Enter the Immortal Cultivation

"Algebraic topology and differential topology are undoubtedly the most meaningful in topology?" Heweier chewed on this sentence and couldn't help but nodded: "It's a bit interesting - but, you actually dare to judge topology as a whole?"

"As a mathematician, I make my own judgment in this field." Wang Qi is neither humble nor overbearing.

"I do have some problems in algebraic topology." He Weier said: "Your ideas seem to be more directed towards group theory and ring theory... Ah, I'm sorry, this is the first thing I thought of. I and I My colleagues have been doing research in this field for a long time, so this was the first thing I thought of.”

Wang Qi nodded, but he was slightly surprised.

With only vague ideas, is it possible to guess the direction of this theory...

Cohomology algebra comes from algebraic topology, but its application is higher than algebraic topology. It is not only a milestone in the development of mathematics, but also can penetrate into many fields of mathematics and promote the overall advancement of mathematics.

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

The resulting mathematical tools eventually point to the field of physics.

One of the most significant achievements is the revelation of the symmetric structure of gauge field theory.

As we all know, in the era when Suan Zhu and Tai Tian Zun had an irreversible relationship, and the Tao of Xiang Xiang was at its peak, He Weier had stayed in the Guiyi Alliance for a long time. He also has a considerable understanding of Tiangexing's system, and wants to follow Tai Tianzun's ideas to complete the theory of "unified field".

However, he failed. At that time, he started from the concepts of electric field and magnetic field of Tiange Tianyuan Group, trying to replace them with electromagnetic potential and the corresponding high-order antisymmetric tensor, and then added it to the momentum-energy-spiritual force tensor of gravity. Derive the field equations by purely mathematical means.

However, this high-level monk from Wanfa Sect not only ignored the specific meaning of his calculations, but also ignored the possibility that his calculations were not constructed at all. He also unfortunately chose the most difficult direction. After the Tianyuan Style reaches the fourth level, even "spiritual energy conservation" [spiritual power-energy conservation] loses its effectiveness - this is obviously contradictory to all current theories. Eventually, Howell gave up on this erroneous theory.

However, the idea is correct.

Wang Qi knew that as long as cohomology algebra promotes the further development of group theory, the canonical groups in Ho Weier's calculations can be extended to non-canonical groups, leading to a mathematical model with practical significance-that is, the strong emphasis later The Standard Model of electroweak unity, the basis of Yang-Mills theory on Earth.

A very close step away.

Ho Weier proposed such a theory because of his understanding of abstract algebra. And because of this theory, he and his classmate Ai Ruoche worked hard in this direction.

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

Wang Qi replied: "This is indeed a good direction. However, I feel that I cannot think about specific issues in this area yet."

He Weier said: "Are you not interested in...metaphysical algebra?"

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

He Weier was shocked, with a strange light in his eyes: "Oh? 'Drink', 'Wine Glass', 'Small Table'? What concepts are you trying to replace?"

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

Zhao Qingtan said in a low voice: "This is an anecdote about the calculation... At first, the calculation master was in charge of the singing court, and he studied number theory. For ten years, he only talked about the field of numbers. Ten years later, the calculation master discussed geometry and read geometry books. After another three years of trying to draw the heavens, the master said: The points, lines and planes are like wine, wine glasses, and a small table. The geometric propositions are nothing like this..."

"What is this..." This monk was born as a commoner, and his talent is not very high. He has recently worked hard to break through the sky, and he doesn't know much about this koan.

Zhao Qingtan, who studied under the Geting School and is related to the Geting School, whispered: "The Master of Calculation once studied geometry. That sentence is his understanding of geometry. The five methods of painting the sky are certainly the basis of geometry, but the God of Geometry 40,000 years ago There is no definition of what is a 'point', what is a 'line', and what is a 'surface'. In the eyes of ancient mathematicians, these truths are self-evident. However, in the eyes of mathematicians, this is not the case. Points, lines and surfaces are also needed. In a strict mathematical sense. In his opinion, there is no definition in the method of drawing the sky and the 'point, line and plane' in the geometry book, and there is no problem if it is replaced by a 'low table with wine glasses'."

"Why a low table with drinks and glasses?"

"Maybe Master Ximen just wanted to have two drinks at night?" Zhao Qingtan stared at Wang Qi and He Weier and kept saying: "It's over... It's over... Even if you really want to do this, There’s no need to say it in person…”

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

——The problem is getting bigger...

