"Algebraic topology and differential topology are undoubtedly the most meaningful in topology?" He Weier chewed on this sentence and couldn't help but nod: "It's kind of interesting - it's just that you dare to judge the whole of topology?"

"I'm making my own judgment in this field as an arithmetic. Pen ~ fun ~ Pavilion www.biquge.info "Wang Qi is neither humble nor arrogant.

"I'm in algebra topology, and I do have some problems. He Waier said: "Your thinking seems to be more focused on group theory and ring theory...... Ah, sorry, this was the first thing that came to my mind. My classmates and I have been researching this field for a long time, so this is the first thing that came to mind. ”

Wang Qi nodded, but he was slightly surprised in his heart.

Is it possible to guess the direction of this theory when you only have vague ideas......

The cohomology algebra comes from the algebraic topology, but it is higher in application than the algebraic topology. It is not only a milestone in the development of mathematics in itself, but also can penetrate into many fields of mathematics and promote the overall progress of mathematics.

This kind of powerful academic thinking will play an important role in many fields such as group theory, ring theory, and algebra theory.

And the mathematical tools that were born from this eventually pointed to the realm of physics.

One of the most notable achievements is the revelation of the symmetrical structure of gauge field theory.

And as we all know, in the era when the Lord and Tai Tian Zun intersected and the way of comparison was like the sky, He Weier had stayed in the Guiyi League for a long time. He also has a considerable understanding of the system of Tiange Xing, and wants to follow Tai Tianzun's ideas to complete the theory of "unified field".

However, he failed. At that time, he started with the concept of electric field and magnetic field of the Tiange Tiantu, and tried to replace them with electromagnetic potential and the corresponding high-order antisymmetric tensor, and then added it to the momentum-energy-spiritual tensor of gravity, and derived the field equation by pure arithmetic means.

It's just that this high-level monk of the Ten Thousand Methods Sect not only ignored the specific meaning of his own equation, but also ignored the possibility of constructing his own equation at all, and unfortunately chose the most difficult direction. After the Tian Yuan style has exceeded the fourth order, even the "conservation of spiritual energy" [spiritual power - conservation of energy] has lost its effectiveness - this obviously contradicts all theories at this stage. Eventually, he abandoned this erroneous theory.

However, this line of thinking is correct.

Wang Qi knew that as long as the cohomology algebra promoted the further development of group theory, the gauge groups in Ho Waier's equation could be generalized to the non-canonical groups, and an arithmetic model with practical significance could be introduced, that is, the standard model of the unity of strong and weak electricity, which was the basis of the Yang-Mills theory on the earth.

It's a step closer.

It was because of his understanding of abstract algebra that he put forward such a theory. And because of this theory, he and his fellow disciple Ai Ruoche have worked hard in this direction.

To be precise, the path Wang Qi is taking today is also based on this senior.

Wang Qi replied: "This is indeed a good direction. However, I don't think I'm going to be able to think about this specifics just yet. ”

He Waier said: "Yes...... Not interested in metaphysical algebra?"

Wang Qi shook his head: "This is a matter of 'wine, wine glasses, and small low tables'. ”

He Waier was shocked, and there was a strange light in his eyes: "Oh? 'wine', 'wine glass', 'small table'?

A monk sitting next to Zhao Qingtan was a little puzzled: "What is the problem? Senior He and Wang Qi are the ...... Is this going to drink? Drinking party?--Senior Brother Zhao, what's wrong with you?"

Zhao Qingtan said in a low voice: "This is a case of reckoning...... At the beginning, the arithmetic master was in charge of the song court at the beginning, mainly studying number theory, and only talked about the number domain for ten years. Ten years later, he studied geometry, read geometry books, and drew the law of heaven. For another three years, the lord said, "The dots, lines, and surfaces are small tables of wine glasses, and geometric propositions are all like ......"

"What is this...... "This monk is from a civilian background, and his talent is not very high, and he has recently worked hard to break through the sky, and he doesn't know much about this public case.

Zhao Qingtan, who was affiliated with the Geting faction, said in a low voice: "The master has studied geometry. That sentence is his understanding of geometry. Although the five methods of drawing the heavens are the basis of geometry, the geometric gods of 40,000 years ago did not define what is a 'point', what is a 'line', and what is a 'surface'. In the eyes of the ancient masters, these truths are self-evident. However, from the perspective of the arithmetic, this is not the case, and the points, lines, and surfaces also require strict arithmetic significance. In his opinion, there is no definition at all for the painting of heaven and the 'point, line and surface' in the geometry book, and there is no problem with changing it to 'small table with wine glasses'. ”

"Why the low table with wine glasses?"

"Maybe Lord Ximen just wanted to drink two cups at night?" Zhao Qingtan stared at Wang Qi and He Waier, and kept saying, "It's over...... Finished...... Even if you really want to do this kind of thing, you don't need to say it to your face......"

The Yuanshen Stage monk was still curious: "Is there anything wrong with this......

-- It's a big problem......

