200.

The emergence of the Atiya-Singh indicator theorem is an excellent example of the unity of modern mathematics.

Its emergence not only communicates the two major fields of analysis and topology in terms of content, but also involves many core branches of mathematics such as channel analysis, topology, algebraic geometry, partial differential equations, and multiple complex functions.

Moreover, the Atiya Singer indicator theorem has gained important application in the "Young-Mills theory" in physics.

Therefore, the Atiya Singer indicator theorem is known as one of the greatest achievements of modern mathematics.

With such a wide range of questions such as the Atiya Singer indicator theorem, there is no doubt that it is super difficult.

If it was before he came to the Arithmetic Monument, even if he gave ten Cheng Li, it would be impossible for him to derive this theorem by himself. Even if he had realized the final form of knowing this theorem, it would not have been possible to deduce this theorem from scratch.

However, after the baptism of nearly 3,000 layers of questions and the refining of the mysterious information in the arithmetic tablet, Cheng Li's mathematical level has made a terrifying leap.

So, in his own imagination, it only took him more than 20 minutes to derive the Atiya Singh metric theorem.

After solving the Atiya-Singh indicator theorem.

Cheng Li came to the 2996th layer, and the problem of this layer is equally difficult, which is a question about "how to solve soliton equations".

The increasing emphasis on nonlinear mathematical problems was also a feature of the development of mathematics in the second half of the 20th century.

In the first half of the 20th century, linear partial differential equations made great progress. However, in contrast, the study of nonlinear equations is difficult. It was not until mathematicians began to study the "soliton" equation that a major breakthrough and development was made in the field of nonlinear equations.

It all started with the study of a phenomenon called "solitary waves".

The isolated wave is the water wave that is triggered when the ship comes to a sudden stop.

As early as 1834, the British engineer Russell studied this kind of water wave, which he described as "a large, rounded, smooth, well-defined isolated crest that leaves the bow of the ship at a very fast speed and moves forward." Its shape and speed did not change significantly as it traveled...... "Russell, in making this description, complained that the mathematicians of the time did not provide the tools to describe this solitary wave mathematically.

It was not until 1895 that the Dutch mathematician Kotwig gave a mathematical model of the solitary wave phenomenon, a nonlinear partial differential equation, which is also known as the KdV equation.

Although the KdV equation was proposed, it could not be solved at the level of mathematics at the time.

As a result, the study of the KdV equation has stagnated for more than half a century.

However, the problem does not end there.

With the development of physics, the study of various waves has deepened.

Many people have started to study solitary waves further.

Then, it was discovered that after the collision of two different solitary waves, they still behaved as two solitary waves with the same shape, and then after the collision and staggered, as if nothing had happened, they continued to move towards their original route.

Therefore, people call this phenomenon of two solitary waves remaining unchanged after colliding as "soliton"

The KdV equation is then called an isoton equation.

As soon as the solitary sub problem appeared, it immediately caused widespread attention.

Because it was discovered that soliton equations can describe the basic equations of mathematical physics for many natural phenomena.

Finally, after the efforts of many mathematicians, a set of "scattering inversion method" was developed, and the soliton equation was successfully solved.

Cheng Li also used the "scattering inversion method" to answer the problem of layer 2996.

Solitons play a wide and important role in the fields of nonlinear wave theory and elementary particle theory.

Its discovery is an illustration of how mathematics leads to major scientific discoveries. It shows that mathematics, as one of the three major links of modern scientific method (theory, experiment, and mathematics), has and will continue to play an important role in many aspects such as contemporary basic theory and applied technology.

Nowadays, many nonlinear equations that are very important in applications, such as the sinusoidal-Gordon equation and the nonlinear Schrödinger equation, have this soliton solution.

It has also been found that there is also a soliton phenomenon in plasma fiber optic communication, and scientists also believe that impulses conducted on nerve axons and erythema on Jupiter can be regarded as solitons.

Therefore, the soliton equation is also a typical example of the major scientific discoveries that have been made through mathematical research.

After the solitary sub-equation problem, Cheng Li encountered the famous "fractal problem" at layer 2997.

In 20th century mathematics, there were two leaps in the concept of geometry, both related to the dimension of space.

One is the leap from finite dimension to infinite dimension.

The other is the leap from integer dimension to fractional dimension.

The leap in the fractional dimension of integer dimensions occurred in the second half of the 20th century, originating in the article "How Long Is the British Coastline?" published by the French mathematician Mondelbro in 1967.

This is, in fact, the beginning of the study of the fractal problem.

The problem of coastline is a practical geographical survey problem, and scientists have found that encyclopedias published by different countries have different lengths of records on the length of the British coastline, and the error is more than 20%!

Then, the mathematician Mondelbro studied this problem mathematically, believing that this extraordinary error was related to the irregular shape of the coastline.

Due to this irregularity, different measurements will be obtained at different measurement scales.

Finally, Mondelbro used the "Kirk curve" as a mathematical model for thinking about the coastline.

The Kirk curve is to take the central third of each side of a flat equilateral triangle as the base, make a small equilateral triangle outward, and then erase the bottom edge of the small triangle to obtain a new closed fold.

Then, repeat the drawing on each edge of the new curve, and you can continue to draw indefinitely.

Such a curve is called a fractal curve.

Such a description may not be easy to imagine and understand.

But in nature, there are many examples of fractals.

For example, a snowflake is a typical fractal pattern, and the above description can be imagined as the depiction process of the snowflake pattern.

A Kirk curve is just one example of geometry with a fractional dimension.

In 1977, Mondelbro officially referred to graphs with fractional dimensions as "fractals".

And the branch of mathematics with such figures as objects - fractal geometry was established.

It was the subsequent study of fractal geometry that led to the discovery of the phenomenon of "chaos" and the establishment of a new field of "chaotic dynamics".