani conjecture, Hasse conjecture, Ulam conjecture or Syracuse conjecture.

means that for each positive integer, if it is odd, multiply it by 3 and add 1, if it is even, divide it by 2, and so on, and finally get 1.

The Collaz conjecture can also be called the “parity-to-even conjecture”.

In 1930, Collaz, a student at the University of Hamburg in Germany, had studied this conjecture, and thus obtained name.

“positive integer”, “even”, odd. Awesome, simple and totally understandable.

To get a positive integer, let this number be x. If the next number is odd, multiply it by three and add one, that is, 3x+1. If x is even, divide it Taking two, that is, x÷2, then this number will eventually become 1 through 4 and 2.

If the assumed number is 3, then it is 3×3+1=10, 10÷2=5, 5×3+1=16, 16÷2=8, 8÷2=4, 4÷2=2, 2÷2=1.

Li Mo checked the content of the question with a pen, and it was completely correct, but how to prove it?

Induction. . no.

Using the theorem to directly prove it. . . no.

Swish. . Swish. . Swish. .

A sheet of paper. . two sheets of paper. . Three sheets of paper. .

One hour. . two hours. . three hours. .

Get out a bottle of energy coffee, now is not the time to save.

It’s dawn. . it’s dark. .

It still doesn’t work! Or not!

He was a little discouraged, closed his eyes, and thought slowly.

It seems that the conventional problem-solving ideas are completely incomprehensible.

Isn’t there still a drop of inspirational water?

There is only one drop in the small bottle, which drips into the mouth and is a little sweet. .

It doesn’t seem to work. . It can’t be fake.

“Wait…I thought about…”, a flash of light suddenly flashed in my mind.

n is an even number, n/2 is an even number, …, always divided by 2 to 1; n is an even number, n/2 is an even number, until n is divided by 2 to the X power, it is an odd number. We denote n divided by 2 to the power of X as n, which can be equivalent to n being an odd number. (When it is even, the number must be decreasing)

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n is odd, n×2+n×1+1 2n+n+1, this must be even, (2n+n+1)/2 n+(n+1)/2, here There are two other cases, it is an even number, it is an odd number; if it is an even number, the cycle ① (the number keeps decreasing when it is an even number), until n+(n+1)/2 is an odd number.

Because: n is odd, and only if (n+1)/2 is even 1 n+(n+1)/2 can be odd.

n is odd, n+(n+1)/2 is odd, continue below:

n+(n+1)/2 is odd, ×2+×1+1 2n+n+1+n+(n+1)/2+1, 2n+1+(n+1)/4 is an even number, divide by 2 2+×1+1 2n+n+1+n+(n+ 1)/2+1

Continue two cases, if it is an even number, if it is an odd number, if it is an even number, cycle ①, ②, (the number is decreasing when it is an even number anyway)

, always Up to 2n+1+(n+1)/4 is odd. Transform to n+(n+1)+(n+1)/4

because: n is odd, n+1 is even, there is only one (n+1)/4 that is even, n +n+1+(n+1)/4 can be odd.

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n+2(n+1)+(n+1)/4+(n+1)/8 is odd, ×2+×1+1

2n+ 4(n+1)+(n+1)/2+(n+1)/4+n+2(n+1)+(n+1)/4+(n+1)/8+1

10n+8+(n+1)/8, for even numbers, divide by 2 5n+4+(n+1)/16

n+4(n+1) +(n+1)/16

Infinite loop until (n+1)/2 gets x power=1

The proof is complete.

For each positive integer, if it is odd, multiply it by 3 and add 1, if it is even, divide it by 2, and so on, and finally get 1. This conjecture is completely correct.

Li Mo put down the pen in his hand and closed his eyes, he felt the storm of wisdom in his mind tumbling, a kind of power in the depth of one’s soul slowly awakening.

Looking at the alarm clock, he hasn’t slept for 74 hours. It was dark in front of my eyes, and I fainted on the bed, with a dying consciousness “I still have papers to write…”

(end of this chapter)