Chapter 361

It took Simon less than twenty minutes to briefly explain to Gu Lu the theoretical framework that has been 30% completed.

Simon adopts the point that Gu Lu said earlier.

That is, starting with the basic definition of algebraic clusters, the concept of non-singular projective algebraic clusters in the Hodge conjecture is redefined.

In this way, the object of study of the Hodge conjecture was determined.

Then, the combinatorial relationship between the harmonic differential form and the upper cohomology class of algebraic closed chains is considered.

This is where something deeper comes in.

At the moment, Simon has not yet built the framework to that level.

After listening to Simon's narration, Gu Lu touched his chin and groaned.

Hodge's conjecture, in the most colloquial terms, refers to the process of breaking down a complex puzzle piece into smaller pieces.

For example, in the process of building a building, it is difficult to see the layout and structure of the building from the outside, but if we simplify the building into a perspective view, we can easily understand the basic structure of the building.

The Hodge conjecture is mainly a way and method to simplify complex geometric problems into simple geometric problems.

Through Hodge's conjecture, it is possible to solve geometric problems that require dozens of pages of paper to be solved in just a few pages.

This is an absolute milestone in the development of the geometric world.

It is even possible to make geometry surpass number theory and become the hottest branch of research in mathematics.

Therefore, in the more than 100 years since the Hodge conjecture was proposed, countless mathematicians have attacked it one after another.

But none of them have failed.

Even the lessons learned from countless failures are pitiful.

This is the reason why the Hodge conjecture is included in the list of the seven mathematical puzzles of the millennium.

High difficulty, as well as ...... Extremely high mathematical value!

Due to the few experiences and theories summarized by former mathematicians, Gu Lu and Simon can almost be said to have started from scratch.

The main purpose of the original mathematician Douglas Hodge's conjecture was to simplify some complex things in the field of geometry and classify them according to their same parts, so that mathematicians can generalize some responsible things.

Gu Lu started from this aspect.

Since Hodge's conjecture was intended to make complex problems simple, Gu Lu asked Simon to start with the simplest algebraic clusters.

The shape of a given object is formed by gluing together simple geometric building blocks of increasing dimensions.

The pile of documents sent by Simon to Gu Lu are all extended under the support of this theory.

…………

"The situation is a little bad......" After listening to Simon's story, Gu Lu sighed lightly.

Simon on the other side of the video also sighed for a long time.

"Yes, the problem we are facing at the moment is very tricky, if we can't solve it, we can only take another path!"

It turned out that Simon's research was having a hard time.

Originally, in a week, Simon could rush the progress of building the theoretical framework to about 40%.

But I was stuck in a puzzle.

Simon has been stuck for more than two days, and his progress is not finished, which is really addictive.

"Is there anything you can do?" Simon chose to turn to Gu Lu for help.

But there is little hope.

Because Simon knows how difficult it is.

It's the equivalent of a dead knot, and it's easy to tie.

But if you want to solve it, it is very difficult.

In the past two days, Simon has lost many brain cells and hair in order to untie this dead knot.

However, little has been achieved.

Gu Lu's fingers tapped lightly on the table irregularly, and he muttered for a few seconds, "I'll try!"

Gu Lu didn't guarantee the ticket 100%, wouldn't it be too embarrassing if the car overturned.

But in Simon's eyes, he thought that Gu Lu had no confidence.

Simon nodded lightly, "Okay, don't put too much pressure on your side, we still have plenty of time anyway, since this road doesn't work, then we can go another way." ”

Gu Lu said before that he would solve the subject within half a year, but Simon didn't listen to it at all.

Because that's kind of.

In Simon's plan, he and Gu Lu can solve this problem in a year to a year and a half, even if it is God's favor.

Compared to the long research cycle of a year, they can still squander a week.

Gu Lu smiled faintly, "Let's wait until I completely fail to say this." ”

"Okay, that's all for this video, and I'll call you back when I get this problem done. ”

After speaking, Gu Lu hung up the video call.

…………

"Let's get to work!"

In the study, Gu Lu moved his wrist and took out a thick stack of scratch paper from the drawer.

Gu Lu was ready to overcome the dead knot that Simon had just said.

In Simon's theoretical framework, he mentions that the geometric starting point of the program becomes obscured after the completion of gluing together simple geometric building blocks of increasing dimensions to form the object of study.

In a sense, you will encounter some parts that do not have any geometric explanation.

And these parts, which have no geometric explanation, are the dead knot that Simon is talking about.

The Hodge conjecture is a geometric conjecture.

But these components cannot be explained by the knowledge of geometry.

If you can't explain it, you can't study it in depth.

Overcoming the Hodge conjecture has become even more nonsense.

"It's still quite tricky!" After clarifying the relationship between the problems, Gu Lu couldn't help but sigh.

No wonder Simon immersed himself in research for two days without a clue.

Because in the eyes of most mathematicians, this situation is indeed a dead knot, the kind that cannot be untied.

But......

Gu Lu doesn't think so.

Gu Lu began to try, and the scratch paper was written one after another.

"No, that's not right, I should probably try to replace these parts with something else......"

Gu Lu wrote and drew on the paper, and an hour passed in a blink of an eye.

"Still can't do it!"

Gu Lu crumpled the scratch paper into a ball, threw it into the paper basket, leaned back in his chair, and looked at the ceiling in a daze.

This was Gu Lu's fifteenth failed attempt.

However, in the last few times, Gu Lu has been close to the truth, but he always feels that something is missing.

"It seems that you have to force me to make a big move!"

Gu Lu sat up straight, opened the mall interface on the system panel, and chose to exchange for a liver-exploding potion.

Opening the potion bottle, Gu Lu drank it all in one gulp.

"Hah, comfortable!"

The second time I drank the liver potion.

Gu Lu could clearly feel that the previously chaotic brain instantly became extremely empty.

The brain is running at full speed and efficiency, and the value of the six attributes is increased to 120%.

Gu Lu held the pen in his right hand and wrote down lines of formulas on the paper.

Now Gu Lu, full firepower!