Super Dimension Technology Era

The home of science fiction is rapidly developing.

And Huang Mingzhe was participating in military training under the scorching sun, but the number of people in his mathematics department was pitifully small, and they were all straight men, a proper monk class.

"One, two, one, take a moment and stand at attention."

"Turn left, stand at attention, stand astride."

The instructors shouted loud slogans, and many freshmen were already sweating. Huang Mingzhe was quite adaptable, mainly because he had the habit of exercising.

The instructor looked at the panting students and shook his head: "Take a break and continue in ten minutes."

"Phew, it's exhausting."

"This sun is too poisonous."

Many people sat on the ground, took off their camouflage hats to fan themselves, or drank mineral water.

Looking at the bronzed skin on his arms, Huang Mingzhe stood for a while.

"Mingzhe, your science fiction home has been very popular recently! But with such a large expenditure, will the capital chain be too tight?" A classmate who was blushing from the sun asked curiously.

"The Science Fiction House is just a sycamore tree, used to attract the golden phoenix. The company's income comes from other places." Huang Mingzhe explained with a smile.

"I see."

The others were also chatting without saying a word. Huang Mingzhe was naturally the focus among them. He was talented, young and wealthy, majestic, and approachable. All the students had to admit that Huang Mingzhe was the best among this batch of students. The presence.

He had been in school for more than a week, and he had received a lot of small pink cards. If Wenna hadn't been by his side all the time, he would probably have been confessed in person by those enthusiastic female classmates and seniors. Being too good is also a kind of distressed.

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

"unity is strength……"

"When the sun sets, the red clouds are flying over the western mountains. The soldiers are returning to the camp from target practice, 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.

The second floor of the teaching building not far away.

Two middle-aged people were looking at the freshmen.

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

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

"However, Huang Mingzhe is quite generous. The investment from Science Fiction House is not small." The dean continued.

"I hope he can balance his studies and business well." Dean Zhu glanced at Huang Mingzhe with some pity. In his opinion, Huang Mingzhe's current business affairs were very likely to drag down his academic development, but everyone had their own ambitions, and he couldn't say anything.

The dean on the side also nodded in agreement.

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

The conclusion about the Poincaré conjecture.

The actual situation is that what Perelman gave is the general idea of ​​the Poincaré conjecture, which is indeed a work of genius, but some of the details are not rigorous. This is why Perelman did not submit the article and only published it in The main reason for being online.

In the case of Qiu Chengtong, Zhu Xiping and Cao Huaidong, academic circles generally believed that Zhu Xiping and Cao Huaidong completed the work of proving Perelman's Poincaré conjecture. However, some people insisted that they had the greatest credit for it, so there was a commotion .

However, no one doubts that the overall 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 higher, so we cannot say that he is plagiarizing.

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

The merits and demerits of this are difficult to explain clearly.

…

After having dinner with Wen Na, Huang Mingzhe browsed international thesis websites alone in the study room of the villa. He rented this villa to make it convenient to live in Yangcheng University Town.

In addition to participating in military training these days, he is also studying mathematics. In fact, Huang Mingzhe no longer needs to go to school. He has already completed all the college content, but he is interested in this platform.

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

Memorizing papers one after another, these papers are all about analysis, topology, algebraic geometry and Hodge conjecture. However, many papers are water-rich papers with too little useful information.

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

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

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 algebraic closed-chain classes.

What does this sentence mean?

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

To put it simply, any geometric shape, no matter how complex it is (as long as you can think of it), can be made up of a bunch of simple geometric figures.

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

For more than a hundred years, mathematicians have continued to build deeper abstractions on the basis of abstraction. Each level of abstraction is further away from the daily world of experience.

Taking group theory as an example, our common "addition, subtraction, multiplication, and division" are abstracted into four operating rules.

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

As a highly professional issue, the object it deals with is so far away from people's intuition 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.

In other words, there is still some debate in the mathematical community whether the formulation of this problem is rigorous and reasonable. Some people even say that the Hodge conjecture should be more accurately called a wild guess.

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

After this conjecture was proposed, there has been no progress. It is still more difficult than Gechai and Riemann Hypothesis. At least Gecai and Riemann Hypothesis still have some staged 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 watershed papers.

However, despite Hodge's conjecture, Huang Mingzhe still figured out a general direction through thinking integration and sparks of inspiration.

Sometimes a direction is also a huge progress. The really despairing thing is the direction without efforts.

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

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

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