Huang's first direction is to integrate analytical topology and algebraic topology.

The English name of topology is Topology, which literally translates as geography, that is, related disciplines similar to the study of topography and landforms.

In the early days of China, it was translated as "Situation Geometry", "Continuous Geometry", and "Geometry under One-to-One Continuous Transformation Group".

However, these translations are not easy to understand, and the 1956 unified "Mathematical Terms" identified it as topology, which is transliterated.

Topology is a branch of geometry, but this kind of geometry is different from the usual plane geometry and solid geometry.

The usual objects of plane geometry or stereo geometry are the positional relationships between points, lines, and planes, as well as their metrical properties.

Topology has nothing to do with the measurement properties and quantitative relationships of the research object, such as length, size, area, and volume.

Topology, on the other hand, is often described as "plasticine geometry", that is, it studies the invariant properties of objects under continuous deformation.

For example, all polygons and circumferences are the same in the topological sense, because polygons can be transformed into circumferences by continuous deformation.

A teacup can be continuously transformed into a solid ring, and in the eyes of topologists they are the same object; Circumference and line segments are not the same in the topographical sense, because turning a circumference into a line segment will always break (discontinuous).

Topology has developed to this day, and theoretically it has been clearly divided into two branches.

One branch is more focused on the use of analytical methods, called point set topology, or analytical topology.

Another branch is more focused on algebraic methods and is called algebraic topology.

These two branches are still unified, and this is also the direction of Huang Mingzhe's research.

Topology has a wide range of applications in functional analysis, Lie group theory, differential geometry, differential equations, and many other branches of mathematics.

However, it is obviously not easy to analyze topology and algebraic topology in a unified manner, and while browsing a large number of papers, I also looked for topology books in the school library.

The body of topological knowledge in his mind was growing rapidly, but mathematics was never an independent system, but a combination of numbers, a collection of formulas.

Constantly stimulating the spark of inspiration, the topology knowledge body, the algebraic geometry knowledge body, the analysis knowledge body and so on for the inspiration spark collision, countless new knowledge burst out in his brain.

The edifice of topology is being built by Huang Mingzhe to be larger, stronger, and more methodical.

……

In class, Huang Mingzhe was dual-minded, thinking about problems while listening to the lectures, and writing and drawing on scratch paper from time to time.

The class is a compulsory course for mathematics majors, mathematical analysis, and the teacher in the class is a professor in his forties, this teacher is already a little Mediterranean, obviously the senior level of mathematics and physics is inversely proportional to the hairline.

And the professor saw that Huang Mingzhe was thinking about topology, but he didn't react and lectured on his own.

The reason why Huang Mingzhe didn't care about him was mainly because he was hit, not only in mathematical analysis, but also in calculus, algebraic geometry, group theory, and topology, Huang Mingzhe could kill him in seconds, and in the face of such students, as a teacher, he was also under a lot of pressure.

A genius can be a maverick, even if he doesn't come to class now, the school doesn't dare to do anything, only if he has enough credits, it's almost enough.

At first, the students were not very convinced Huang Mingzhe, the aura of the top student in the college entrance examination is nothing in college, and there are not a few cases where the top student in the college entrance examination is oblivious to everyone after going to college.

But after getting along, they realized that they were too naïve, and the strength of the coercion was not what they could imagine.

In the class, there are only two people who can talk to Huang Mingzhe, who may be sympathetic to each other, and the others don't have much in common with Huang Mingzhe, because they can't keep up with the rhythm.

After one lesson, the afternoon class ended, by which time many students had already left the lecture hall.

"Mingzhe, can you discuss it?" A bald head with glasses leaned over and asked.

"Say." Huang Mingzhe replied succinctly.

"I have some questions about the topology, why ......?" asked the bald head.

Huang Mingzhe replied as he continued his topological research on scratch paper.

"Zishang, the class is forming a modeling team, are you interested in participating?" The squad leader asked with a smile.

The bald Gao Zishang waved his hand: "You please ask Gao Ming, I'm not interested in this aspect." ”

"What about you?"

"I'm working on my dissertation, so you get the idea."

Thesis? Be a human being! Still don't let people live? The squad leader's whole person was not good, and he had to look at another person with expectant eyes.

"Don't look for me, I haven't been available lately." Li Qun directly ignored the squad leader's complaining little eyes.

The class leader had no choice but to go to other classmates.

"Are Li Qun and Zishang interested in joining my club?" Huang Mingzhe asked suddenly.

"Your community? When did you form a club?" Li Qun asked as he opened his trademark little eyes.

"I just passed the approval of the student union yesterday, and it is a learning interest group called the Truth Society." Huang Mingzhe explained.

Li Qun and Gao Zishang glanced at each other, and then nodded.

"If you agree to join, I will give you an application form for joining the company, and you can fill it out and give it to me." After Huang Mingzhe finished speaking, he took out two application forms from his backpack.

After the two of them took it, they began to fill it out.

"Mingzhe, our society still has confidentiality regulations?" Li Qun asked in surprise.

Huang Mingzhe explained half-truthfully: "There are no rules, after all, we have to discuss a lot of academic issues, which may involve technology and the like, so be prepared." ”

"I see."

"By the way, how many people are there in our club now?" Gao Zishang asked after filling out the application form.

"Five people, the three of us, and the two people who came from Shanmei with me, if you have a candidate, you can introduce them, but the recruitment philosophy of our Truth Society is that we would rather be lacking than abundant, and don't recruit people who don't have real materials." Huang Mingzhe said.

Gao Zishang and Li Qun also have no opinions, after all, people are divided into groups and things are gathered by like, and they don't want some people who don't know anything to join the club.

"Mingzhe, what's wrong with your paper?" Li Qun glanced at the scratch paper on his desk.

"I'm integrating analytical topology and algebraic topology, and I already have an idea."

"Are you planning to unify topology? That's not a small difficulty! Li Qun said in surprise, he thought that Huang Mingzhe planned to study one of the analytical topologies or algebraic topologies, but he didn't expect to integrate the two branches.

"Unified topology is a must, otherwise there is no way to attack the Hodge conjecture." Huang Mingzhe replied without raising his head.

"Hodge's conjecture?" Gao Zishang and Li Qun looked at each other.

"Honestly, I think it's a little more promising to prove Gochai." Li Qun spread his hands and smiled bitterly.

"If I don't give it a try, how do I know if it doesn't work, and whether it proves Hodge's conjecture or not, it won't prevent me from unifying topology." Huang Mingzhe said with a smile.

"Then I wish you to achieve a unified topology as soon as possible." Li Qun could only bless.

In fact, Huang Mingzhe has almost completed the first stage of unified topology, and the ideas and formulas have been memorized in his mind, and now he is close to integrating the paper.