Chapter 145 If you can complete it, your contribution will be greater than Newton's!

On the Internet, a cross talk star made a famous line.

"You don't understand dad's happiness at all."

In fact, the essence of the meaning is a replica of the emperor using a golden hoe to hoe the ground, but it was expressed in more ridiculing language.

It is difficult for poor people to understand the happiness of rich people, just as it is difficult for ordinary people to understand the happiness of highly intelligent businessmen.

It just so happens that from time to time, some amazingly talented people will appear in this world, who will humiliate the IQ of ordinary geniuses over and over again.

It's like in that era when technology was still very backward, people couldn't even figure out how Einstein arrived at the constant speed of light and his conclusions about the relativity of time and space.

After all, the core idea of ​​the special theory of relativity of this physics guru directly challenges the intuitive understanding and empirical common sense of Newton's classical mechanics.

How can time expand if it is eternal?

How could the speed of light be constant? It was even introduced into the mass-energy equation?

The most speechless thing is that mass can be converted into energy?

You must know that in classical physics at that time, mass and energy were regarded as completely different physical quantities. They were each conserved and could not be converted into each other. This is common sense!

But the fact is that a series of experiments later gradually proved Einstein's point of view.

Especially after human scientists discovered nuclear fission and nuclear fusion, research on atomic nuclei found that Einstein knew it too well!

After a boy and a fat man showed great power, the mass-energy equation became an unquestionable basic formula in physics.

In a sense, Qiao Yu also wanted to do something like this. But mathematics is different from physics, and Qiao Yu's ideas are freer.

In order to save more time when asking Professor Zhang for advice tomorrow, Qiao Yu fell into an exciting state of creation.

He needs to give Professor Zhang a few examples.

For example, the number 1.

This enlightening number, in the system designed by Qiao Yu, the modal number of 1 will no longer be a fixed value, but will show different changes as the modal space (α, β) changes.

modal characteristics.

It is recorded as N_α,β(1). And because it has some unique properties under this fixed axiom system.

For example, the automorphism of modal unit numbers.

Expressed as a formula:

This means that although the modal space is changing, the modal units always appear as unit elements in any mode.

In other words, no matter how the mode changes, the modal unit number always has the conceptual concept of 1, but it may exist in different forms.

At the same time, due to the change of modes, different modal dependencies need to be shown in different modal spaces.

For example, in the complex field:

In essence, the concept of automorphic representation space of Langlands program has been introduced here. In other words, the automorphic representation space is correspondingly structured.

In the same way, if you want to continue to operate the number 1, you can also use the concept of modal convolution. In Qiao Yu's construction, modal convolution Gm is an extremely important operation.

The number of modal units appears as the neutral element of modal convolution in convolution. For any modal number N_α, β(n) there are:

In addition, for better operation in the future, the modal unit number must also be self-referential.

A simple 1, in this framework, can be either a complex phase modal unit number, an exponential recursion unit number, or a multi-dimensional representation unit number.

With these definitions, some concepts in classical number theory can be transformed.

For example, in classical number theory, the formula for an arithmetic sequence is: a_n=a_1+(n1)d.

When this formula is extended to the modal space, so that the tolerance and term value of the sequence can depend on the changes of the modal parameters (α, β), then the modal arithmetic sequence will be recorded as:

The purpose of doing this is actually very simple.

Since the existing tools cannot solve a series of problems with prime numbers, we can simply upgrade the number theory problems to the dimension of modal space.

This allows Qiao Yu to use a series of tools he defined under this axiom system to solve outstanding number theory problems.

Qiao Yu thinks this can be called a modal Langlands program.

To be honest, this kind of creation feels very exciting. It's like really building a new digital universe, and Qiao Yu is even addicted to it.

Of course, although this feels great, there is still too much work to be done to make these tools and operations relevant to classical number theory.

But Qiao Yu doesn't need to think so much now. He only needs to construct this multi-level structure containing different modal spaces.

Then tomorrow I will discuss it with Professor Zhang who made this suggestion to him. The specific improvement will be a huge project.

By the time Qiao Yu felt sleepy, it was already three o'clock in the morning.

