Chapter 119 Kakutani Conjecture, Institute of Aeronautical Materials and New Research
The scholars in the conference room were very tired after listening, but they still insisted on listening to the end because they found that the method of shaping functions taught by Wang Hao was very clever.
Many of the ideas and methods in it are not formal, and in a rigorous mathematical system, they can be said to be in the wrong direction.
For example, in the derivation process, a probabilistic method is used. If the derivation is analyzed and deduced using a probabilistic method, the final result will definitely be inaccurate.
This also leads to the fact that in the area delimited by the decision function, some Mersenne numbers may be Mersenne prime numbers, but there is a high probability that they are not Mersenne prime numbers.
However, the purpose of deriving the function is not to make a perfect proof, but to find Mersenne prime numbers with a greater possibility. It relies on mathematical methods to achieve the purpose of direct application, and the effect will be very significant.
They can think of problems in many application fields.
For example, the purpose of searching for singularities in particle collision physics experiments is to find different points. Rigorous proof is not required. As long as it is found, it will be a great achievement.
It may also be used in astronomy. In a large amount of complicated data, if you use mathematical calculations to find special points, you may make special discoveries.
etc.
This method of using loose mathematics to cleverly derive equations and functions may be very promising in applied research.
Many people feel they have gained a lot.
Wang Hao's gains were even greater. The "Research on Probability of Prime Number Distribution" increased his inspiration value by nearly thirty points. It can be said that the research has reached the stage where it is just a step away.
In addition, he found relevance between his research and teaching content.
Because some inspirations were discovered in the classroom, including functional analysis and probability theory, which are directly related to analyzing probability, the research process he conducted will also have a certain relevance.
"There may be many ways to solve a problem, including finding Mersenne prime numbers, and other research. There may be many ways to solve it."
"The teaching content is directly related to the direction of inspiration and the solution to the problem."
The same goes for Luo Dayong's 'Graph Isomorphism Problem'. He took a course on 'Nonlinear Functional Analysis' and found a solution that started with methods in the field of functional analysis.
After Wang Hao finished the report, he thought about a lot of things.
He explained functions and the process of shaping functions very carefully, and then he just answered two small questions, and the report ended.
"Pa bang bang~~"
The conference room burst into warm applause, and every scholar who came to listen to the report felt that they had benefited a lot.
Wang Hao walked down the stage and shook hands with everyone who came over. He also received a lot of praises, "You are so young and promising! Your research really opened my eyes. It turns out that some loose mathematical methods can still produce such results." effect."
“It was the first time I saw probability techniques used in deriving functions, and it was an eye-opener!”
"Wonderful, so wonderful. After listening to your report, this trip was worth it!"
Wang Hao greeted everyone with a smile.
After the report on Mersenne primes ended, everyone walked out of the conference room. After a short rest, some people left early. They still had their own work to do.
Those scholars from other regions have nothing to worry about.
People from the Mathematical Science Center invited them to visit the campus of Shuimu University.
Shuimu University can be said to be a famous attraction. The campus is still worth a visit. There are many classic and famous buildings, full of historical and cultural heritage.
Wang Hao and Pan Weiguo walked behind the crowd together.
They kept talking.
Pan Weiguo really had a lot of emotions in his heart. He recalled that more than a year ago, Wang Hao was still a doctoral student under him, and he patiently guided him to complete his doctoral thesis.
In the blink of an eye, one year has passed.
At that time, I certainly could not have imagined that so many things would happen in one year. First, Wang Hao stayed in school and participated in the project of the Alloy Laboratory of Donggang University. After only three months, he was suddenly dismissed.
Later I learned that Wang Hao had been invited by Zhou Qingyuan to Xihai University, and I began to hear about the research he had completed, and even occasionally saw news about him in the news.
Whenever he saw Wang Hao's news on the news, Pan Weiguo always felt very happy, and later he felt very unbelievable.
He was initially pleased because he had always thought Wang Hao was very good, and some of his ideas during his Ph.D. studies were always surprising. When he arrived at Xihai University, it was normal for him to put in the effort to do research, and it turned out to be fruitful.
