Super Dimension Technology Era

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

The English name of topology is Topology, and its literal translation is topography, which is a related discipline similar to the study of topography and landforms.

In the early days in China, it was translated as "situational geometry", "continuous geometry", "geometry under one-to-one continuous transformation group\

,"However, these translations are not easy to understand. The unified "Mathematical Terms" in 1956 identified it as topology, which was transliterated.

Topology is a branch of geometry, but this geometry is different from ordinary plane geometry and solid geometry.

The usual research objects of plane geometry or solid geometry are the positional relationships between points, lines, and surfaces and their metric properties.

Topology has nothing to do with the length, size, area, volume and other metric properties and quantitative relationships of the studied objects.

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

For example, all polygons and circles are topologically equivalent because polygons can be transformed into circles through continuous deformation.

A teacup can be continuously transformed into a solid ring. In the eyes of topologists, they are the same object; while a circle and a line segment are different in a topological sense, because turning a circle into a line segment will always break (discontinue).

The development of topology to this day has been very clearly divided into two branches in theory.

One branch focuses on using analytical methods to study, which is called point set topology, or analytical topology.

Another branch focuses on using algebraic methods to study, called algebraic topology.

These two branches now have a unified trend, and this is also the direction of Huang Mingzhe's research.

Topology is widely used in functional analysis, Lie group theory, differential geometry, differential equations and many other branches of mathematics.

However, it is obviously not an easy task to unify topology and algebraic topology. While browsing a large number of papers, I also looked for topology-related books in the school library.

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

Constantly stimulating sparks of inspiration, the body of topology knowledge, the body of algebraic geometry knowledge, the body of analytical knowledge, etc. are collided with sparks of inspiration, and countless new knowledge bursts out in his brain.

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

…

In class, Huang Mingzhe was multitasking, listening to the lecture while thinking about problems, and writing and drawing on scratch paper from time to time.

The class in class is mathematical analysis, a required course for mathematics majors. The teacher is a professor in his forties. This teacher is already somewhat Mediterranean. Obviously, the degree of seniority in mathematics and physics is inversely proportional to the hairline.

When the professor saw Huang Mingzhe thinking about topology, he showed no reaction and continued to teach.

The reason why Huang Mingzhe was ignored was mainly because he was hit hard. Not only in mathematical analysis, but also in calculus, algebraic geometry, group theory, and topology, Huang Mingzhe could kill him instantly. Facing such students, as a teacher, it was also very stressful.

Geniuses can be independent. Even if he doesn't come to class now, the school won't dare to do anything. As long as he earns enough credits, that's pretty much it.

At first, the students were not convinced by Huang Mingzhe. The aura of being the top scorer in the college entrance examination is nothing in colleges and universities. It is not uncommon for the top scorer in the college entrance examination to disappear from everyone after entering college.

However, after getting along with each other, they realized that they were too naive, and that the power of the cheat was beyond their imagination.

In the class, there are only two people who can talk to Huang Mingzhe. It may be the sympathy of geniuses. The others don't have much in common with Huang Mingzhe because they can't keep up with the rhythm.

After one class, the afternoon class ended, and many students had already left the lecture theater.

"Mingzhe, can we discuss this?" A bald man wearing glasses came over and asked.

"Say." Huang Mingzhe replied concisely and concisely.

"I have some questions about analyzing topology, why..." The bald head started asking questions like a barrage of questions.

Huang Mingzhe continued topological research on the scratch paper while answering.

"Zi Shang, our class is forming a modeling team. Are you interested in participating?" the squad leader asked with a smile.

Bald Gao Zishang waved his hand: "Please hire Gao Ming, I'm not interested in this aspect."

"What about you Mingzhe?"

"I'm working on my thesis, so you know."

Essay? Please be a human being! Are you going to let others live? The squad leader's whole body was not feeling well. He could only look at the other person with expectant eyes.

"Don't look for me, I'm not free recently." Li Qun ignored the squad leader's sad eyes.

The monitor had no choice but to find other students.

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

"Your club? When did you form a club?" Li Qun opened his iconic little eyes and asked.

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

Li Qun and Gao Zishang looked at each other and then nodded.

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

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

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

Huang Mingzhe explained half-truthfully: "There is no rule without rules. After all, we have to discuss many academic issues, which may involve technology and the like. It's just a matter of being prepared."

"I see."

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

"Five people, three of us, and two people who came from Shanmei with me. If you have candidates, you can introduce them. However, our recruitment philosophy of the Truth Society is to rather have a shortage than an overabundance. If you don't have real people, don't leave. Recruited," Huang Mingzhe said.

Gao Zishang and Li Qun didn't have any objections. After all, people were divided into groups and birds of a feather flocked together, and they didn't want people who didn't know anything to join the club.

"Mingzhe, how's your paper going?" Li Qun glanced at the draft paper on his desk.

"I am integrating analytical topology and algebraic topology, and I already have an initial idea."

"Are you planning to unify topology? This is not easy!" Li Qun said in surprise. Previously, he thought Huang Mingzhe planned to study either analytic topology or algebraic topology, but he did not expect to integrate the two branches.

"Unified topology is necessary, 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 more promising to prove my guess." Li Qun spread his hands and smiled bitterly.

"If you don't give it a try, how will you know it doesn't work? Whether or not the Hodge conjecture is proven will not prevent me from unifying topology." Huang Mingzhe said with a smile.

"Then I wish you to realize the unified topology as soon as possible." Li Qun could only wish.

In fact, Huang Mingzhe has almost completed the first stage of unified topology. The ideas and formulas have been memorized in his mind. Now he just needs to integrate the paper.

The name of this book, "The Redemption of Civilization", will soon be renamed "The Era of Super-Dimensional Technology". I hope everyone will support it!