Hua Luogeng did not ask any more questions. In the field of study, he never doubted Yu Hua's own strength. He picked up the tea cup and took a sip, and spoke slowly.
With the completion of the 'basic' advanced mathematics course, Yu Hua's mathematics level has reached a point where he can begin to contact real mathematics.
the way.
Which path to choose for research is the core question faced by a beginner in mathematics.
Standing on the edge of the cliff, below is the bottomless abyss of mathematics. Number theory, topology, algebraic geometry, geometry, fractions and other high information entropy monsters are constantly surging, staring at the beginners of mathematics standing on the edge of the cliff.
In front of these monsters, there is only one path to choose from. Once determined, there is no turning back. You will either become famous or remain unknown.
Why?
Because people have limited time, energy, talent, talent, and information reception efficiency, they are destined to only choose one direction.
Mathematics has developed continuously over thousands of years, from the initial general arithmetic stage to today's dozens of branches of mathematics and dozens of fields of mathematical research. It covers so much content and covers a wide range of knowledge that ordinary people will spend their entire lives.
, it is extremely difficult to study one of these fields and obtain results.
Even those talented geniuses can only make waves in the main subject areas and cannot cross over number theory and algebraic geometry to make achievements in the two fields.
it's out of the question.
The abstraction and rigor of mathematics are like an extremely strong cage. No matter how clever the human brain is, it cannot break free from this cage.
Of course, beings like Euler, Newton, Gauss, and Archimedes do not feel any "mathematical constraints."
"Go back to Professor, the students have been selected." Yu Hua heard this and gave a direct reply without hesitation.
He has already determined his development path in the field of mathematics.
Hua Luogeng asked with concern: "What is it? You should understand the importance of the future path. I hope you choose carefully and don't be anxious. Once the direction is determined, it cannot be changed."
The meaning of being unable to change does not mean that someone forced Yu Hua not to touch other mathematical trunks, but... time.
When he took root in the first direction and devoted himself to research for more than ten years, he found that he could not achieve results.
It's too late to turn back at this time.
The golden period for mathematicians to produce results is over. In middle age, people's energy and time will further decline, and they will be unable to support high-intensity mathematical research.
"Students are going to engage in number theory research and produce some results to lay the foundation. In the future... they may want to prove Goldbach's conjecture." Yu Hua looked solemn and gave the path he chose. He paused and slowly said what he had planned from the beginning.
Good goal.
Study number theory and prove your guess.
This is the path Yu Hua chose after much thought, and it is also the path of the current optimal solution.
The end of the advanced mathematics course does not mean that Yu Hua's mathematical journey has stopped. The level of mathematics determines the upper limit of the scientific research path.
If you want to achieve your goals, you must never abandon your main subject of mathematics.
As the only queen of mathematics, the status and identity of number theory have never wavered. The brilliance and profundity of number theory illuminate the spiritual world of the entire human civilization. Engaging in mathematical research in the field of number theory can greatly improve Yu Hua’s own mathematical level. This is one of the reasons.
.
Secondly, compared to studying topology and algebraic geometry, Yu Hua has a good basic environment for number theory. Hua Luogeng is a top researcher in the field of analytic number theory. There is also a strong number theory research group in China, which can provide Yu Hua with
Good research foundation and environment.
Third, once your number theory research level is sufficient, you can enter Gechai and obtain academic honors and scholar status through the '5+5' proof process.
Achievements and identity are things that Yu Hua lacks.
As for the fields of topology, algebraic geometry and calculus, there is no rush for the time being.
These fields can be read as related knowledge, but the main direction number theory is the best.
"It is indeed easy to produce results in the field of number theory. However, number theory is not easy to study, especially if you want to prove Goldbach's conjecture. At present, Goldbach's conjecture is still at the stage where it cannot be proved. The mathematics community is very concerned about the progress of proving Goldbach's conjecture.
Stay at '5+7', as Mr. Lacey proved this year."