What was incredible later was that the results were too many and too big.
Fourier transform assists in constructing mathematical models?
New algorithm for multiplying large numbers?.
Proof of regularity of the Monge-Ampere equation?
Existence and boundedness argument of Artyn's constant?
Mersenne primes…
Pan Weiguo felt very shocked when he thought that these studies belonged to Wang Hao and were conducted in just over half a year.
Wang Hao's genius has far exceeded his expectations. Only one year later, even he himself has been left behind.
Pan Weiguo asked with a wry smile and a long sigh, "You have just completed the research on Mersenne prime numbers. Do you have any plans for the next step? Research on the probability of prime number distribution, do you have any specific ideas?"
He knew that Wang Hao had applied for the Outstanding Youth Science Fund.
Wang Hao nodded and said, "I already have a new research direction, which is a new mathematical method. I hope that through this mathematical method, I can solve the proof problems of infinite increase and decrease of numbers through fixed calculation formulas."
He and Cao Dongming also said similar things, but Cao Dongming patted him on the shoulder and said "come on" and didn't know what he meant specifically.
Pan Weiguo was different. He immediately reacted, "Kakutani conjecture?"
Wang Hao nodded slightly, then shook his head and said, "Not only the Kakutani conjecture, but also 3X+2, 3X+3, or the palindrome conjecture, etc. There are many similar problems."
"I want to study a new mathematical method to solve this type of problem."
This type of problem contains many contents, and the Kakutani conjecture is just one of them, and it can also be said to be the most classic problem among them.
Kakutani guess has many names.
Amrican calls the problem the 'hail conjecture' because if you follow the problem and calculate it, the graph will look like hail.
International regular conferences call it the ‘Kratz problem or 3X+1 problem’ because the mathematician Kratz raised this problem at a formal meeting seventy years ago.
Many scholars in China call it the Kakutani conjecture because this problem was introduced to China by a Japanese mathematician named Kakutani.
The content of Kakutani's conjecture is also easy to understand - write any positive integer N and transform it according to the following rules: if it is an odd number, the next step becomes 3N+1; if it is an even number, the next step becomes N/
2.
No matter N is any number, it will eventually be unable to escape to the bottom and fall into the number 1.
This is a matter of calculating numbers through a column formula, continuously increasing and decreasing to explore the final number.
There are many similar problems in mathematics. They all change numbers through a disadvantage, and then continue to cycle, either increasing or decreasing, or increasing and decreasing simultaneously.
Pan Weiguo naturally understood what Wang Hao was talking about. Because of this, he knew how difficult the research was.
It can even be said that it is impossible...
Pan Weiguo's first reaction after hearing this was that this kind of research was impossible to complete. A year ago, he would have said directly, "Pause it, don't waste time on this kind of impossible research."
Now Pan Weiguo can’t say anything about it, because Wang Hao has made many achievements, and they are all very influential content.
Now they are not in the same school. At most, it can only be said that they were former tutors and students, or they were just friends.
Pan Weiguo had no way to ask Wang Hao to stop his research. He thought for a long time and carefully organized his words, "Wang Hao!"
"I think we should not be too arrogant when doing research. For example, for some difficult or even impossible research, we should adopt a happy-go-lucky mentality."
"It would be best if there is progress. If there is no progress, it doesn't matter."
Pan Weiguo felt that Wang Hao would definitely not listen to his persuasion.
Young people!
Having just completed several results, there must be a rush of momentum, but unexpectedly Wang Hao nodded in agreement, "Yeah, I think so too. It's better to just take things as they come with this kind of research."
Pan Weiguo immediately felt relieved. He felt that his persuasion was effective, and Wang Hao still valued his words.
He nodded with satisfaction, "That's the mentality you have to have."
…
Wang Hao and Pan Weiguo had lunch together and then went to the hotel room to rest.
At around four o'clock in the afternoon, he saw the car coming to pick him up at the door of the hotel, so he got in the car and went to the Aviation Materials Institute.
