A genius? I just love studying.

Chapter 108 Condensed Matter Mathematics

17 p.m.
In Lin'an, at the Barbary headquarters, in the examination room,
Deng Leyan's hair was as messy as a bird's nest, his eyes were bloodshot, and his face was somewhat yellow.

To get a high score, he ate in front of the computer for eight hours straight, not wasting a single second, and only handed in his paper when the exam ended.

His efforts paid off. He answered the first three questions correctly and wrote out most of the process for the fourth question. However, he still had some problems with the final calculation. Unfortunately, there wasn't enough time, otherwise he could have gotten 20 points on the fourth question.

However, he also wrote out a lot of solutions and thought processes for questions 5 and 6. Although he didn't get the final answer, he should still be able to get some points for the steps.

Based on the calculations, I should be able to get over 80 points, and possibly even over 90.

Based on past experience, a score of 90 or above gives you a chance to win a silver medal!
Deng Leyan was very satisfied with the result.

Even if that person is very strong, they can only get a silver medal at most, right?

They might not even get a bronze medal.

He acknowledged that Chen Hui was very strong, but the requirements for depth of knowledge in the preliminary and final rounds are different!

Getting up, Deng Leyan walked out of the examination room with the other candidates and followed his coach Li Bin towards the hotel. Confidence returned to Deng Leyan's chest.

The next step is to prepare for the CMO position.

The CMO officially starts on July 10th, but will last for a week. There will be an opening ceremony on the first day, exams on the second and third days, and some activities in the following days, such as an awards ceremony and lectures on cutting-edge mathematics.

So they were to set off for the capital in early July.

This year's CMO summer camp was held at Yanbei University in Beijing.

Asai wants to win an award, and he can't slack off in CMO either. He's determined to win the gold medal, but what he wants to compete for is a perfect score in CMO and a spot in the IMO!

But these are all things for later.

Right now, all he wants to do is get back to the hotel and get some sleep.

……

On July 8th, at Chengdu Tianfu Airport, the power strips next to the charging seats in the waiting area were already full, connected to various chargers. The other end of the charger cables was connected to each passenger waiting for their flight, like embryos connected to a mother, drawing energy through the umbilical cord (charging cable).

Strangely, among these people, there was a teenager who was holding a stack of A4 paper, placed it on the table next to the charging socket, and was reading it seriously with a pen in his other hand, occasionally taking notes.

They were completely out of place.

"Liquid Tensor Experiment"!
Ma Jingtang, president of the Chengdu Mathematical Society, stood behind Chen Hui, staring blankly at the title of the paper.

The Liquid Tensor Experiment is a research project proposed by Fields Medal winner Peter Schultz and mathematician Dustin Clausen. It aims to unify the three major fields of geometry, functional analysis, and p-advanced numbers in mathematics through the "Condensed Matter Mathematics" project.

As a mathematician, Ma Jingtang was certainly aware of this famous paper that had been published three years earlier.

However, as a mathematician who did not study this field, Ma Jingtang could only understand the title of the paper.

Okay, he admits that even though he studies this field, he might not be able to understand it.

So, this little guy can understand it?
Looking at the stack of A4 papers that was already mostly flipped through, and watching Chen Hui diligently taking notes, Ma Jingtang felt a bit conflicted, because he couldn't even understand the notes himself...

He wanted to believe that Chen Hui understood, but it also seemed too absurd.

Mathematics is different from other disciplines. In other disciplines, as long as you're not too stupid, you can understand most papers. At least, scholars who study this field can understand them.

However, in mathematics, some cutting-edge research findings are so complex that no more than two people in the world can understand them.

This is why most professional mathematics journals have low impact factors.

If others can't even understand your paper, how can they cite it?

"An entirely English paper?"

"This guy is really good at pretending!"

In the crowd, Deng Leyan snorted and put away the "Lectures by Exam Setters" in his hand, clearly unconvinced.

Everyone else was reviewing for the CMO exam, but Chen Hui was the only one reading papers, which was really conspicuous.

He admitted that Chen Hui was quite talented, but he had heard that Chen Hui's grades in other subjects were not very good, so how could he understand the entire English paper?
Just as he expected, Chen Hui was having some difficulty reading this all-English paper; otherwise, he wouldn't have been struggling to fully understand it even after several days.

Putting aside the difficulty of the paper itself, Chen Hui had to translate some of the specialized mathematical terms into Chinese first, and then look up the corresponding explanations, and even the derivation of theorems and formulas, before he could understand them.

As a result, reading papers is naturally very slow and very difficult.

But the effect was undoubtedly enormous!
Your math level has improved from 2 (61%) to 62%.

Your English level has improved from 2% to 3% (Level 2).