When Hua Luogeng heard Yu Hua's answer, he thought thoughtfully. He was not particularly surprised that Yu Hua was preparing to enter the field of number theory, but he was a little surprised by Yu Hua's guess. He looked at Yu Hua and said slowly: "You want to prove my guess?"
, you have to compete not only with yourself, but also with all the mathematicians in the world. This is a long process, so you must be mentally prepared."
"Student understands." Yu Hua nodded seriously. Of course he knew the difficulty of number theory and guessing.
Classified according to the information entropy value, the information entropy value in the field of number theory ranks first among all the main branches of mathematics.
Among other things, Ge Guess, twin prime numbers, and Riemann's hypothesis, these are the ultimate mathematical problems that have troubled human intelligence for hundreds of years in the field of number theory but cannot be solved.
The value of information entropy is off the charts, and it is so difficult to understand that it is almost indescribable and unthinkable.
As for why I should take the field of pure mathematics as my main focus, it is really a helpless move.
There is no way to do it. It is too difficult to produce results in physics. The academic level, equipment, and environment are all lacking. How can we do physics research?
Another point is that the pressure from peer competition is too damn high.
Physics giants of this era are almost everywhere. Schrödinger, Planck and other first-line physics giants are all still alive, and the emperor of physics at the top of the pyramid in the field of physics - Einstein.
When Yu Hua goes to study in the United States, he will truly step into the world's academic community and face the pressure emanating from these physics giants.
Not to mention Yu Hua’s biggest problem when it comes to chemistry is the lack of equipment and environment for chemical research.
The environment in the Republic of China was not suitable for chemical research. The small chemical laboratory that cost one thousand oceans to build basically had no research conditions. It was barely possible to develop three types of gunpowder technology, and it was impossible to conduct other chemical research.
At this stage, for Yu Hua, it is best to achieve results in the field of pure numbers.
"Don't worry about engaging in number theory research just yet. We'll wait until you get into Tsinghua University. There are still about ten days left before the joint entrance examination in May. After the joint entrance examination, there will be the entrance exam for recommended students. During this time, you should consolidate your studies and don't fall behind at the critical moment."
As if like an elder, Hua Luogeng slowly told him that the study of number theory cannot be accomplished in one day. Remember, the most important thing right now is the joint entrance examination in May and the examination for recommended students. He does not want Yu Hua to have any problems.
"Students understand." Yu Hua nodded.
"Okay, that's it for today. I won't go to Tsinghua Park next week. I will stay in No. 4 Middle School. Remember to write an article about fractions. The specific content is up to you. There is a copy of Tsinghua University for you on the table outside.
Journal, Master congratulates you on your submission." Hua Luogeng said with a smile.
"Master taught me well." Yu Hua felt a little happy after hearing this, and then flattered him.
"Go and have a look. This issue of the journal is a hot commodity and has been snapped up outside the school." Hua Luogeng smiled and waved his hand.
Yu Hua packed up his things, said goodbye to his master Hua Luogeng, left the study, and came to the main room. There was a thick book on the dining table. When he took a closer look, he saw the title of the Journal of Tsinghua University was written on the surface, and next to it was the April 2 issue of 1937 and other basic information.
.
"Mechanical drawing has been completely printed, and the name has been changed to Chinese Mechanical Drawing. It's interesting. However, this is Zhang San's business and has nothing to do with me. As a high school student, it feels good to be in the Tsinghua Journal." Yu Hua picked up the Tsinghua Journal carefully.
Looking through the catalog, he saw the journal articles that were ranked first, and he affirmed in his heart that Tsinghua University had lived up to his expectations.
After briefly looking through the published mechanical drawings, I stopped paying attention and turned to the sixth article "Reconstructing the Lebesgue Integral".
The mechanical drawing compiled by Zhang San has nothing to do with him, but this mathematics paper officially published in the Journal of Tsinghua University is different and can bring him real honor and fame.
After all, he is one of the authors of the article appearing in this issue of the journal under his real name and identity.
An article written by a unique high school student has been included in the top academic journal Tsinghua Journal. What is this if not an honor?