"Mr. Schultz, I heard that you are tackling the NP complete problem, is there any progress now?"

Mochizuki Shinichi took his coffee and looked at Schultz.

At that time, because of the proof of the ABC conjecture, Schultz went to Japan to debate with Shinichi Mochizuki, but no one could convince the other party.

Although Pang Xuelin later proved the ABC conjecture, Shinichi Mochizuki finally admitted his mistake.

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

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

However, Schultz's reaction was a little flat, and he shook his head with a smile and said: "I don't have a clue yet, most of my energy is still on how to combine Ponzi geometry with arithmetic geometry, I always feel that there is some kind of connection between the two theories, and if it is studied thoroughly, it may be possible to produce some wonderful chemical reactions." As for the NP totality problem, I have studied this proposition as a lifetime project. ”

"The correlation between arithmetic geometry and Ponzi geometry?"

Everyone couldn't help but look at each other.

In the field of arithmetic geometry, Schultz can be regarded as a grandmaster-level figure of the founding school, and even Pang Xuelin does not dare to say whether the research in this field has reached the level of Peter Schultz.

Therefore, it was a little surprising and at the same time somewhat clear that Schultz was trying to study the correlation between arithmetic geometry and Ponzi geometry.

If it weren't for his ideas in this area, Peter Schultz probably wouldn't have left Germany and come to such an unfamiliar environment as Jiang University to conduct research.

You must know that this guy even refused Princeton's invitation before.

However, as for the NP complete problem, everyone was not surprised by Peter Schultz's statement.

Liu Tingbo, who was on the side, said with a smile: "I think it's better not to be directly proven as a complete problem with NP, otherwise someone like me who is engaged in cryptography research will be unemployed." ”

Hearing Liu Tingbo say this, everyone immediately laughed.

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

To put it more seriously, the monetary systems of countries around the world based on modern crypto systems will completely collapse, let alone bitcoin and the like.

And this proposition has far more impact than just cryptography, but also on complex systems theory.

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

However, the current methods of dealing with complex systems rely heavily on numerical calculations, and most of the problems are difficult to solve analytically, and it is naturally impossible to make effective predictions.

Once it is proven that P=NP is possible, the trader can find the shortest route, the factory can reach maximum productivity, and flights can be properly arranged to avoid delays......

In a word, any problem can be optimally solved in the shortest possible time, mankind can make better use of the available resources, more powerful tools and methods will emerge in the scientific, economic and engineering communities, major breakthroughs will become continuous, and the Nobel Prize selection committee will be busy.

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

However, regardless of whether the result is true or not, it is very difficult for mathematicians to prove 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 the Hodge conjecture and gave a report at the International Congress of Mathematicians.

Pang Xuelin even put forward the 15 questions of Ponzi, pointing out the direction for the development of the mathematical 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 glanced at each other, and they all felt a little surprised.

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

Therefore, it should be logical for Pang Xuelin to engage in the research of the Riemann conjecture next.

They didn't expect that Pang Xuelin suddenly became interested in the existence and smoothness of the NS equation.

Pang Xuelin smiled and didn't explain.

The reason why the existence and smoothness of the NS equation were chosen as the next research direction was more because of the need to accurately calculate the plasma turbulence problem in the nuclear fusion reactor.

If this proposition is solved, it will be very simple to design fusion reactor control software.

The NS equation is very complex and involves the coupling of velocity pressure, first-order partial derivative, second-order partial derivative, nonlinear term, and so on.

At present, people's understanding of the NS equation is still far from enough.

It is not clear whether there is a solution to such a complex NS equation, let alone whether the solution is continuous.

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

Many people may say that it doesn't matter if the equation can't be solved, we have a computer, and we can give numerical solutions through numerical simulations and the method given by Pang Xuelin to solve nonlinear equations.

But numerical solutions involve a balance between accuracy and computing power, you have to calculate accurately, the computer takes a long time, draw a three-dimensional grid, the inverse relationship between the number of grids and the cubic of the grid size, the number of nodes is roughly the same, the number of your algebraic equations explodes, and a problem even takes decades.

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

Considering the problem from the nature of the solution of the NS equation 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, which is a bit like the Zordan curve theorem, we can probably judge that it must be right, but there is a big problem in proving it.

The first step is to prove the existence of understanding, and then see how large the solution space is, and whether it can be solved analytically or asymptotely.

The long-term behavior smoothness of the solution, and even the topology of the solution space is studied, or the equation is defined in the solution space, and then the solution space of the equation and its topological differential properties are studied.

The existence and smoothness of the NS equation is the study of these problems.

If fully understood, the human understanding of fluid mechanics will progress by leaps and bounds.