"The study of Goldbach's conjecture is only S level in difficulty?"
Wang Hao was indeed very surprised. He had always thought that the world's top mathematical problems would be S+ level in difficulty, such as the NS equation.
But if you think about it carefully, you can understand it.
The NS equation is not only a mathematical problem, but also a systematic study. It is a very complex problem. Because of this, it can be selected as one of the seven major mathematical conjectures of the millennium.
Goldbach's conjecture is very famous, but it was not selected as the Millennium Mathematics Conjecture. One of the reasons is that it is just a mathematical problem related to prime numbers.
Of course, the difficulty of a research cannot be judged by the Millennium Mathematics Conjecture. After all, there are some factors of human judgment involved.
From another perspective, it can be understood by comparing it with the Kakutani conjecture.
The Kakutani conjecture is just an 'incidental research' to S-level research results. The research is mainly about mathematical methods to solve a type of problem, which includes the Kakutani conjecture, as well as other conjectures and problems.
The main results of this research are mathematical methods, not problems that the methods can solve.
Goldbach's conjecture is a question related to prime numbers. It is slightly more difficult than Kakutani's conjecture, but in the end, it is just a mathematics question.
From this perspective, S-level difficulty is already very high.
The main reason why Goldbach's conjecture is well-known is that it is easy to understand. Even elementary school students can understand it and even think about it deeply.
In addition, the conjecture has been circulating for more than two hundred years and has been continuously proposed by the mathematical community, so it will naturally become very famous.
In this way, Wang Hao also gained a more detailed understanding of the system's judgment of the difficulty of R&D projects.
To put it simply, questions with difficulty levels below D are ordinary questions.
Level D difficulty has reached the level of scientific research and can be said to be innovative research.
Level C difficulty has certain application value or is much more difficult, reaching the ordinary SCI level. Some excellent applied research will have great influence.
Level B difficulty can be said to be at the level of top journals. The research may not necessarily have much application, but the difficulty is definitely very high.
Level A difficulty is not a problem that can be solved generally. It is like the innovation of large number multiplication algorithm. Problems of similar difficulty may not have progressed for more than ten or twenty years.
S-level difficulty is already the top research and the most difficult question. Every S-level research can be said to shock the world.
At S+ level difficulty, it is difficult to make a judgment.
Wang Hao's understanding of S+ level difficulty is systematic engineering, or research that can lead to great progress in theory or technology.
After deciding to study Goldbach's conjecture, Wang Hao also started preliminary work.
He first found a lot of relevant information and papers.
Then, start researching.
These papers are all related to Goldbach's conjecture, including Mr. Chen Jingrun's proof paper on '1+2'. The name of the paper is "Representing a large even number as the sum of a prime number and the product of no more than two prime numbers."
》.
1+2, of course, does not mean 1+2=3.
Goldbach's conjecture appeared in 1742.
At that time, Goldbach proposed the following conjecture in his letter to Euler: Any integer greater than 2 can be written as the sum of three prime numbers.
Goldbach couldn't prove it himself, so he wrote to ask the famous mathematician Euler to help prove it.
However, Euler could not prove it until his death.
However, Euler still conducted a lot of research. In his reply to Goldbach's conjecture, he proposed another equivalent version, which is now the most widely circulated version, that is, 'Any even number greater than 2 can be written as
The sum of two prime numbers'.
Because of this, there is a saying of ‘1+1’.
1+1 is the sum of two prime numbers.
What Chen Jingrun proved about ‘1+2’ is that ‘any sufficiently large even number can be expressed as the sum of two prime numbers, or the sum of a prime number and a semi-prime number’.
The method he used was the most classic ‘sieving method’.
Historically, all progress in proving Goldbach's conjecture has used the sieve method. The sieve method, also known as the sieve method, is easy to understand.
First, arrange the natural numbers in order, starting with the number 1. 1 is not a prime number or a composite number, so it must be crossed out.
The second number 2 is left as a prime number, and all numbers after 2 that are divisible by 2 are crossed out.
The first uncrossed number after 2 is 3. Leave 3 behind and cross out all the numbers after 3 that are divisible by 3.
