201.

Chaos dynamics is an important branch of complexity science, and it is also a hot topic in the scientific field before Cheng Li's crossing. Chaos refers to seemingly random irregular movements that occur in a deterministic system. A system described by a deterministic theory behaves as uncertain, unrepeatable, and unpredictable, which is the phenomenon of chaos. Chaos is an intrinsic characteristic of nonlinear systems, and it is a common phenomenon in nonlinear systems. As a result, chaos is ubiquitous in real life and in practical engineering-technical problems.

The well-known weather system is one of the most typical chaotic systems, which makes accurate weather forecasting very difficult. Even the most advanced computers on Earth today cannot accurately simulate the Earth's weather system.

Because it's a huge chaotic system.

The greatest significance of the emergence of chaos dynamics is that the discovery of chaos in deterministic systems has changed the perception that people have always thought of the universe as a predictable system.

With the equation of determinism, no stable model can be found, but the result is random, which completely breaks the illusion of Laplace's deterministic "causal deterministic predictability". Chaos theory, on the other hand, studies how to control complex unstable events to a steady state.

In the classical mechanical systems that preceded the advent of quantum mechanics and chaotic dynamics, physicists and mathematicians of the 18th and 19th centuries had a strange obsession with being accurate and measurable.

At that time, people believed that everything in the universe should be precise and measurable.

So there are even some deterministic views, that is, at the moment of the Big Bang, what the universe should be like tens of billions of years after that, it was decided at that moment.

However, the advent of chaotic dynamics illustrates that even when all initial conditions are equal, random results can be produced in chaotic systems.

In mathematics, the development of linear equations to nonlinear equations with uncertainties is an important reason for this conceptual change.

The birth of chaotic dynamics is actually a mathematical phenomenon discovered by Mondelbro when he studied fractals.

It was then that people found its application in reality based on the phenomena shown in this mathematical formula, and thus developed a completely new discipline such as chaotic dynamics.

Therefore, fractal and chaotic dynamics are also a typical example of the combination of mathematics and practical application in the 20th century, developing each other and complementing each other.

From a fractal function, Mondelbro discovered the value of the so-called "attractor", and then found that this fractal function with the value of the attractor can iterate the result of irregular vibrations, which is called chaos.

What's even more amazing is that Mondelbro discovers many hidden phenomena behind the chaotic behavior.

This kind of search for the hidden order law behind the chaotic disorder results is the main research content of chaotic dynamics.

And because of the iterative process, even the simplest powertrain requires a huge amount of computation.

Therefore, the study of fractal geometry and chaotic dynamics can only be carried out with the help of computers.

It was with high-performance computers that Mondelbro generated a large number of exquisite and wonderful fractal patterns, which made mankind realize for the first time that the patterns generated by computers according to mathematical formulas can be so beautiful.

Of course, fractal geometry and chaotic dynamics don't just play the role of computer artists, they have proven to be new mathematical tools needed to describe and explore the abundance of irregularities in nature.

Moreover, after entering the 21st century, before the passage of programmography, with the rapid development of science, fractal geometry and chaotic dynamics are constantly showing their amazing charm.

And at that time, mankind did not realize how important the study of chaotic dynamics was, and even how advanced it was.

When Cheng Li was answering the fractal question on the 2997th floor, Xiao Shutong hid in the dark and watched with interest.

"It seems that the original plane that this guy has crossed over, and the civilization in which he is located has touched the important threshold of chaos and fractional dimension, which is an important threshold as a watershed. ”

Among the thousands of civilizations in the heavens and worlds, it is an important threshold to be able to discover the existence of dimensions, and then further discover that dimensions are not only integers, but also scores and even irrational numbers, which is an important sign of the level of civilization.

Stephen Hawking once gave a vivid example to illustrate the fractional dimension: there is a hair, which is one-dimensional from a distance, and three-dimensional when viewed with a magnifying glass. If you are faced with a magnifying glass with a high enough magnification, you can also see the possible 4-dimensional and 5-dimensional spaces and even 11-dimensional spaces from the three-dimensional space-time.

"But it seems that they haven't done a lot of research on this? The tech tree is crooked? Or hasn't they discovered the mysteries of the plane yet? In short, the civilization he used to live in is quite interesting. Xiao Shutong said with interest.

After Cheng Li answered the fractal question on the 2997th floor, he didn't think much about it, and went directly to the 2998th floor.

I'm afraid he didn't expect at this time that the questions about fractals and chaos answered at this level would have a great impact on him in the future.

He quickly solved the problem of "proof of the classification theorem of finite monogroups" at layer 2998 after solving the fractal problem of layer 2997.

Then, Cheng Li finally arrived at the 2999th floor.

And at this time, it happened to be the time when Tuomu Zhenren entered the demon and was promoted to become a god-turning powerhouse.

At the same time, whether it is Cheng Li or Qingling Island, for everyone, they have entered the most critical moment.

After Cheng Li saw the problem on the 2999th floor, his heart was relieved, but at the same time, he was tight.

The reason for the release is that the question is classic and has already been proven in 1994, and he is also familiar with the proof process.

Then I became nervous again, because even this question is only the 2999th layer, so what will be the problem on the 3000th floor?

Originally, Cheng Li thought that this question would be placed on the 3000th floor, which would be the best.

But now, this question has been placed on the 2999th floor, so Cheng Li already has a bad premonition about the 3000th floor.

"The problem with the 2999 floor is this...... The problem with the 3000th layer won't be that...... That's not good, that question is not ordinarily difficult, it's an epic difficulty!" Cheng Li thought with some concern.

However, the situation was urgent, and he didn't have time to think about it, so he began to answer this classic question on the 2999th floor.

"Please prove that when the integer n > 2, there is no positive integer solution for the equation x^n+y^n=z^n for x,y,z. ”

The formulation of this problem is simple, but its place in the history of mathematics is extraordinary.

It is known as Fermat's theorem.