Super Dimension Technology Era

In the Truth Society.

After giving instructions to Li Qun and the others for two hours, Huang Mingzhe looked at the night sky with a thin moon and stars.

The development of cities not only brings light, but also brings light pollution. The dazzling Milky Way when I was a child can now only be seen in the wilderness.

He turned around and looked at the blackboard on the wall, which was filled with dense formulas and derivation processes.

Although his Huang's chaotic topology is already approaching the Hodge conjecture, the final step is often the most difficult step.

These days, he focused on studying analysis and algebraic geometry, and polished Huang's chaotic topology even more sharply. However, facing the last step of Hodge's conjecture, he still felt helpless.

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

After simplifying some complex things and classifying them according to their identical parts, it is convenient for mathematicians to summarize some responsible things.

The basic idea is to ask to what extent we can form the shape of a given object by gluing together simple geometric building blocks of increasing dimensions.

The result is powerful tools that allow mathematicians to make huge strides in classifying the wide variety of objects they encounter in their research.

Unfortunately, in this generalization, the geometric starting point of the program becomes blurred.

In some sense, certain components must be added that do not have any geometric interpretation.

The Hodge conjecture asserts that for a particularly perfect type of space called projective algebraic varieties, components called Hodge closures are actually (rational linear) combinations of geometric components called algebraic closures.

In short, no matter how majestic and strange a palace is in this world, it can be built with building blocks.

To complete the Hodge closed chain, the premise is that the entire universe can be constructed with countless geometric components. As long as there is one thing that cannot be constructed with geometric components, the Hodge conjecture will not be true.

In this way, the difficulty becomes extremely huge.

Huang Mingzhe stared at the blackboard thoughtfully.

In fact, among the daily applications of Hodge's conjecture, the most obvious one is finite element analysis.

Suddenly his eyes widened, finite element analysis! Finite element inverse analysis! Huang Mingzhe thought of the finite element inverse analysis technology he had obtained before.

This technology is a technology that can decompose all items into geometric components.

His brain started to work quickly, and he collided with the related knowledge body of finite element inverse analysis, Huang's chaotic topology and Hodge's conjecture.

In an instant, countless knowledge spewed out, forming a brand new body of knowledge - [Finite element inverse analysis - geometric algebraic cluster group and chaotic topological fuzzy cluster group]

This body of knowledge does not prove the Hodge conjecture, but divides the Hodge conjecture into two parts, the geometric algebraic cluster group and the chaotic topological fuzzy cluster group.

Among them, the geometric algebraic cluster group represents the ordered computable part, while the chaotic topological fuzzy cluster group represents the fuzzy uncomputable part.

The relationship between the two is like the bricks and cement in building a house. There are parts that can be expressed by geometric components, and there are other parts that cannot be expressed by geometric components, that is, chaotic topological fuzzy clusters.

However, this relationship also requires a finite reference value, that is, the smallest unit that defines the geometric components. In this way, an object will form a geometric algebraic cluster group and a chaotic topological fuzzy cluster group, or only a geometric algebraic cluster group.

The minimum unit can be infinitely small. After defining the minimum unit, the components of the object must partially support the Hodge closed chain, and the remaining parts are chaotic topological fuzzy clusters.

If Huang Mingzhe can deduce the types of chaotic topological fuzzy cluster groups, it may be possible to prove part of the Hodge conjecture.

Based on mathematics, the rule that numbers can be infinitesimal can be deduced that objects can also be infinitesimal. The existence of infinitesimal objects means that Hodge conjectures that there is a dead end that can never be approached.

That is, the Hodge closed chain can only be established in the case of finite elements.

Huang Mingzhe's brain immediately came up with countless formulas, and then he typed quickly on his laptop.

Lines of formulas and numbers appeared on the screen, and he was making crazy deductions.

A week later.

It's quiet at night.

Huang Mingzhe stopped his slightly sore fingers, stood up and hammered his arms and shoulders.

At this time, three formulas of chaotic topological fuzzy cluster groups have been obtained on the screen, namely quasi-geometry-fuzzy cluster-chaos formula, differential geometry-fuzzy cluster-chaos formula, and topological geometry-fuzzy cluster-chaos formula.

Coupled with the formula of the finite element-geometric algebra cluster group, it can be proved that the Hodge conjecture is true for H^2 under finite element conditions. Similarly, the Hodge conjecture is also true for the Hodge class of degree p, where p\u003cn, n is Given the dimensions of the above projective algebraic varieties, then for the Hodge class with degree 2n-p, the Hodge conjecture also holds.

However, all this is only true in the case of finite elements. If it is infinitely small or infinitely large, the Hodge closed chain cannot be established.

Unless humans can prove that the number is finite, the Hodge closed chain can only be infinitely approximated, but can never form a closed chain.

Obviously the number must be infinite, and finite numbers are illogical.

Just like pi, no matter how you calculate it, you can't get the final number, because pi is an infinite non-cyclic number, and you can only get an approximation.

After reading the 526-page derivation process and the 12 final formulas, Huang Mingzhe knew that he had ended the Hodge conjecture.

For a moment, he felt empty in his heart, and he had overcome a problem that had been bothering him for several months.

In addition to the excitement, there is also a sense of loneliness at the top.

Sitting on the sofa, a pot of tea was steaming, and Huang Mingzhe poured it to himself.

There was a faint sound of footsteps outside the corridor, and then the wooden door slowly opened. Li Qun was carrying some seafood porridge for takeout, followed by Zhu Xiping and Gao Zishang.

"Why is Zhu Yuan here free?"

"I heard that you have been in seclusion for more than a week, so I came over to see you. The whole world knows the difficulty of Hodge's conjecture. There is no need to rush for success." Zhu Xiping consoled him with concern.

"Thank you Zhu Yuan for your concern." Huang Mingzhe said with a smile.

"That means the days are long."

"It's been proven."

"It has been proven..." Zhu Xiping was stunned before he finished speaking. He asked uncertainly: "Proved? Has the Hodge conjecture been proven?"

"To be precise, it was falsified." After Huang Mingzhe finished speaking, he took a sip of tea.

Li Qun and Gao Zishang were stunned.

Gulu! Zhu Xiping grabbed Huang Mingzhe's shoulders with trembling hands, and asked in a high-pitched and urgent tone: "Mingzhe, this joke is not allowed."

"The proof process is on my laptop." Huang Mingzhe said, pointing to the laptop on his desk.

Zhu Xiping quickly ran over and opened the paper to take a look, but when he saw the 526 pages of proof process, his head suddenly became big.

Although it only involves those 12 formulas, the problem is that the derivation process here is no longer understandable to ordinary mathematicians.

Even if Zhu Xiping is asked to deduce it again after reading it, he probably won't be able to deduce the complete process.

After roughly reading the introduction and conclusion, Zhu Xiping said with a wry smile: "This is not something that a mortal can accomplish. Do you plan to publish it in the Annual Journal of Mathematics?"

"Of course, this is theoretical mathematics, and there is no use hiding it." Huang Mingzhe spread his hands and smiled.

Mathematics guys, don’t take yourself too seriously (ω)hiahiahia