The Science Fiction World of Xueba

"Mr. Schultz, I heard that you are working on NP-complete problems. Have you made any progress?"

Mochizuki held a cup of coffee, looked at Schultz and said.

Because of the proof of the ABC conjecture, Schultz went to Japan to debate with Mochizuki Shinichi, but no one was able to convince the other party.

Although Pang Xuelin later proved the ABC conjecture, Mochizuki finally admitted that he was wrong.

But the relationship between him and Schultz has not been very good.

Therefore, as soon as Mochizuki asked this question, several other people also stopped talking and turned their eyes to Schultz, for fear that the two would quarrel again.

However, Schultz's reaction was a little dull, and he shook his head with a smile and said: "I don't have any clues yet. Most of my energy is still on how to combine Ponzi geometry and arithmetic geometry. I always feel that the two There is a certain connection with the former theory, if the research is thorough, some wonderful chemical reactions may be produced. As for the NP-complete problem, I have already regarded this proposition as a project to study in my lifetime."

"Relationship between arithmetic geometry and Ponzi geometry?"

Everyone couldn't help but looked at each other.

In the field of arithmetic geometry, Schulz can be regarded as a master figure who founded the school. Even Pang Xuelin dare not say whether his research in this field has reached the level of Peter Schulz.

Therefore, everyone was a little surprised by Schulz's attempt to study the relationship between arithmetic geometry and Ponzi geometry, but at the same time it was a little clear.

If it weren't for his ideas in this regard, Peter Schulz probably wouldn't have left Germany to do research in such an unfamiliar environment as Jiangda University.

You must know that this guy even rejected the invitation from Princeton before.

As for the NP-complete problem, everyone was not surprised by Peter Schulz's statement.

Liu Tingbo on the side said with a smile: "I think it's better not to prove the NP-complete problem directly, otherwise people like me who do cryptography research will lose their jobs."

Hearing what Liu Tingbo said, everyone immediately laughed.

What Liu Tingbo said is correct. If NP=P, it basically means that for any practical encryption system, there is a positive integer k, and an algorithm with a running time of O(X^k) can break it.

To put it seriously,

The currency systems based on the modern encryption system in countries around the world will completely collapse, not to mention Bitcoin and the like.

Moreover, this proposition affects far more than cryptography, and will also have a huge impact on complex system theory.

Including artificial intelligence, condensed matter, life sciences and other systems, these are closely related to human life.

However, the current means of dealing with complex systems relies heavily on numerical calculations, and most problems are difficult to find analytical solutions, and naturally it is impossible to make effective predictions.

Once it is proved that P=NP, the merchant can find the shortest route, the factory can reach the maximum productivity, and the flight can be properly arranged to avoid delays...

In a word, any problem can be optimally solved in the shortest time, human beings can make better use of available resources, more powerful tools and methods will appear in the scientific, economic and engineering circles, and major breakthroughs will become The steady stream will keep the Nobel Prize selection committee busy.

Of course, this is an ideal world. Most mathematicians, including Pang Xuelin, believe that the greatest possibility is that P≠NP.

But no matter whether the result is true or not, it is very difficult for mathematicians to prove that P=NP or P≠NP.

At this time, Schultz said: "Professor Pang, have you decided on the next research direction?"

More than two months ago, Pang Xuelin and Perelman collaborated to complete the proof of Hodge's conjecture, and made a related report at the International Congress of Mathematicians.

Pang Xuelin even proposed Ponzi's Fifteen Questions, which pointed out the direction for the development of the mathematics community in the next few decades.

Therefore, everyone is very interested in Pang Xuelin's next research direction.

Pang Xuelin smiled and said: "The existence and smoothness of the NS equation!"

"Not the Riemann conjecture?"

Tao Zhexuan, Perelman and others looked at each other, feeling a little surprised.

Pang Xuelin has completed the proofs of the BSD conjecture, the Hodge conjecture, the ABC conjecture, the twin prime conjecture, and the Polignac conjecture. The latter three conjectures are basically closely related to the distribution of prime numbers.

Therefore, Pang Xuelin's next research on Riemann's conjecture should be regarded as a matter of course.

They did not expect that Pang Xuelin suddenly became interested in the existence and smoothness of the NS equation.

Pang Xuelin smiled without explaining.

The reason why I chose to solve the existence and smoothness of the NS equations as the next research direction is more because of the need to accurately calculate the plasma turbulence in the nuclear fusion reactor.

If this proposition is solved, then designing fusion reactor control software will become very simple.

NS equations are very complex, involving the coupling of velocity and pressure, first-order partial derivatives, second-order partial derivatives, nonlinear terms and so on.

People's current understanding of the NS equation is still far from enough.

For such a complex NS equation, people do not know whether there is a solution, let alone whether the solution is continuous.

In a sense, NS equations are to fluids what Newton's second law is to classical mechanics.

Many people may say that it does not matter if the equation cannot be solved. We have a computer, and we can give a numerical solution through numerical simulation and the method of solving nonlinear equations given by Pang Xuelin.

However, the numerical solution will involve a balance between accuracy and computing power. If you have to calculate accurately, the computer will take a long time to draw a three-dimensional grid. The inverse relationship between the number of grids and the cube of the grid size, The number of nodes is roughly the same, and the number of algebraic equations you have exploded, and a problem may even take decades to calculate.

Therefore, Pang Xuelin must solve the problem from the source.

Considering the problem from the nature of the NS equation solution itself, on the one hand, the solution must exist, because if it does not exist, then the fluid phenomenon in our life should not exist, or the NS equation itself cannot describe the fluid well.

The second possibility can be ruled out. The problem is to prove its existence strictly. This is a bit like the Jordan curve theorem. We can all judge that it must be right, but there are big problems in the proof up.

The first step is to prove the existence of understanding, and then look at how big the solution space is, and whether we can find an analytical solution or an asymptotic solution.

The smoothness of the long-term behavior of the solution, and even study the topology of the solution space, or define the equation on the solution space, and then study the solution space of the equation on the solution space and its topological differential properties.

The existence and smoothness of NS equations are to study these problems.

If it is fully understood, human beings' understanding of fluid mechanics will advance by leaps and bounds.

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