Ultra-Dimensional Technology Era

Faced with this situation, everyone should be jealous.

It's a pity that CUHK is not a fool. Seeing that it is about to succeed, it came to discuss cooperation. In fact, CUHK is a soft persimmon. When selecting academicians, why didn't they come to CUHK.

Zhu Xiping directly pushed these so-called cooperation.

As for the pressure from the domestic mathematics association and Peking University, compared with these achievements, it is nothing.

When Huang Mingzhe's Truth Society grows stronger, then we can see who has the bigger fist. The academic world is not about power, but about academic knowledge.

Otherwise, those people would not have anything to do with Qiu Chengtong. After all, his academic status and reputation are all there.

Chapter 47 Limited establishment

In the Society of Truth.

After giving advice to Li Qun and the others for two hours, Huang Mingzhe looked at the moonless night sky.

The development of cities not only brings light, but also light pollution. The bright Milky Way in childhood can only be seen in the wilderness.

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

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

These days, he has focused on learning analysis and algebraic geometry, and has sharpened Huang's chaotic topology, but he still feels helpless when facing the last step of Hodge's conjecture.

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

After simplifying some complex things, they are classified according to their same parts, so that mathematicians can generalize 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 dimensionality.

This eventually led to powerful tools that have allowed mathematicians to make enormous 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 a sense, certain parts without any geometric interpretation must be added.

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

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

To complete the Hodge closed chain, the premise is that the entire universe can be composed of countless geometric parts. As long as there is one thing that cannot be composed of geometric parts, Hodge's conjecture will not hold.

In this way, the difficulty is very great.

Huang Mingzhe stared at the blackboard in deep thought.

In fact, the most obvious application of Hodge's conjecture in daily life is finite element analysis.

Suddenly he widened his eyes, 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 was running quickly, and he had an inspirational spark collision between the finite element inverse analysis and related knowledge bodies of Huang's chaotic topology and Hodge's conjecture.

Countless knowledge spewed out in an instant, forming a brand-new body of knowledge——[Finite Element Inverse Analysis—Geometric Algebraic Clusters and Chaotic Topological Fuzzy Clusters]

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

Among them, geometric algebraic clusters represent ordered computable parts, while chaotic topological fuzzy clusters represent fuzzy non-computable parts.

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

But this relationship also needs a finite reference value, that is, the minimum unit that limits the geometric parts, so that an object will form a geometric algebraic cluster and a chaotic topological fuzzy cluster, or only a geometric algebraic cluster.

But the limited minimum unit can be infinitely small. After the minimum unit is limited, the components of the object must partially support the Hodge closed chain, and the remaining part is the chaotic topological fuzzy cluster.

If Huang Mingzhe can deduce the types of chaotic topological fuzzy clusters, it may be possible to prove a part of Hodge's conjecture.

And based on the rule that numbers can be infinitely small in mathematics, it can be deduced that objects can also be infinitely small. The existence of infinitely small objects means that Hodge conjectures that there is a dead angle 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 gave out countless formulas, and then he typed quickly on his laptop.

Rows of formulas and numbers appeared on the screen, and he was frantically deriving them.

a week later.

Silent 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 clusters have been drawn on the screen, namely quasi-geometry-fuzzy cluster-chaotic formula, differential geometry-fuzzy cluster-chaotic formula, topological geometry-fuzzy cluster-chaotic formula.

Combined with the formula of finite element-geometric algebraic clusters, it can be proved that the Hodge conjecture is true for H^2 under the finite element condition, and the Hodge conjecture is also true for the Hodge class of degree p, where p

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

Unless human beings can prove that the number is finite, the Hodge closed chain can only approach infinitely, but never form a closed chain.

Obviously, the number must be infinite, and the finite number is illogical.

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

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 a difficult problem that had troubled him for several months was overcome by himself.

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 slightly, and Huang Mingzhe was drinking it by himself.

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

"How come Zhu Yuan is free?"

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

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

"That is, the future will be long."

"It's been proven."

"It's been proven..." Zhu Xiping was stunned before he finished speaking, he asked uncertainly, "Hodge's conjecture has been proven."

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