The first uncrossed number after 3 is 5, leave 5, and then cross out all the numbers after 5 that are divisible by 5...
If you continue to do this, all the composite numbers not exceeding N will be screened out, leaving all the prime numbers not exceeding N.
This method sounds very simple. In fact, because the screening process is endless, mathematical analysis methods must be used, which involves combinatorial mathematics problems.
Combinatorial mathematics can, to a certain extent, be discrete mathematics.
In a broad sense, the analysis of combinatorial numbers is discrete mathematics, but in terms of practical application, combinatorial mathematics in a narrow sense is the remaining part of discrete mathematics after removing graph theory, algebraic structure, and mathematical logic.
Discrete mathematics is Wang Hao’s ‘specialty’.
Therefore, Wang Hao easily understood Chen Jingrun’s research paper and understood the logic of the method.
At the same time, I also made a judgment - just like the common view in the mathematics community, Mr. Chen Jingrun has applied the sieve method to the extreme and has only completed the proof of '1+2'.
In other words, this road is impossible.
Just like the study of the exact value of π, even if a computer is used to calculate tens of billions of digits, it is impossible to obtain an accurate value of π. π can still only be represented by symbols, not an exact number.
In other words, it is impossible to solve an irrational number simply using calculation methods, and it is impossible to prove the '1+1' problem using the 'sieve method'.
Wang Hao put down the paper in his hand and couldn't help but sigh, "It's so difficult to prove Goldbach's conjecture!"
He sighed. Another reason was that after reading several related papers, the task inspiration value only increased by a pitiful 1 point.
This shows that the ‘sieving method’ simply won’t work.
No matter how many similar research papers you read, it will not help you solve Goldbach's conjecture. It will even affect your own thinking and judgment, which will have a negative effect on your research.
"It seems that we still need to find new methods, and group theory is a good starting point." Wang Hao thought.
Next to Zhang Zhiqiang, listening to Wang Hao's whisper, he couldn't help but curled his lips, "Goldbach's conjecture is difficult? I also said that Riemann's conjecture is difficult!"
He came over curiously and asked, "Wang Hao, why did you start studying Goldbach's conjecture?"
Wang Hao said depressedly, "Because I can't find the direction, I have been studying the NS equation, but the research got stuck and there was no progress, so I wanted to change the direction."
"Isn't this span too big?" Zhang Zhiqiang twitched his lips, "NS equations, Goldbach's conjecture, from partial differential equations to number theory, I always feel that you should specialize and study in one direction."
He seemed to be filled with emotion as he spoke, and said with emotion, "It's just like life. Only by being dedicated can you reap your own love."
"The same goes for you, Wang Hao. What do you think, don't you consider finding a girlfriend? I've been here for you, Brother Zhang. If you have any emotional problems, you can definitely ask me."
Wang Hao looked at Zhang Zhiqiang strangely, looked at him carefully, and asked, "Do you have a girlfriend?"
"this……"
"Have you found someone you like? Are you pursuing it 'dedicatedly'?"
"This...haha..."
Wang Hao suddenly understood and nodded, "So, you haven't caught her yet, right? That means you don't have a girlfriend yet."
Zhang Zhiqiang suddenly said depressedly, "You don't have to hit people like this, right? You don't either."
"This is different."
Wang Haodao, "I am single proactively, but you are passive, and you are ten years older than me."
"No matter how nice you say it, you are still single!" Zhang Zhiqiang retorted firmly.
Wang Hao shrugged nonchalantly.
At this time, there was a female doctoral student wearing glasses at the door. She knocked on the door and walked into the office. She looked at Wang Hao with admiration and said in an extremely gentle voice, "Teacher Wang, your theory of annihilation force is really amazing."
, I read your analysis and research and was completely attracted by the descriptions inside."
"I believe that it must be the most amazing prediction in physics and will become a Nobel-level discovery."
Zhang Zhiqiang felt numb all over after hearing this, and sat aside full of envy and jealousy.
"oh……"
Wang Hao was a little surprised. When other people talked about his research, they usually talked about mathematics. Why did they suddenly talk about annihilation force?
To be continued...