Zhao Qingtan almost squeezed out his voice: "Wang Qi is tantamount to saying that the Geting School does not have clear definitions of the concepts of environmental theory - this is to say that the Geting School is fundamentally incompetent."

He Weier did not expect Wang Qi's tone to be so loud. He pondered for a moment and asked, "Can you tell me what you think?"

"I am not saying that there is a problem with the theories of the predecessors, but that some of the concepts of the predecessors have become blurred after the introduction of new systems." Wang Qi corrected a little, and then said: "When Senior Xi first took over the Goting School, he mainly studied number theory and had a result in the theory of class domains. I am also thinking about how to clearly display the class domain theory through cohomology and continue to promote it. Now..."

What Wang Qi said is also one of the most famous applications of homological algebra.

He Weier's eyes trembled.

He felt something very vague. That thing has not yet taken shape, but... very beautiful.

What Wang Qi said is exactly what he, a disciple of the Goting School, is familiar with.

Wang Qi spoke very quickly - in fact, his current theory is only in its infancy. If he discusses it with others, it will take three days and three nights to discuss it. But if he just talks about it, it will be done soon.

After Wang Qi finished speaking, He Wail looked at him deeply and said, "Good boy... Wait a minute, I have a few more questions."

It can be seen that He Wail also has a certain understanding of Wang Qi's current progress. He did not ask questions casually, but each question hit the nail on the head. There are many things that Wang Qi must involve in his future theory.

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

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

"Although Wang Qi used ideas and conjectures to explain many places in the question and answer just now... But why, looking at his calm appearance, it seems that those are not just conjectures?"

Some people's hearts began to beat.

"Wang Qi's ideas have not been proven yet, but he said them openly... These are the specific directions of research! If I prove it..."

Wang Qi's words brought up many questions. These problems are not special or particularly difficult problems. They are closely integrated with the existing theoretical framework. According to the "classification of problems" that Wang Qi once made [the speech Wang Qi gave when he won the Daoqi Award, which is the classification made by the Bourbaki school], these are all "problems that generate general theories."

——If I go back now, write down these problems and claim them as my own, can I... leave my name in history?

More than one cultivator had similar dark thoughts.

However, after seeing the expressions of He Wail and Wang Qi in the discussion, they gave up the idea.

Plagiarizing other people's ideas and research directions will be despised in the modern law immortal way.

Even in the melon field and plum, you still have to avoid suspicion. And now, these problems were all raised by Wang Qi in front of He Wail. ​​Unless one of them came over and said, "In fact, I have also thought about similar problems. I think it should be..." Otherwise, this free and easy cultivator will inevitably think that this is "plagiarism."

Being hated by a free and easy cultivator... is really not worth it.

Especially, this free and easy cultivator is the leader of a powerful school. Although the Ge Ting faction has inevitably declined because of Wang Qi, it is still a top-ranked force.

If they are really remembered by He Wail for plagiarizing Wang Qi's ideas, they will encounter many obstacles in the next thousands of years.

After giving up their own ideas, more people have a kind of... indescribable shock.

——Is he really a beginner?

——Why can Wang Qi, who is also a beginner, see so much?

——For him, we can only have the idea of ​​plagiarism...

During the communication, the sun gradually fell,

Wang Qi stood up as usual and said: "This is all I can communicate today. Please do as you please. If you want to communicate again, please come back tomorrow."

Just when Wang Qi was about to turn around and leave, He Wail called out: "Wait a minute, Wang Qi. Can we talk alone?"

Wang Qi nodded, and the time and space around He Wail 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: "Studying mathematics."

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

"After all, it was me who ruined Senior Xi's ideals?" Wang Qi also sighed helplessly: "But this is not my original intention. Senior Xi is still one of the people I respect most... It's just that mathematics is free, I just discovered it."

"I know." He Waier's tone was stern: "But you actually followed the master's ideas back then and continued Continue walking. In the eyes of others, you are despising the master. "

"This is also not my intention." Wang Qi said: "I like this idea too much, you can't stop me from using it, right? Besides, you should be able to see it, senior. What I hope to get is not the form of symbols, but the mathematical structure hidden under the formulas and theorems..."

"Others may not see it this way." He Wail looked at Wang Qi and said: "And you have offended Lian Zong."

"That group of narrow-minded guys, they don't allow this to be used, and they don't allow that to be used. I can't stand it." Wang Qi shook his head and felt helpless.

"So, Wang Qi, join the Ge Ting faction. "

"As for the Ge Ting faction, I am also...wait a minute, senior, isn't this topic a bit too jumpy?" (To be continued ~^~)