The Science Fiction World of Xueba

There used to be a saying in the mathematics circle: as important as Einstein was to physics, Grothendieck was as important to mathematics.

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

Grothendieck's mathematics has always been known for being difficult, because he hardly considers specific examples, but starts from the most abstract point of view to think about the grand mathematical structure behind a certain mathematical problem.

Far Abelian geometry is the grand framework left by Grothendieck in his posthumous work "Draft Programme", but it is a pity that the greatest mathematician of the twentieth century lived in isolation before he could fill it with flesh and blood. passed away.

Shinichi Mochizuki developed Grothendieck's Far Abelian geometry theory, and in 1996 proved a special case of the Far Abelian geometry conjecture proposed by Grothendieck in the "Draft Program", thus becoming famous in the international mathematics community.

This is why he was invited to the 1998 International Congress of Mathematicians.

In 2012, more than ten years later, Mochizuki developed a generalized Teich-Miller geometry theory on the basis of Far Abelian geometry to prove the ABC conjecture.

It's a pity that this set of theories is just like its name, it seems to be written in an alien language, it is highly abstract, and it is difficult to get started.

Coupled with a large number of concepts, a messy logical system.

As a result, the mathematical community has been unable to verify Mochizuki's theory for many years.

Even later, the German god of learning Peter Schulz and the German number theorist Jacob Stix spent several months simplifying Mochizuki Shinichi's paper and pointed out that there were loopholes in Mochizuki Shinichi's paper.

But Shinichi Mochizuki retorted immediately, thinking that there were problems with their simplification, and the two sides fell into a war of words, and neither could persuade the other.

If it were in the real world, Pang Xuelin might not have the heart to spend a few years learning Yuan Abelian geometry and Mochizuki Shinichi's generalized Teich-Miller geometry theory, and then verify whether the proof of the ABC conjecture is correct or not.

After all, it is a thankless task to do this kind of confirmatory pure number research, no matter what the result is, the verifier will not get any benefits.

But in the world of The Martian, he has plenty of time and energy.

...

In the following time, Pang Xuelin devoted himself to the related research of Far Abelian geometry and generalized Teich-Miller geometry theory.

This theory is abstract and obscure, and it is 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 contacting the earth, in addition to sending some words such as "um" and "oh", the replies became shorter and shorter, and the time intervals became longer and longer.

The expert team on Earth quickly discovered Pang Xuelin's anomaly. They reminded Pang Xuelin several times and asked psychologists to intervene. Unfortunately, the two sides were separated by tens of millions of kilometers.

Pang Xuelin became more and more silent and had more and more time to think.

Eating, daily work, and sleeping seemed to be mechanical actions. In the rest of the time, apart from reading Mochizuki's related works, he used the rest to think.

He was unshaven and smelly all over, but he didn't seem to notice it.

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

He deduced day and night, chewed and understood Mochizuki Shinichi's works, and the manuscript paper on the table became thicker day by day. It is also gradually deepening.

But for some reason, the more he studied, the more Pang Xuelin was troubled by the many complicated concepts in it.

As Tao Terence said, Mochizuki further complicated the concepts proposed in Far Abelian geometry, but did not propose some new thinking that touches the essence of mathematics.

This made Pang Xuelin faintly feel that Mochizuki Shinichi might have gone on a wrong route.

But one thing is certain, the use of far Abelian geometry can indeed show the similarity of the addition structure and the multiplication structure, and the core of the ABC conjecture is related to these two problems.

It's just that Pang Xuelin always feels that with the existing far-Abelian geometric framework, it may be difficult to solve this problem.

Something entirely new had to be added to this framework.

Perhaps Mochizuki Shinichi and Pang Xuelin had the same idea at the beginning, so he developed a generalized Teich-Miller 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 come up with a new theoretical system just like Mochizuki Shinichi.

But this difficulty is too great, Pang Xuelin has no clue.

Just when his research was in trouble, on this day, a slight vibration from outside the habitat made Pang Xuelin wake up from his contemplation.

He hurriedly put on the EVA spacesuit, went outside the cabin, and found a cylindrical spaceship about 20 meters long and about five meters in diameter, one kilometer away from the habitat.

The billowing smoke and dust generated by the spacecraft engine swept towards the habitat, and Pang Xuelin came back to his senses: "This is...the second batch of supplies has arrived?"

He hurried back to the habitat cabin, ready to confirm with the earth.

Turning on the communication system of the habitat cabin, a series of characters appeared on the computer screen.

The 792nd Martian day.

[16:20] JPL: Pang, a new batch of supply spacecraft is expected to arrive on Mars in 20 days, please make relevant preparations.

[19:25] JPL: Pang, please reply.

...

The 793rd Martian day.

[9:45] JPL: Pang, have you indulged in your research again? The expert panel does not recommend you to do this. If you do not communicate with the outside world for a long time, it is easy to cause loss of language skills. If you see the message, please reply as soon as possible .

...

The 798th Martian day.

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

...

The 808th Martian day.

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

...

812th Martian day:

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

...

Pang Xuelin looked at it for a while, thought for a while, and then typed a reply on the keyboard.

[14:25] Habitat: I'm really sorry, I've been thinking about something during this time, so the reply is a bit slow. Don't worry about me, I'm fine on Mars and I'm happy with my life now. In the past few days, I will clear out the materials in the supply cabin as soon as possible. If there is any task arrangement, I can directly send the relevant task log. Also, Watney, great to hear you're home, give my regards to Colonel Lewis and the others.

[14:39] JPL: My God, Pang, you are finally online. We are all worried that you are going crazy. It is great to know that you are fine. If possible, I hope you can report that you are safe every day.

[15:08] Habitat: I'll try my best. I'm researching something during this time, and it's at a critical juncture, so I'm sorry...