Just as Chen Hui was slightly distracted, another comment popped up in front of him.

My proficiency has improved again!
Although this has become a common sight these days, Chen Hui couldn't help but feel a hint of surprise in his eyes.

Since I started reading academic papers, although my reading speed is extremely slow, my proficiency has improved very quickly, at a rate of almost 1% per day.

He finished his exam on June 29th, and that afternoon he downloaded the paper from ArXiv, printed it out, and started studying it. In just nine days, his proficiency has already increased by 9%, a speed he never dared to imagine before!
It's a pity that Asai's final results haven't come out yet; otherwise, he might have been able to get another free attribute point.

Actually, getting involved with this paper was a misunderstanding.

He originally planned to follow Fang Wen's advice and delve into the mathematics of condensed matter physics, so he searched for condensed matter mathematics online. The mathematics in condensed matter physics should be condensed matter mathematics, right?

However, it wasn't until he downloaded the paper from the renowned mathematical genius Peter Schultz and spent a day reading it that he realized that condensed matter mathematics and condensed matter physics were not entirely unrelated, but rather completely unrelated.

Logically, he should have pulled back from the brink at this point, cleared up the mess, and quickly gone back to study the mathematical knowledge in condensed matter physics.

But by the time he discovered it, his mathematical proficiency had already improved at a rate he had never witnessed before.

Since reading this paper can quickly improve proficiency, why not read it anyway? Let's get our math level to 3 first!
So he read it all in one go, and in nine days he actually managed to completely understand the paper.

Not only did I thoroughly understand it, but I also learned about all the related knowledge involved in this paper.

This was a learning method that Chen Hui had never experienced before, but he felt it was exceptionally good.

Before this, his studies always involved completing one area at a time. For example, when learning abstract algebra, he would follow the textbook from simple to complex, progressing from sets to group theory and then to rings and fields.

Just like building a house, you start with the foundation, taking all aspects into account. First, you gather all the materials needed to build the house (learning basic knowledge). Then, through problem-solving and thinking, you build a solid foundation from these materials, and then gradually build up the structure. This learning method is certainly sound; it's steady and reliable, the right path. A house built this way is undoubtedly the most solid, without any long-term problems. Once you reach your limit, you can continue to break through without even much effort, reaching heights that humanity has never achieved before.

However, this only applies to learning basic knowledge. If one continues to learn in this way, even a genius would never be able to learn all the knowledge.

He didn't even have time to learn all the knowledge step by step before his lifespan was exhausted.

Not to mention breaking new heights.

His approach to studying academic papers, if compared to building a house, is like this: regardless of whether the foundation is solid or not, he's determined to break through the sky.

First, set a goal, then find the materials you need. Once you find them, don't worry about how sturdy they are, just pile them on the ground. Don't worry about their potential, just pile them into a cone shape with a sharp point pointing to the sky. This way, you can break through to a new height in a short time.

Regardless of whether he can continue to rise, just tell me if he's caused a major disaster.

However, this learning method is not without its drawbacks. Many people may not have the opportunity to make a breakthrough, or you may be lucky enough to make a breakthrough once, but it is difficult to make a breakthrough again. In fact, because the foundation has been moved, if you want to rebuild a new building, you need to break the original cone and start from scratch, which is a very difficult process!

Everyone is aware of the drawbacks of doing this, but like a thirsty traveler in the desert facing a murky puddle, he is not unaware of the problems, but he simply has no other choice.

In the desolate wilderness of the vast desert, water is extremely scarce. Even if the puddle of water may harbor germs, one has no choice but to bend down and drink it in order to survive, even knowing that it may bring adverse consequences.

Of course, Chen Hui's current approach will not cause too serious consequences. He is still exploring within the known scope of the mathematical edifice. He only needs to fill in other parts later to solidify the foundation.

Time passed slowly. I closed the paper and tried to recall its contents in my mind.

Schultz and Clausen found that traditional mathematics’ fields of geometry, functional analysis and p-adducts are difficult to reconcile due to conceptual differences, and while the Langlands program attempted to unify number theory, algebraic geometry and group representation theory, it was still insufficient in its integration of broader fields.

To this end, they proposed condensed matter mathematics, attempting to reveal the deep connections between different branches of mathematics by redefining topology, and ultimately achieving a "grand unification" from geometry to number theory.

The key to condensed matter mathematics lies in redefining topology, which is the cornerstone of modern mathematics!

Traditional topology focuses on the continuous deformation of shapes, while condensed matter topology introduces more abstract mathematical objects, such as condensed matter space, to unify similar phenomena in geometry, analysis and other fields into instances under the same framework.