Cao Dongming and several others were already waiting at the door.
Wang Hao got out of the car and shook hands with several people one by one.
"welcome!"
"Professor Wang Hao, you are very welcome. I heard Professor Cao say that you are very knowledgeable in the field of data mining in materials research."
"I know you from the news. They all say you are a star in mathematics..."
A few compliments made the scene more lively.
After some introductions, Wang Hao learned that most of them were researchers in the project that Cao Dongming was responsible for.
They entered the gate together and were taken on a tour of the Aviation Materials Institute.
During the visit, it can be found that the Aeronautical Materials Institute does not pay much attention to Wang Hao's arrival. When people from other projects or departments were introduced, they just greeted Wang Hao politely and then continued to do what they were doing.
work, and some even just continued chatting with other people without paying any particular attention to them.
In fact, this is also very normal.
Wang Hao was invited by Cao Dongming. Cao Dongming is indeed a leading figure in the field of titanium alloys, but in the entire Aeronautical Materials Institute, he can only be said to be a figure.
The Institute of Aeronautical Materials is really too big, and there are too many experts and scholars in it. There are many experts like Cao Dongming, who are among the best in a certain field of research.
In terms of professional title level, Cao Dongming is already the top professor, but the Academy of Aeronautical Materials has six permanent academicians and more than 100 well-known materials experts and academic leaders.
In such a huge materials research institution, even the best experts will become ordinary.
In fact, when Cao Dongming invited Wang Hao to give a report, he told others, including the heads of several project teams and two resident aviation academicians, but the response from others was not very enthusiastic.
A big reason is that Wang Hao is a mathematical computer expert, but he is not a famous data mining expert and seems to have nothing to do with materials research.
The project undertaken by Peng Hui's team has been classified as a major secret. Others do not know the extent of the results and the extent of Wang Hao's personal contribution to research and development.
Their impression of Wang Hao is still that of a young mathematics professor who is very talented and is reported to be a future Fields winner.
But, so what?
This has nothing to do with aviation materials research.
Some people even think that Cao Dongming was a little out of his mind and crazy when he invited Wang Hao to give a data mining report.
Mathematics and data mining are not the same field!
Cao Dongming said that Wang Hao is a data mining expert, but the Institute of Aeronautical Materials has several experts in the field of data mining. They still focus on material calculations and material experimental data analysis.
Isn't this the same as having a layman give lectures to an expert?
Because of this, when many people saw Wang Hao, they either didn't know about it, and those who knew about it were just surprised. Only Cao Dongming and the researchers in the project he was responsible for were very enthusiastic about Wang Hao.
Wang Hao didn't feel anything.
The world does not revolve around him alone. It is impossible for everyone in such a large aviation material institute to be very enthusiastic towards him. Others are normally polite, which makes him feel natural.
Under the hospitality of Cao Dongming and his team, Wang Hao visited the two largest buildings of the Aeronautical Research Institute, and also went to the aviation equipment room at the back to have a look. There were many aviation materials and equipment, which was the first time he had heard of them.
, the first time I saw it, I felt it was an eye-opener.
Cao Dongming is indeed very enthusiastic about Wang Hao.
While walking and talking, he kept talking about topics related to data mining, and then asked Wang Haodao, "The research on titanium alloys and the analysis of experimental data for each project can be said to be a new research."
"Professor Wang Hao, you are an expert in this field. In your opinion, can there be a universal analysis method that can be used in the research and development of all alloy materials?"
This question is really difficult to answer.
Wang Hao thought about it carefully and said thoughtfully, "All alloy material research and development... is difficult. I am a layman and don't understand alloy material research and development."
"If it's just about the research and development of beta-type titanium alloys, I know a little bit about it, maybe I can do it..."
He was a little unsure.
Wang Hao thought Cao Dongming's idea was very good, so he simply opened the system and created a task--
【Task 1】
[Research project name: General method for analyzing experimental data of β-type titanium alloy R&D (R&D difficulty: B).]