Under normal circumstances, Qiao Yu actually lives a very regular life and goes to bed at eleven o'clock.

He can even go to bed without looking at his phone.

There are only a few moments when I am so passionate about mathematics that I am so focused that I forget to feel sleepy. I accidentally stay up until the early hours of the morning.

But it doesn't matter, because when he feels sleepy, he really can't hold on for a second.

As for washing, it has become a very luxurious thing at this time.

He stood up and staggered into the bedroom. As soon as he lay down on the bed, he was already snoring slightly in less than thirty seconds.

You can often sleep very soundly this way.

…

For a child who has decided to shoulder the burden of supporting his family since the fifth grade, Qiao Yu knows one thing very well, that is, this is a world full of competition.

There will be no pie in the sky. Whatever you want, you have to fight for it yourself.

To achieve this, you have to do the right things at the right time according to your goals.

For example, if he wants to become a star-level professional game player, he must spend a lot of time practicing in the game every day, trying to figure out the advantages and disadvantages of each game character's skills, constantly honing his skills, and mastering various tactics.

, and a tacit understanding with your companions...

But now if he wants to become a mathematician, he must devote time and energy to study and research, and obtain results that can be recognized by people.

In Qiao Yu's opinion, this is fair. Just like what he once said to Zhou Shuang, if your efforts are not rewarded, then you have to get out in time.

If he can get satisfactory rewards for his hard work and can get along well with the people around him, it is enough to show that he is not only suitable for this task, but also can achieve a win-win situation with those who cooperate with him.

There is no doubt that Qiao Yu now feels that he is indeed suitable to be a future mathematician. The path chosen by the good old man is quite good and suitable for him.

Then he should seize the opportunity to make some achievements, satisfy everyone's expectations and achieve himself at the same time.

So even though he didn't go to bed until three in the morning, Qiao Yu climbed out of bed energetically at seven-thirty the next day and continued his research.

Even though Professor Zhang Yuantang’s lecture only started at ten o’clock today.

But the extra preparation he made in the early stage meant that the question-and-answer session that Director Tian helped him secure could improve efficiency.

In other words, he can squeeze the teachers who are invited to teach him more experience and knowledge.

This is nothing to feel guilty about.

After all, being able to invite a professor to give such an academic lecture is not something you can do just based on face. After all, you have to pay for it.

Qiao Yu felt that he was just letting Director Tian spend the money more cost-effectively.

…

The two-hour lecture was packed with seats, but in fact, Qiao Yu felt that the lecture did not yield much.

Because the content of the lectures given to the public is actually similar to the ideas expressed in the papers.

Qiao Yu can also understand this.

After all, professors also want to save face. In public, they will have various scruples and will not discuss some content that is too radical or uncertain.

For example, many people like to use the word "obvious" in the process of mathematical proof. Even some professors often use these two words on the blackboard during class.

So many times these two words appear a bit taken for granted.

That's all in private, but if the boss uses these two words during a lecture, and someone obviously questions this when asking questions, two situations may occur.

The first is for the boss to explain in just a few lines and give proof. That is, it is indeed obvious. This will make the person asking the question look like a fool.

The second type is when the boss writes to prove why it is obvious, but finds that it is not so obvious, and cannot prove it for a while, which makes the person giving the lecture on the stage look like a fool.

Not only was this situation embarrassing at the time, but it would also be embarrassing if word spread about it.

Therefore, when giving lectures, the boss will definitely avoid saying things that have not been well thought out or even that he may not be sure of.

Even if there is, it will be placed in the final outlook.

But discussing it in private is different. It won't hurt face anyway, and the professors will be more bold. Some new ideas can be discussed without any scruples.

Therefore, compared to the public lectures, Qiao Yu was more looking forward to the private exchanges in the afternoon.

This is what Tian Yanzhen promised him yesterday.

But what surprised Qiao Yu was that after the morning lecture, Director Tian didn't ask him to go to dinner with him.

I just mentioned to him that if I go to his office at two o'clock in the afternoon, Professor Zhang will also be there.
To be continued...