Of course, Xu Chuan never believed that his opinion on an unresolved issue must be right.

After all, he is just a person who has learned a little more knowledge than ordinary people. He is not an omniscient and omnipotent god.

But on the P=NP? problem, or on P-type problems and polynomial decomposition problems of large positive integer factors, the senior student in front of me should be one of the people who have gone the furthest so far, or in other words, the person who has gone the furthest.

.

What if she thinks P=NP? The conjecture may be incorrect. Combined with the opinions of most people in the mathematical community and his own intuition, maybe P=NP does not exist.

That is to say, NP-type problems can never collapse into P-type problems.

Some people may wonder that since the polynomial decomposition problem of large positive integer factors has been confirmed, why is P not equal to NP? Shouldn't it be a step closer to P=NP?

For this problem, can we only say that P=NP? The conjecture itself is not a completely defined mathematical problem.

Among the seven millennium problems of the Clay Mathematics Institute, it is called the 'Non-deterministic Polynomial problem, that is, the non-deterministic problem of polynomial complexity.'

P=NP? In the conjecture, P and NP on both sides are not fixed. It targets endless polynomial and non-deterministic problems. In this case, it is not easy to prove that P≠NP.

If P=NP, you need to ensure that every NP-type problem can collapse to a P-type problem. If P≠NP, then you need to prove that every potential algorithm will fail.

The algorithms and problems here do not only refer to the present, but also include everything in the past and future.

So rather than saying that the P=NP? problem is a mathematical conjecture, it is better to say that it is a way of thinking, a method of classifying and understanding problems based on their inherent difficulty.

.......

Opposite me, Liu Jiaxin nodded and said softly: "Well, maybe this problem has no solution. We can neither prove P=NP nor P≠NP."

"I tried to solve an NP-complete problem in the past, but found that it was impossible to find an algorithm that could solve the problem in all situations. I could only try my best to achieve the best results."

Xu Chuan nodded and said with a smile: "It seems that we have reached a consensus."

Smiling, he leaned back in his chair and continued: "If we talk about the problem alone, it is not just the P=NP? problem, there are many problems that are the same, and often we cannot solve it directly. But

Many times, the process of studying them is the most essential thing."

"For example, now, the problem of polynomial decomposition of large positive integer factors has given us a general framework and tools, which helps us think about how to deal with difficult problems arising from actual needs, and can also help us better improve mathematics.

and developments in other sciences.”

"And these are the most important!"
Chapter completed!