The rapid development of science fiction houses in the siege of cities and land.

And Huang Mingzhe is participating in military training under the scorching sun, but there are few people in their mathematics department, and they are all straight men of steel, proper monk class.

"One, two, one, take a break."

"Turn left, stand upright, straddle."

The instructors shouted loud slogans, and many freshmen were already sweating at this time, but 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." ”

"Whew, tired man."

"The sun is too poisonous."

Many people sit directly on the ground, take off their camouflage caps and fan the wind, or pick up mineral water and drink it violently.

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

"Mingzhe, your sci-fi home has been hot lately! But with such a large expenditure, will the capital chain be too tight?" A classmate with a flushed face asked curiously.

"The home of science fiction is nothing more than a plane tree, which is used to attract the golden phoenix, and the company's income comes from other places." Huang Mingzhe explained with a smile.

"I see."

The others also chatted without a word, Huang Mingzhe was naturally the focus of them, talented, young and golden, magnificent, approachable, and all kinds of perfection, and the students had to admit that Huang Mingzhe was the best existence among this class of students.

He came to school for more than a week, and he received a lot of small pink cards, if Wen Na hadn't been by his side, it is estimated that he would have been confessed to those enthusiastic female classmates and senior sisters in person, and it was a distress to be too good.

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

"Unity is strength ......"

"The red glow flies in the west mountain at sunset, the soldiers return to the camp when they shoot the target, return the camp, and the red flowers on their chests reflect the colorful glow......"

Although most of the students did not have all five notes, it did not prevent them from singing with high morale.

Not far from the second floor of the school building.

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

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

"It's okay to pay attention to it, after all, the top student in the college entrance examination doesn't mean everything." Dean Zhu of the School of Mathematics said flatly.

"But Huang Mingzhe is a big deal, and the investment of the science fiction house is not small." The Dean of Students continued.

"I hope he balances his studies and business." Dean Zhu glanced at Huang Mingzhe with some pity, in his opinion, Huang Mingzhe's current business affairs are very likely to drag down the development of his studies, but everyone has their own ambitions, and he can't say anything.

The dean on the side also nodded in agreement.

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

The coffin closure of the Poincaré conjecture.

The fact is that Perelman gives the general idea of Poincaré's conjecture, which is indeed a genius work, but there are some details in it that are not rigorous, which is the main reason why Perelman did not submit the article and only posted it online.

In the Yau Chengtong, Zhu Xiping, and Cao Huaidong incidents, scholars generally believe that Perelman's Poincaré conjecture proved that Zhu Xiping and Cao Huaidong completed the work, but some people insisted that they had the greatest credit in it, so there was a storm.

However, no one disputes that the whole big idea of the proof was given by Perelman.

It can only be said that Zhu Xiping's mathematical talent is undeniable, but his personal utilitarianism is higher, and it cannot be said that he is plagiarism.

In fact, in the history of academia, there have been many similar things, and many scientists have given general ideas, and then they have been proved by others.

It is difficult to explain the merits and demerits of this.

……

After having dinner with Wen Na, Huang Mingzhe browsed international essay websites alone in the study room of the villa, which he rented to facilitate living in Yangcheng University Town.

And these days, in addition to participating in military training, he is studying mathematics, in fact, Huang Mingzhe does not need to go to school now, he has completed all the university content, but he likes this platform.

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

I memorized papers one after another, and these papers were all analytical, topology, algebraic geometry, and Hodge conjectures, but many of them were water-rich water papers, and there were too few dry goods.

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

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

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

What does this mean?

A "nonsingular projective algebraic cluster" refers to the "surface" of a smooth, multidimensional object generated by the solution of an algebraic equation.

To put it simply, any shape of geometry, no matter how complex it may be (as long as you can think of it), can be put together from 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 100 years, mathematicians have continued to build deeper abstractions on top of abstractions, and each level of abstraction is more distant from the everyday world of experience.

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

The Hodge conjecture is a problem born out of the extreme abstraction system of modern mathematics.

As a highly specialized problem, it deals with objects that are so far removed from people's intuition that it is difficult to judge not only 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, whether the formulation of this question is rigorous and reasonable is still controversial in the mathematical community. Some even say that the Hodge conjecture should more accurately be called an inconsequential guess.

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

And after this conjecture was proposed, there has been no progress, and it is still more difficult than the Gochai and Riemann conjectures, at least the Gochai and Riemann conjectures still have some phased results, while the Hodge conjecture is standing still.

Huang Mingzhe browses no less than a thousand papers on algebraic geometry, analysis and topology these days, while the papers related to Hodge's conjecture are all irrigation papers.

However, although Hodge's conjecture did not move, Huang Mingzhe still figured out a general direction through the integration of his mind and the spark of inspiration.

Sometimes a direction is also a huge progress, and the real thing that makes people desperate is not working on the direction.

Huang Mingzhe's idea is to break the whole into parts, and since the Hodge conjecture cannot be completed in one step, it is divided into several parts, first proving the parts, and then integrating them into the overall Hodge conjecture.

Since Hodge's conjecture requires the correlation of algebraic geometry, analytical, and topology, he intends to correlate the relationship between analytic geometry, analytical topology, and algebraic topology.

Complete these three parts of the proof and you can attack the Hodge conjecture.