The top student must be diligent

He looked at Xiao Yi with curiosity.

Xiao Yi waved his hand: "Aren't all the official documents publicized? You can find out by searching the government website."

"So this is true?" Liang Qiushi's eyes lit up.

What kind of feeling is this?

Isn't it just like my own mentor suddenly became an academician!

Well... Strictly speaking, it feels even better than becoming an academician!

"Teacher, you are awesome!"

He said sincerely.

Xiao Yi waved his hand: "Okay, the question has been answered, go do your thing."

He didn't know what to say about these two positions.

At the beginning, it was just said that he would be a consultant, and Ye Mei said that he would be the chief consultant of these two heavyweight units directly!

Even for life.

As for the chief scientist...

Forget it, it is almost a icing on the cake in front of the position of lifelong chief consultant.

Shaking his head, he continued to think of those mathematical problems in his mind.

There were naturally many problems, so much so that he was now in a dilemma.

However, at this time, Liang Qiushi looked at Xiao Yi's tangled expression and suddenly said, "Teacher, why don't you consider the hail conjecture?"

Xiao Yi was stunned, "Hail conjecture?"

Hail conjecture, also known as Collatz conjecture and Kakutani conjecture, is a very interesting problem in mathematics.

Similarly, it is also a number theory problem, and its description is very simple, and elementary school students can understand it: write any positive integer N, if it is an odd number, the next step becomes 3N+1; if it is an even number, the next step becomes N/2, and the numbers obtained in each step will continue to be transformed according to this rule.

Then, people will find that no matter what N is given at the beginning, it will eventually cycle to 1.

This problem looks simple, but like many other number theory conjectures, it has trapped the entire mathematical community for a long time.

Until 2027, it has been almost 90 years.

After thinking for a while, Xiao Yi suddenly felt that this problem was really good.

Because it is not like the number theory conjectures he has studied before, all of which belong to prime number problems.

This problem is a pure number game.

And the process of proving it is the process of finding the rules of this seemingly simple mathematical game.

Different from the various problems he studied in the past.

Well...

If this conjecture is used as a problem to relax during this period, it is indeed very good.

So he nodded to Liang Qiushi and said, "Okay, thank you for your suggestion first."

Liang Qiushi was stunned again.

No, his teacher really intends to study this problem?

Then he...

Can we open a bet next time and bet on what the next well-known mathematical conjecture that will be proved will be?

Isn't this a sure thing?

Chapter 256 Geometric Langlands Program

Time passed quietly.

Since he decided to study the hail conjecture, it was naturally not just talk.

So from that day on, Xiao Yi began to focus his main energy on the hail conjecture.

Of course, it was probably a long time since he had studied pure mathematical problems, so at the beginning, Xiao Yi even felt a little uncomfortable.

After all, although mathematical tools are indispensable in the process of studying nuclear fusion, for nuclear fusion, the mathematical tools used are all "useful", that is, these mathematical tools themselves are prepared for practical applications.

And the mathematical tools used in the process of studying pure mathematics are basically "useless". Although they may be very useful for studying pure mathematics, they are not very useful for applications.

So in the past few years, the mathematical tools used by Xiao Yi have been useful, and now suddenly using these useless mathematical tools does make him feel a little uncomfortable.

"Tsk tsk, this is what is called unfamiliarity."

In the school office, Xiao Yi sighed.

However, for him, it is not a problem.

As the relevant mathematical knowledge is recalled in his mind, the unfamiliarity will gradually fade away.

"However, this question does have a different feeling in it."

Simply using up a few pieces of draft paper, and placing them on the table, Xiao Yi rubbed his chin and raised his eyebrows.

Well, it is indeed very different.

Other mathematical conjectures about prime numbers all involve analytic number theory or algebraic geometry, but the hail conjecture, which is also a conjecture in number theory, involves other aspects of mathematics.

For example, dynamical systems.

Of course, this dynamical system refers to the dynamical system in mathematics, not any other dynamical system.

A system that uses functions to describe the changes of a point in space over time is a dynamical system. Of course, such mathematical methods can be applied to dynamical systems in engineering without any problems.

In short, it is probably like an iterative process.

The calculation process of the hail conjecture is probably equivalent to such an iterative process. Each step is transformed according to the parity of the current number, thus forming a whole sequence of digital changes.

In addition, according to the theory of fixed points and periodic orbits in dynamical systems, the hail conjecture is equivalent to that for any starting positive integer, it will eventually enter a 4-2-1 cycle, that is, reach a fixed point or periodic orbit.

Then, if such a fixed point or periodic orbit can be found based on such a theory, it can provide very important help for proving the conjecture, or even directly complete the proof.

Of course, it is not just that.

This seemingly simple problem may involve more fields.

For example, strange attractors in hybrid theory, as well as topological entropy and complexity, etc.

In short, this problem is definitely not simple.

Otherwise, some mathematicians would not call it "an extremely difficult problem, completely beyond the scope of current mathematics", or even think that "mathematics is not ready to deal with such a problem".

"Well... So, do we need new mathematical tools?"

Xiao Yi gradually pondered.

Mathematicians believe that this problem is beyond the scope of current mathematics, or that mathematics is not ready to deal with such a problem. Basically, it means that the current mathematical community does not have mathematical tools that can solve this problem well.

So, it is necessary to invent new mathematical tools.

"Hmm... maybe the Langlands Program would be a good angle?"

Recalling the progress in mathematics in recent years, three years ago, in 2024, the geometric Langlands conjecture was solved.

Obviously, although he has become the main protagonist in mathematics over the years, other mathematicians have not fallen behind.

The geometric Langlands conjecture is a series of conjectures and conclusions obtained by stating the Langlands Program in number theory on the function field of algebraic curves.

It is somewhat different from the Langlands Program. It can mainly connect algebraic geometry, representation theory, and even quantum mechanics. It can be said that it plays a very important role in mathematics.

When the paper was first published three years ago, Xiao Yi was invited to serve as a reviewer of this paper.

But unfortunately, he refused because of other important topics at the time.

Now, can the now proven geometric Langlands conjecture help the study of the hail conjecture?

Although theoretically, the connection between the two is still a bit too weak. One involves highly abstract theories such as algebraic geometry and representation theory, and the other involves relatively specific problems such as number theory and dynamical systems. It seems that there is basically no connection between them.

However, for mathematics, sometimes there seems to be no connection between the two, but this is just because there is no attempt.

As the saying goes, how can you know if you don't try?

So Xiao Yi started to try.

So putting the hail conjecture aside for the time being, Xiao Yi first found the paper that proved the geometric Langlands program.

To find the relationship between the two, you have to figure them out first.

This paper that proves the geometric Langlands conjecture is more than 800 pages long and can be said to be quite complicated.

Of course, there are nine authors of this paper, including a mathematician from China named Chen Lin, who won the IMO gold medal when he was fifteen years old and is also a young mathematical genius.

"Well, I have something to do in the next week."

Xiao Yi stretched and then began to read the paper.

For others, it might take a long time to read an 800-page paper, but for him, it only takes a few days.

Especially now that he has a lv7 BUFF, it is not difficult at all. Even for him, a week is a bit slow.

Mainly because he has other tasks.