The Science Fiction World of Xueba

The mathematical community once circulated a sentence: How important is Einstein to physics, and how important is Grothendieck to mathematics.

In the field of modern algebraic geometry, Grothendieck is a well-deserved pope.

Grothendieck's mathematics has always been known for its arduousness, because he hardly considers specific examples, but from the perspective of abstraction as much as possible, thinking about the grand mathematical structure that governs a mathematical problem.

Far Abelian geometry is the magnificent framework left by Grothendieck in his posthumous Draft Programme, but unfortunately he has not yet rushed to fill it with flesh and blood, and the greatest mathematician of the twentieth century is living in a stray He passed away.

Xin Yueyue newly developed Grothendieck's theory of far Abelian geometry, and in 1996 proved the special case of a far-Abelian geometry proposed by Grothendieck in the Draft Program, thereby gaining popularity in the international mathematical community.

That's why he was invited to the 1998 International Congress of Mathematicians.

十几 In 2012, more than a decade later, Mochizuki developed a generalized theory of Teichmuller geometry on the basis of Far Abelian geometry to prove the ABC conjecture.

Unfortunately, this theory is just like its name. It is written in an alien language. It is highly abstract and difficult to get started.

加上 Plus a variety of concepts, complex logic system.

导致 This has led to the failure of the mathematical community to verify Mochizuki Shinichi's theory for many years.

Even later, the German scholar Peter Schultz and the German number theorist Jacob Stix spent months simplifying the article of Mochizuki Shinichi, and pointed out that there were loopholes in Mochizuki Shinichi's thesis.

But Mochizuki immediately retorted that there was a problem with their simplification, and the two sides were engaged in a war of words, and no one could persuade the other.

If in the real world, Pang Xuelin is afraid to spend years studying Far Abel geometry and Mochizuki Shinichi's generalized Teichmuller geometry theory, and then verifying that the ABC conjecture is correct.

After all, doing this kind of confirmatory pure number research is a difficult task, and no matter what the result, the verifier won't get any benefit.

But in Mars rescue the world, he has time and energy.

Uh ...

For the next time, Pang Xuelin devoted himself to the research of Far Abelian geometry and generalized Tichmuller geometry theory.

理论 This theory is abstract and obscure and difficult to understand. Pang Xuelin can faintly feel the grand mathematical structure hidden behind this theory.

Therefore, in addition to eating, sleeping, and completing basic daily tasks, Pang Xuelin reads, thinks, and researches almost all the time.

Even when he was connected with the earth, in addition to some words like "um" and "oh", the reply became shorter and shorter, and the time interval became longer.

的 The expert team on the earth quickly discovered Pang Xuelin's anomaly. He reminded Pang Xuelin several times and asked psychologists to intervene. Unfortunately, the two sides were separated by tens of millions of kilometers. Pang Xuelin had no time to deal with them.

Xi Pang Xuelin became more and more silent and more and more time for thinking.

I eat, work daily, and sleep as if it were a mechanical act. For the rest of the time, he reads about the new works of Mochizuki and thinks about the rest.

His beard was sour, his body was sour, but he didn't notice it.

With the exception of harvesting potatoes every three months, replanting the next batch, and doing some basic inspections of the habitat, he devoted all his time to research.

He deduced day and night, chewed up understanding of Mochizuki Shinichi's works, and the manuscript paper on the table became thicker day by day. He understood Far Abel's geometry and the generalized theory of Teichmuller's geometry proposed by Mochizuki Shinichi. It is gradually deepening.

But I don't know why. The more I study, the more Pang Xuelin gets confused by many complicated concepts.

As Tao Zhexuan said, Mochizuki Shinichi further complicated the concepts proposed in Far Abelian geometry, but did not put forward some new thinking that touched on the essence of mathematics.

This made Pang Xuelin faintly feel that Mochizuki Shinichi might be on a wrong line.

But one thing is certain, using Far Abelian geometry, it can indeed show the similarity between the addition structure and the multiplication structure, and the core of the ABC conjecture is related to these two issues.

I just think that Pang Xuelin always solves this problem with the existing Far Abel geometry framework.

Something new must be added to this framework.

Maybe the original idea of ​​Xinyi and Pang Xuelin was the same, so he developed the generalized Teichmuller theory on the basis of Far Abelian geometry.

Unfortunately, what he added is not convincing.

If I want to prove the ABC conjecture, I am afraid that I have to be the same as Mochizuki Shinichi, and I have to propose a new theoretical system.

But this is too difficult, Pang Xuelin has no clue.

Xun just as his research was in trouble, on this day, a slight vibration from outside the habitat made Pang Xuelin sober in thought.

He quickly put on the EVA spacesuit and came to the outside of the cabin, and found that a cylindrical spaceship about 20 meters long and about 5 meters in diameter appeared one kilometer away from the habitat.

的 The billowing smoke and dust inspired by the spacecraft's engine swept towards the perch, and Pang Xuelin then came back to himself: "This is ... the second supply has arrived?"

He hastily returned to the habitat, ready to confirm with the earth.

Open the communication system of the perch and a series of characters appear on the computer screen.

Day 792 Mars.

[16:20] JPL: Pang, a new supply spaceship is expected to arrive on Mars in twenty days. Please be prepared.

【19:25】 JPL: Pang ~ www.readwn.com ~ Please reply when you receive it.

Uh ...

Day 793 Mars.

[9:45] JPL: Pang, did you go to the mini-research again? The expert team does not recommend you to do this. If you do not contact the outside for a long time, it will easily lead to a lack of language skills. If you see the message, please reply as soon as possible .

Uh ...

Day 798 Mars.

17 [17:30] JPL: Pang, today the satellite observed that you had an EVA, and I hope you are all safe.

Uh ...

Day 808 Mars.

[8:30] JPL: Pang, the supply spacecraft will land on the Asidaria Plain in four days. Please reply as soon as you receive the message.

Uh ...

Day 812 Mars:

[9:12] JPL: Pang, this is Watney. The supply ship landed today, I hope you are all safe.

Uh ...

Xi Pang Xuelin watched for a while and thought for a while before typing the reply on the keyboard.

[14:25] Habitat: I'm really sorry, I have been thinking about something during this time, so the response is a bit slow. Don't worry about me. I live well on Mars, and I am satisfied with my life now. In the next few days, I will clear out the supplies of the supply tank as soon as possible. If there is any task arrangement, I can directly send the relevant task log. In addition, Watney, I am glad to hear from you that you have said hello to Colonel Lewis on my behalf.

[14:39] JPL: My God, Pang, you are finally online. We are all worried that you will go into the devil. It is really good to know that you are okay. If you can, I hope you can report peace every day.

[15:08] Habitat: I try my best, I'm working on some things during this time, it's the most important moment, so sorry ...