For example, the phenomenon of "approximate isomorphism" in different fields can be interpreted through condensed matter topology as a manifestation of the same mathematical structure.

The main content of this paper is to prove the core theorem 9.4 of condensed matter mathematics with computer assistance.

It provides new tools for solving long-standing mathematical problems; for example, it simplifies complex problems in p-adduct arithmetic and opens up new avenues for interdisciplinary research in number theory and geometry.

Interesting!
Chen Hui opened his eyes, feeling a sense of lingering enjoyment, much like the illusion of hearing beautiful music with its lingering melody.

However, he could sense that he had not fully grasped the paper yet, and there were still many parts that he only vaguely understood. This paper was beyond his current reach; he had merely jumped up to peek into that world.

Chen Hui didn't care, as long as he could improve his proficiency.

He still has plenty of time!
However, there's no need to obsess over condensed matter physics. You could look for simpler papers that you can understand on a tangible level, which might be more efficient for learning.

Of course, the mathematical knowledge of condensed matter physics that Fang Wen suggested should also be studied.

Room temperature superconductivity and controlled nuclear fusion also hold a fatal attraction for him.

Even if it's not for making money!
Behind them, Deng Leyan, who had been secretly complaining, suddenly frowned.

Seeing Chen Hui's focused expression, he suddenly felt calmer, and he was now somewhat wavering.

Perhaps, that guy really can understand it?

That focused expression can't be faked.

He calmed his chaotic thoughts and picked up "Lectures by Test Setters" again. No matter what others did, he had to get a gold medal in the top 60 at this CMO and then make it to the IMO!

"Alright, everyone, get your ID cards ready and get ready to board."

After an unknown amount of time, Ma Jingtang clapped his hands and said something to the contestants around him. Then a large group of people stood up from their seats and went to the boarding gate to queue up.

The CMO training starts on July 10th, but they need to report on the 9th. They go there a day early to adapt to the environment and strive to participate in the competition in the best condition and achieve good results.

The CMO is organized by provincial teams, and Chengdu Province is naturally organized by the Chengdu Provincial Mathematical Society.

Normally, this kind of thing wouldn't be Ma Jingtang's turn, but this year is different. He was feeling restless and decided to lead the team himself.

There were 30 contestants from Chengdu Province participating in the competition. In addition to their respective coaches and several staff members from the Mathematics Association, there were nearly 50 people. The group boarded the plane in a large group, taking up almost half of the economy class of the Airbus A330 wide-body aircraft.

After boarding the plane, Chen Hui took out a large, black-covered book from his bag, placed it on the tray table, and immersed himself in studying once again.

This is "Differential Geometry and Lie Groups" by the famous Japanese mathematician Shoichi Kobayashi. This book discusses fiber bundles and connection theory in depth, which is exactly the knowledge needed in condensed matter physics. Speaking of which, Fang Wen borrowed this book for Chen Hui from the Chengdu University Library.

Condensed matter physics mainly involves algebraic topology, category theory, and higher-order algebra. Category theory and higher-order algebra are exactly the areas that Chen Hui is good at, but he still needs to brush up on topology.

Topology is not only used in condensed matter physics, but it is also an indispensable part of condensed matter mathematics proposed by Peter Schulz. Topology has become an essential foundational language of mathematics today.

"Chen Hui, take a break."

Sitting next to Chen Hui, An Chengzhang reminded him with concern that he knew Chen Hui was prone to motion sickness, and who knew if he would get airsick. Studying was important, but ensuring he arrived at Yanbei University in good condition was equally important.

Zhang Anguo took leave to accompany his daughter to have surgery, so this time only An Chengzhang led the team from Rongcheng No. 2 Middle School.

Chen Hui was the only student from Rongcheng No. 2 Middle School to participate in the CMO, while An Chengzhang was essentially a one-on-one private coach!

Of course, An Chengzhang felt that he couldn't teach Chen Hui anything anymore; he could only act as his personal secretary...

"It's okay, I took motion sickness medication before boarding the plane."

Chen Hui turned around and smiled, then continued to immerse himself in the ocean of knowledge of topology.

An Chengzhang gave a helpless, bitter smile.

"Please fasten your seatbelt, straighten your seat back, stow your tray table, and keep the window shade open. For flight safety, please ensure that your mobile phone and all electronic devices, including those with flight mode, are switched off."

The next moment, the flight attendant, who was reading the announcement, stopped at Chen Hui's row and looked at Chen Hui, who was reading a book. "Sir, could you please put away your tray table?"

Chen Hui turned to look at the smiling flight attendant and reluctantly put away his tray table.

Furthermore, the cabin lights had already been dimmed, so there was no way to read the book at all.

(End of this chapter)