Omnipotent Data

Chapter 451

Jacobian conjecture, the English name Jaobian conjecture.

The simplest form of introducing the Jaobian conjecture is: the Jaobian conjecture for two variables: given two polynomials f(x, y) and g(x, y) on the domain k with a feature of 0, the following Jaobian conditions are satisfied:

j_{x,y}(f(x,y),g(x,y) = non-zero constant in k.

Then we get k[x,y]=k[f,g].

This is the specific content of Jacobi's conjecture.

As one of the famous conjectures in the field of algebraic geometry, the Jacobi conjecture is not difficult to understand.

People with a little knowledge of calculus can easily understand it.

Therefore, the Jacobi conjecture has always been a hot field of research.

Since it was proposed in 1939, nearly a hundred years of development have brought mathematicians closer and closer to the real proof.

Maybe four or five steps, or maybe only one step.

Theories about the Jacobi conjecture have gradually been improved, and some have even formed a separate research direction.

It can be said that in such an environment, it is only a matter of time before the Jacobi conjecture is proved to be successful.

Only difference, someone pushed the door open in the end!

And Cheng Nuo wanted to be the one who opened the door.

In terms of difficulty, in all mathematical conjectures, Jacobi conjecture is only included in the third echelon.

The second-tier ABC conjectures, Kakutani conjectures, and four-color conjectures are too difficult for Cheng Nuo to consider.

After some selection, Cheng Nuo felt that Jacobi's conjecture was the most appropriate.

Besides, since a vague direction has been figured out in his mind, Cheng Nuo thinks he can try it.

If you want other people to come, you will have a rare opportunity to lead a subject. It must be an ordinary difficulty seeking stability and full qualifications.

Can Cheng Nuo is different.

He stayed at Cambridge University for only half a year at most.

There is no use for a mixed qualification at the Institute of Mathematics and Physics, because he will not live in Cambridge forever.

Rather than just mixing the first half of the year, it's better to start a big one.

Jacobi conjectures that although it is not comparable to the great mountains that have been standing for hundreds of years in mathematics, it can barely be counted as a small mountain.

It just so happened that Cheng Nuo wanted to check whether he could climb this mountain with all his strength.

How proud to engrave your name on the highest point of the mountain!

…………

March 15th.

In three days, Cheng Nuo's application for the subject was passed and it was put under the name of the Institute of Mathematics and Physics at Cambridge University.

Ording assigned Cheng Nuo an empty office on the third floor of the Institute of Mathematics and Physics.

The efficiency of the institute is extremely fast.

On the next day, all funds, equipment, and personnel were credited.

Cheng Nuo also met Denton and Joya in the office.

"How about the two seniors, this time it is not three days, but we will fight side by side for the next six months!" Cheng Nuo said hello with a smile.

Denton smiled bitterly, "Cheng Nuo, you still don't call us senior. If you want to graduate, we might call you senior now."

Cheng Nuo shrugged and stopped struggling with this. "I'll give you two briefly talk about our research topic this time."

"The name of the subject we studied is called "Keller Mapping Local Bijectivity Method of Jacobi Conjecture". In short, it is..."

After hearing Cheng Nuo's account, Denton was horrified and speechless.

He widened his eyes and swallowed fiercely, "Cheng Nuo, you have to prove Jacobi's conjecture!!"

Cheng Nuo grinned, showing a row of white teeth, "To be precise, it is us! It is we who want to prove Jacobi's conjecture!"

"This is crazy!" Joya shook his head and exclaimed.

They were only three students, but they challenged the famous Jacobi conjecture in mathematics. It was incredible!

Cheng Nuo hugged the shoulders of the two of them, looked through the window, and looked into the distance, "I guess it is placed there, isn't it just for people to conquer! And what can't we do if we want the person to conquer?"

"Our country in China has a saying, "You may fail if you try, but you will never succeed if you don't try! Believe me, we can definitely!"

"Yeah!" The two nodded their heads, their eyes gradually becoming firm.

…………

half year later!

Spring goes and autumn comes.

On the path leading to the Institute of Mathematics and Physics, the breeze was blowing, and maple leaves were flying in the air.

Inside an office on the third floor.

Cheng Nuo turned his pen, leaned back in his chair and looked out the window, looking at the autumnal Cambridge University, his eyes slightly surprised.

"Almost, it's time to leave here!" Cheng Nuo sighed lightly.

Dong dong dong

"Come in!"

The office door was pushed open.

Denton, wearing a peaked cap, held a stack of documents on Cheng Nuo's desk, his face filled with joy, "Cheng Nuo, I have shown our proof process to Director Alding."

"Oh?" Cheng Nuo turned the seat around and touched his chin. "What did the director say?"

"The director of this document took it and looked at it for four days. When it was returned to me, he didn't say anything, but... the look in my eyes was strange!" Denton scratched his head.

Cheng Nuo smiled, "The director didn't say that there was a problem with our certification process, right?"

Denton scratched his head, "That's not true. The director said that our paper is perfect, and he can't pick out any flaws, so let's just submit it."

Denton continued, his expression full of excitement, "To be honest, I really didn't expect that we can really prove the Jacobi conjecture in half a year!"

Cheng Nuo picked up the tea cup and took a sip.

Compared to Denton's excitement, Cheng Nuo seemed more indifferent.

In fact, as early as about two months after the start of the research, when the deduction result of that time came out, Cheng Nuo knew that his proof was in the right direction.

Now that I got this answer, it was in my expectation.

Since Alding said there was no problem, there was no big surprise in 80%. After all, Alding has also been the review editor of the Yingguo Mathematics Journal "Journal of the Yingguo Mathematical Society".

Jacobi conjecture... I really proved it by myself!

The expected excitement and excitement did not appear at this moment.

The natural process made Cheng Nuo feel a little swollen.

Jacoby guess?

It's just a little three-level conjecture.

It's proved, what is there to show off?

When will the Riemann conjecture be proved, it will not be too late~www.readwn.com~ is the pit occupied? "Cheng Nuo asked George with a smile.

George nodded, "I have posted the preprint of the paper on arXiv."

"That's good." Cheng Nuo tapped on his forehead, "but this paper must hurry to vote. The research on Jacobi conjecture in various universities has never stopped. It would be too uncomfortable if someone else preempted it. "

"But, should I submit it to which journal?" Cheng Nuo frowned.

"Just vote for "Journal of Yingguo Mathematical Society"!" An old voice came. Director Ording walked in without knocking on the door. "After all, I am one of the reviewing editors of this journal. I write a letter of recommendation and it is estimated that your paper will be published as soon as possible."

"Unexpected, really unexpected, I didn't expect much, but I didn't expect you to really tinker it out." Ording looked at Cheng Nuo with complicated eyes.

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