Zhao Qingtan almost squeezed out his voice: "Wang Qi, this is equivalent to saying that the Geting faction does not have a clear definition of these concepts - this is to say that the Geting faction is not good at the root." ”

He Waier didn't expect Wang Qi's tone to be so big. He pondered for a moment and asked, "Can you tell me what you think?"

"I'm not saying that there is a problem with the theories of your predecessors, but that some of the concepts of your predecessors have become blurred after the introduction of the new system. Wang Qi first corrected a little, and then said: "When my predecessors first took charge of the Song Garden, they mainly studied number theory, and there was a result of class field theory, and I was also thinking about how to clearly display the class field theory in the same tone and continue to promote it. Now ......"

What Wang Qi is talking about is also one of the most famous uses of cohomology algebra.

He Waier's eyes twitched.

He sensed something very vague. That kind of thing hasn't taken shape yet, but ...... It's beautiful.

What Wang Qi was talking about was exactly what he, a disciple of the Geting Sect, was familiar with.

Wang Qi spoke very quickly -- in fact, his current doctrine was only a sketch, and if he discussed it with others, he would not be able to finish it in three days and three nights. But if you just say it, it will be done in no time.

After Wang Qi finished speaking, He Waier looked at him deeply: "Good boy...... Wait a minute, I still have a couple of questions. ”

It can be seen that He Waier also has a certain understanding of Wang Qi's current progress. He didn't ask random questions, but every question was to the point. There are many things that must be involved in Wang Qi's theory after the future.

Soon, the faces of those who had communicated with Wang Qi changed one after another.

"We all felt that Wang Qi was just a beginner in this field...... But is he really a beginner in his current performance?"

Although in the Q&A just now, Wang Qi used ideas and conjectures to explain in many places...... But why, looking at his calm appearance, it seems like those are more than conjectures?"

Some people's hearts began to pound.

Wang Qi's thoughts have not been proven, so he said it openly...... If I prove it, it's all the specific direction ......of research!

Wang Qi's words brought out many problems. None of these issues are special or particularly difficult. They are closely integrated with the existing theoretical framework, and according to the "classification of problems" that Wang Qi once made (the speech he made when Wang Qi received the prize of the Taoist instrument, that is, the classification made by the Bourbaki school), these are "problems that produce general theories".

――If I go back now, write down these questions, and keep them for myself, wouldn't it be okay...... Going down in history?

More than one monk had a similar dark thought.

However, after seeing the expressions of He Waier and Wang Qi discussing, they dispelled this idea again.

Plagiarizing other people's ideas and research directions will be despised in today's Fa Immortal Dao.

Under the melon field and plums, it is still necessary to know and avoid suspicion. And now, these questions are all said by Wang Qi in front of He Waier. Unless one of them leans over and interjects right now, "Actually, I've thought about similar issues, and I think I should ...... them," the monk would inevitably think it was "plagiarism."

Disgusted by a monk of the Respite...... It's in the middle of it, and it can't be drawn.

In particular, the monk was also the leader of a strong academic faction. Although the Geting faction has inevitably declined because of Wang Qi, it is still the number one force.

If they were really remembered by He Weier for plagiarizing Wang Qi's ideas, they would face a lot of resistance for thousands of years to come.

And after dispelling their own ideas, more people have a ...... Indescribable shock.

――Is he really a beginner?

――Why are you a beginner too...... Wang Qi can see so much?

-- We can only have the idea of plagiarism for him......

In the midst of the exchange, the sun gradually sets,

Wang Qi stood up as usual and said, "That's all I can communicate with today." Feel free to do so, and if you still want to communicate, please come back tomorrow. ”

Just as Wang Qi was about to turn around and leave, He Waier shouted, "Wait a minute, Wang Qi." Can you talk about it alone?"

Wang Qi nodded, and the time and space around He Waier suddenly became blurred. Then, he and Wang Qi disappeared out of thin air.

At the same time, on the top of the mountain, He Waier looked at Wang Qi, shook his head and smiled bitterly: "Wang Qi, do you know what you are doing?"

Wang Qi said: "Study arithmetic. ”

"You're doing something very offensive. He Waier shook his head: "You understand, right?"

"After all, it was I who ruined the ideals of Xi's predecessors?" Wang Qi also sighed helplessly: "But this is not my intention. Nozomi is still one of the people I respect the most...... It's just that arithmetic is self-contained, and I just discovered it. ”

"I know. He Waier's tone was stern: "However, you actually continued to follow the master's train of thought back then. In the eyes of others, you are despising Master. ”

"That's not what I intended. Wang Qi said: "I like this idea so much, you can't help me use it, right? What I hope to get is not the form of symbols, but the structure of arithmetic hidden under equations and theorems......"

"Other people don't necessarily see it that way. He Waier looked at Wang Qi and said, "And you also offended Lian Zong." ”

"Those narrow-minded guys, this is not used, that is not used, I can't see it. Wang Qi shook his head, also feeling quite helpless.

"So, Wang Qi, join the Geting faction. ”

"For the Geting faction, I am also ...... Wait a minute, senior, isn't this topic a little too jumpy?" )