Ultra-Dimensional Technology Era

"The House of Science Fiction is just a sycamore tree, which is used to attract Golden Phoenix. The company's income comes from other sources." Huang Mingzhe explained with a smile.

"I see."

Others chatted without saying a word, and Huang Mingzhe was naturally the focus among them. Talented, young and rich, handsome, and approachable, all the students had to admit that Huang Mingzhe was the best student in this year The presence.

He has been in school for more than a week, and he has received a lot of pink cards. If Wen Na had not been by his side, he would have been confessed to his face by those enthusiastic female students and seniors. Being too good is a kind of distressed.

Next, the instructors entered the singing session and led their respective classes to perform singing.

"unity is strength……"

"The red clouds fly from the western mountains at sunset, and the soldiers shoot targets to return to the camp, to return to the camp, and the red flowers on their chests reflect the colorful clouds..."

Although most of the students are tone deaf, it does not prevent them from singing with high spirits.

Not far from the second floor of the teaching building.

Two middle-aged people are looking at the new students.

The dean pointed to the playground: "Dean, the first young man in the first row is Huang Mingzhe."

"Just pay attention. After all, the top score in the college entrance examination does not mean everything." Dean Zhu of the School of Mathematics said flatly.

"However, Huang Mingzhe is a big spender, and the investment of Science Fiction House is not small." The dean continued.

"I hope he can balance his academics and business." Dean Zhu gave Huang Mingzhe a pityful look. In his opinion, Huang Mingzhe's current business affairs are very likely to hinder the development of his studies, but everyone has his own ambitions, so he can't say anything.

The dean at the side also nodded in agreement.

In fact, this Dean Zhu is still quite a controversial figure, mainly because of the Poincaré conjecture back then, plus he was involved in the confrontation between Qiu Chengtong and Peking University, and Chi Yu was affected by this incident.

The final conclusion on the Poincaré conjecture.

The actual situation is that Perelman gave the general idea of ​​the Poincaré conjecture, which is indeed a work of genius, but some of the details are not rigorous, which is why Perelman did not contribute, but only published in The main reason online.

In the case of Qiu Chengtong, Zhu Xiping and Cao Huaidong, the academic circle generally believed that Zhu Xiping and Cao Huaidong completed the completion of Perelman's Poincaré conjecture proof, but some people insisted that they had the most credit for it, so there was a disturbance .

However, no one doubts that the general idea of ​​the entire proof was given by Perelman.

It can only be said that Zhu Xiping's mathematical talent is undeniable, but his personal utilitarianism is a bit high, so it cannot be said that he is plagiarizing.

In fact, there have been many similar things in the history of academia. Many scientists gave general ideas, which were then proved by others.

The merits and demerits of this are hard to say clearly.

……

After having dinner with Wen Na, Huang Mingzhe browsed the international thesis website alone in the study of the villa. He rented this villa so that he could live in Yangcheng University City.

Besides participating in military training these days, he is studying mathematics. In fact, Huang Mingzhe can no longer go to school. He has already completed all the content of the university, but he likes this platform.

For example, the school's library, degrees, alumni, etc. are all wealth, and going to school has no effect on him.

Memorizing papers one after another, these papers are analysis, topology, algebraic geometry, and Hodge's conjecture, but many papers are water-rich papers, and there are too few dry goods.

Judging from the direction of the thesis that Huang Mingzhe read, his topic is about to come out - Hodge's conjecture.

The Hodge conjecture was proposed by Professor Hodge, a British mathematician and chairman of the 1958th International Mathematical Congress in 13.

That is: for the space of projective algebraic varieties, on non-singular complex projective algebraic varieties, any Hodge class can be expressed as a rational linear (geometric component) combination of algebraically closed chain classes.

What does this sentence mean?

"Non-singular projective algebraic varieties" refer to the "surfaces" of smooth multidimensional objects generated by the solution of an algebraic equation.

Simply put, any geometric figure of any shape, no matter how complex it is (as long as you can imagine it), can be assembled with a bunch of simple geometric figures.

Since the birth of Galois' group theory, modern mathematics has become more and more inclined to extract an abstract understanding of the nature of things.

For more than 100 years, mathematicians have continued to build deeper abstractions on the basis of abstraction, and each level of abstraction is further away from the daily empirical world.

Taking group theory as an example, our general "addition, subtraction, multiplication, and division" are abstracted into four algorithms.

The Hodge conjecture is a difficult problem born under the extremely abstract system of modern mathematics.

As a highly specialized problem, the object it deals with is far from people's intuition, so that not only is it difficult to judge whether the conjecture itself is right or wrong, but even the formulation of the problem itself seeks to establish a real consensus.

That is to say, whether the formulation of this question is rigorous and reasonable, there is still some controversy in the mathematical community.Some even say that the Hodge conjecture should more accurately be called a wild guess.

The proof of Hodge's conjecture will establish a fundamental connection between the three disciplines of algebraic geometry, analysis and topology.

After this conjecture was put forward, there has been no progress. It is still more difficult than Ge Guess and Riemann's conjecture. At least Ge Guess and Riemann's conjecture still have some phased results, while Hodge's conjecture remains unchanged.

Huang Mingzhe has browsed no less than a thousand papers related to algebraic geometry, analysis, and topology these days, but the papers related to Hodge's conjecture are all flooded papers.

However, even though Hodge guessed that he would stay where he was, Huang Mingzhe still figured out a general direction through thinking integration and sparks of inspiration.

Sometimes one direction is also a huge progress. What is really desperate is that there is no direction to work hard.

Huang Mingzhe's idea is to break the whole into parts. Since Hodge's conjecture cannot be completed in one step, he split it into several parts, first proves the part, and then integrates it into the whole Hodge's conjecture.

Since Hodge's conjecture needs to connect the three parts of algebraic geometry, analysis and topology, he intends to first connect the relationship between analytic geometry, analytical topology and algebraic topology.

After completing the proof of these three parts, we can launch an attack on Hodge's conjecture.

Chapter 24 The Road to Topology

Huang Mingzhe's first direction is to integrate analytical 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 landform.

In the early days of China, it was translated into "geometry of situation", "continuous geometry", "geometry under one-to-one continuous transformation group",

However, these kinds of 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 the usual plane geometry and solid geometry.

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

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

And 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 the same, 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 the topological sense, because turning a circle into a line segment will always break (discontinuous).

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