The private room suddenly became quiet.
At this moment, the professors' curiosity had been piqued, and they were waiting silently for Zhang Chunlei to pose the question.
After all, group theory is a separate branch of mathematics. Even if you have completely and systematically taught yourself advanced mathematics, you will be blinded when faced with group theory topics.
They have heard that math geniuses in high schools learn advanced mathematics and linear algebra in advance.
But high school kids understand group theory...
That was really just a knife stabbed in the butt - it opened my eyes.
After a while, Zhang Chunlei had already thought of the topic and said: "Well, listen up, little guy, this is a proof question. In a finite group G, for two different second-order elements, if they are not common yoke, then there exists another second-order element which is interchangeable with the former.”
When this question was uttered, all the professors in Yajian admired in their hearts that Lao Zhang was really good at asking questions.
how to say?
This is not a difficult problem in group theory, it can even be said to be a basic question, and it is also very interesting.
But to solve this problem, you must have a thorough understanding of several extremely important concepts in group theory.
For example, finite groups, conjugation, commutability, orders of groups, elements...
At the same time, you also need to have pioneering mathematical thinking, because if you want to solve this problem quickly, you can actually use mathematical methods that you have been exposed to indirectly in high school.
It is indeed a wonderful question.
It is difficult to say that for those who have studied systematically and understood group theory, it does not take long to figure it out.
It’s not difficult to say, even if the world champion of the Mathematics Olympiad came, he probably wouldn’t even be able to understand the questions.
Looking at Qiao Ze who was already deep in thought, Zhang Chunlei said with a smile: "Haha, kid, don't be anxious, think slowly, as long as before the end of tea today..."
"I have already thought of how to prove it, using induction." Qiao Ze suddenly interrupted Zhang Chunlei.
"Huh?" Everyone was stunned.
Damn it, is it too fast?
It is no exaggeration to say that many professors present only have a clue...
"Suppose there is a second-order element m, mm equals 1 mx equals xm and my equals ym."
"Suppose mk is equal to (xy)^k. If mk is equal to (yx)^k, the proof is complete.
"If mk is not equal to (yx)^k, then for j less than k,"
"If j+k is equal to an even number, then h exists, 2h is equal to j+k, (xy)^h is not equal to (yx)^h,"
"If j+k is equal to an odd number, then h exists, 2h+1 is equal to j+k, z is equal to (xy)^(h+1), zy is not equal to xz"
"Then (yx)^h is not equal to (xy)^(h+1), so it can be proved that mk is not equal to mj."
"Finally, because G is a finite group, this process will definitely end."
"The proof is over."
Li Jiangao silently took a cup of tea that Zhang Chunlei had just brewed from the tea set and drank it in one gulp.
As long as you're not the one being shocked, it's still fun.
Especially looking at the dazed and complicated expression on Lao Zhang's face opposite him made him want to laugh.
Now you all know that this kid is crazy, right?
"Ahem... Do you really understand group theory?"
After reacting, Zhang Chunlei sighed with emotion, then looked at many professors who were still in a daze and said: "Look, who said that our Chinese generation is inferior to the previous generation? Today's children have already thoroughly understood group theory when they were in high school. !I had never even heard of the term group theory when I was in high school.”
"Who is not, Professor Li, where did you kidnapped this kid?" someone couldn't help but ask.
"Haha, drink tea, drink tea, we agreed not to talk about this." Li Jiangao smiled and pretended.
Because he knew that the more mysterious the relationship was, the more interested these people would be in Qiao Ze.
"It's your turn to tell me what the research topic is." Qiao Ze ignored everyone's admiration and still looked at Zhang Chunlei seriously and asked.
"Okay, but you have to tell me first, why are you so concerned about my Changjiang Scholars' topic selection?"
"Because I want to become a Yangtze River Scholar with Uncle Li in the future, and then become an academician, so I want to know first how difficult it is to become a Yangtze River Scholar."
"puff……"
As soon as Qiao Ze finished speaking, Li Jiangao spit out the whole mouthful of tea he had just swallowed. Fortunately, he reacted quickly, turned his head in an instant, and sprayed all the tea outside, otherwise the good tea worth at least a thousand yuan would have been wasted.
"I'm sorry, I'm sorry, Tong Yan Wuji, Tong Yan Wuji..." Li Jiangao explained with a blushing face as he put down the tea cup.
Qiao Ze looked at Li Jiangao curiously and asked, "Don't you want to be a Yangtze River scholar?"
"Haha..." Now everyone in Yajian laughed.
Qiao Ze didn't understand what these people were laughing at, but he just felt a little unhappy.
As if he noticed something, Zhang Chunlei waved his hand, stopped laughing, and then said seriously: "Okay, okay, now it's my turn to fulfill my promise. The topic I reported at that time was group theory in designing molecular structure calculation models. Applications.
Specifically, the model built using group theory completely restored the molecular orbital calculation model and calculation results of the hyperconjugation effect in toluene. Can you understand? Of course, it cannot be said that the completion of this topic is all my fault. The teachers in the School of Chemistry also gave me a lot of help.
But this topic selection itself has no reference significance. However, in the future, when you and your Uncle Li really want to apply for the Yangtze River Scholars topic selection, you can consider my point of combining academic and application and choose topics that can solve some practical problems. This is In recent years, the Yangtze River and Distinguished Young Scholars have tended to select topics more favorably. "
Zhang Chunlei's words made Qiao Ze fall into silence again.
But this time the professors didn't have any expectations for Qiao Ze.
In fact, even if a high school student understands some group theory, it is impossible for him to fully understand the significance of this result from Zhang Chunlei's few words. Mathematics is a basic subject. When it comes to selecting topics for research, if you want to solve practical problems, you have to cooperate with other disciplines.
Only pure number theory research is no longer included in this list.
It's just that these days, it's too difficult to get ahead by doing pure number theory research and projects. It can even be said that the available roads are almost blocked.
But then again, Qiao Ze's performance has surprised the mathematics professors who are used to seeing geniuses.
Studying group theory by yourself in high school is really something only a mentally ill person can do. After all, he won’t pass the college entrance examination.
The scary thing is that he seems to have learned it.
However, when the professors' inquiring eyes began to focus on Li Jiangao and wanted to inquire about the child's situation, Qiao Ze spoke again: "If you want to put it this way, if you use group theory to build a self-supervised feature decoupling framework, it should also Is it a practical application of group theory?”
"In my idea, this framework can be used to allow computers to perform downstream causal inference tasks, so that the program has causal inference capabilities and unsupervised representation learning capabilities. In this way, we may be able to create intelligent programs that are smarter than chat GPT, and can also Reduce the current dependence of artificial intelligence on big data. And there is no need to cooperate with other colleges, because I also know something about computers."
"If this topic selection is given to the Yangtze River Scholars Review Team, will they be able to recognize it?"
After finishing speaking, Qiao Ze looked at the strange looks of these professors and added: "This is an idea I had before, but it may not be possible to make it happen."
