There is a saying in the world of mathematics that as important as Einstein is to physics, Grothendieck is as important as it is to mathematics.

In the field of modern algebraic geometry, Grothendieck is the Pope.

Grothendieck's mathematics has always been known for its difficulty, because he thinks about the grand mathematical structures that govern a mathematical problem from the point of view of the abstract possible.

Far Abelian geometry was the grand framework left by Grothendieck in his posthumous work, The Draft Program, but unfortunately before he could fill it with flesh, the greatest mathematician of the twentieth century passed away in solitude.

Shinichi Mochizuki developed Grothendieck's theory of far-abelian geometry, and in 1996 proved the special case of a far-abel geometry conjecture proposed by Grothendieck in the Draft Program, thus gaining fame in the international mathematical community.

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

More than a decade later, in 2012, Shinichi Mochizuki developed a generalized Tayhimüller geometry theory based on far-abelian geometry to prove the ABC conjecture.

Unfortunately, as the name suggests, this set of theories is written in an alien language, which is highly abstract and difficult to get started.

Coupled with a variety of concepts and a complex logical system.

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

Even later, Peter Schulz, a German scholar, and Jacob Stitch, a German number theorist, spent several months simplifying Shinichi Mochizuki's paper and pointed out that there were loopholes in Shinichi Mochizuki's paper.

But Shinichi Mochizuki immediately retorted, arguing that there was a problem with their simplification, and the two sides were locked in a war of words, and neither could convince the other.

In the real world, Pang Xuelin probably wouldn't have the heart to spend a few years studying Far Abelian geometry and Shinichi Mochizuki's generalized Teishmüller geometry theory, and then verify whether the ABC conjecture is correct or not.

After all, doing this kind of confirmatory pure number research is a thankless task, and the verifier gets little benefit regardless of the outcome.

But in the Martian world, what he has is time and energy.

……

In the following years, Pang Xuelin devoted himself to the study of far-abelian geometry and generalized Teishmüller geometry.

This theory is abstract and obscure, and it is difficult to understand, but 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 studies almost all the time.

Even when he was in contact with Earth, in addition to sending some words such as "um" and "oh", his replies became shorter and shorter, and the time interval became longer and longer.

The expert group on the earth quickly discovered Pang Xuelin's abnormality, reminded Pang Xuelin several times, and asked psychologists to intervene, but unfortunately the two sides were separated by tens of millions of kilometers, Pang Xuelin didn't have the time to deal with them at all, and they couldn't do anything with Pang Xuelin.

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

Eating, daily work, and sleeping seemed to have become mechanical actions, and the rest of the time, he spent the rest of his time thinking about it except for reading Shinichi Mochizuki's related works.

He had a scruffy beard and a sour body, but he didn't realize it.

He devotes all of his time to research, except for harvesting potatoes every three months and replanting the next batch, as well as doing some basic checks on the perch.

He worked day and night to deduce, chewing up and understanding Shinichi Mochizuki's writings, the manuscript paper on his desk became thicker day by day, and his understanding of Far Abelian geometry and Shinichi Mochizuki's generalized Teishmüller geometry theory gradually deepened.

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

As Tao Zhexuan said, Shinichi Mochizuki further complicates the concepts proposed in Far Abelian geometry, but does not propose some new thinking that touches on the essence of mathematics.

This made Pang Xuelin faintly feel that Mochizuki Shinichi was probably on the wrong route.

But one thing is certain, the similarity between the additive and multiplicative structures can indeed be shown in far-abelian geometry, and the core of the ABC conjecture is related to these two major problems.

It's just that Pang Xuelin always feels that with the existing far-abelian geometric framework, I am afraid that this problem will be solved.

Something completely 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 Teishmüller theory on the basis of far-abelian geometry.

Unfortunately, what he added was not convincing.

If you want to prove the ABC conjecture, I'm afraid you'll have to come up with a completely new theoretical system, just like Shinichi Mochizuki.

But this difficulty is too great, and Pang Xuelin has never had a clue.

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

He hurriedly put on an EVA spacesuit and came to the outside of the cabin, only to find that a cylindrical spacecraft about 20 meters long and about 5 meters in diameter had appeared a kilometer away from the inhabitation module.

The billowing smoke and dust excited by the spaceship engine swept towards the perching module, and Pang Xuelin came back to his senses: "This is...... The second batch of supplies has arrived? ”

He hurriedly returned to the perching chamber, ready to confirm with Earth.

Opening the communication system of the perching pod, a series of characters appeared on the computer screen.

792nd Martian Day.

[16:20] JPL: Pong, the new batch of supply ships is expected to arrive on Mars in twenty days, so be prepared.

[19:25] JPL: Pong, please reply if you receive it.

……

793rd Martian Day.

[9:45] JPL: Pang, are you sinking into the mini research again, the expert group does not recommend that you do this, if you do not contact the outside world for a long time, it is easy to cause a lack of language ability, if you see the message, please reply as soon as possible.

……

798th Martian Day.

[17:30] JPL: Pong, today the satellite observed that you did an EVA, I hope you are well.

……

808th Martian Day.

[8:30] JPL: Pong, the supply ship will land on the plains of Acydaria in four days, please reply as soon as you receive a message.

……

812th Martian Day:

[9:12] JPL: Pong, I'm Watney, the supply ship landed today, I hope you're all well.

……

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

[14:25] Perch: I'm really sorry, I've been thinking about something all this time, so the reply is a bit slow. Don't worry about me, I'm doing well on Mars and I'm happy with my life right now. In the next few days, I will clear out the supplies in the supply compartment as soon as possible, and if there is any task arrangement, I can directly send the relevant task logs. Also, Watney, it's good to hear that you're home, and to say hello to Colonel Lewis on my behalf.

[14:39] JPL: Oh my God, Pong, you're finally online, we're all worried that you're going crazy, it's really good to know you're okay, if you can, I hope you can report your safety every day.

[15:08] Perch: I'm trying, I'm working on something during this time, and it's a bit of a crunch time, so I'm sorry......