Omnipotent Data

Chapter 451

Jacobi conjecture, 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 field k with characteristic 0, the following Jaobian conditions are satisfied:

j_{x, y} (f(x, y), g(x, y) = nonzero constant in k.

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

This is the specific content of the Jacobi conjecture.

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

Anyone 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 has brought mathematicians closer and closer to the real proof success.

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

Theories about the Jacobi conjecture have gradually been perfected, 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 proves successful.

It's just that someone pushed open the door at last!

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

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

The difficulty of the ABC conjecture, the Jiaogu conjecture, and the four-color conjecture that ranked in the second echelon was too high, so Cheng Nuo didn't consider it for the time being.

After making a selection, Cheng Nuo felt that Jacobi's conjecture was the most suitable.

Besides, now that he had figured out a vague direction in his mind, Cheng Nuo thought he could give it a try.

If you want someone else to come, it is rare to have the opportunity to lead a topic, and you must choose a normal difficulty to seek stability and accumulate full qualifications.

But Cheng Nuo is different.

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

It is useless to stay in the Institute of Mathematics and Physics to mix qualifications, because he will not live in Cambridge forever.

Instead of just messing around in the first half of the year, it's better to just make a big one.

Jacobi conjectures that although it is not comparable to the few mountains that have stood in the mathematics world for hundreds of years, it can barely be regarded as a small mountain.

Just in time, taking this opportunity, Cheng Nuo wanted to test whether he could climb this mountain with all his strength.

How proud it is to carve your name on the highest point of a mountain!

…………

March 15.

Within three days, Cheng Nuo's project application was approved, and it was placed under the name of the Institute of Mathematics and Physics of Cambridge University.

Ordin 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.

The next day, the funds, equipment, and personnel will all arrive in the account.

Cheng Nuo also met Denton and Qiao Ya in the office.

"Hi two seniors, this time it's not three days, but we will fight side by side for the next six months!" Cheng Nuo greeted with a smile.

Denton smiled wryly, "Cheng Nuo, it's better not to call us senior. If you want to graduate, we're afraid we will call you senior now."

Cheng Nuo shrugged his shoulders and stopped worrying about it, "Let me briefly tell you two about our research topic this time."

"The title of our research project is called "The local bijection method of the Keller map of the Jacobi conjecture". In simple terms, it is..."

After listening to Cheng Nuo's narration, Denton was too shocked to speak.

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

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

"This is crazy!" Joya exclaimed shaking her head.

They are just three students, but they challenged the famous Jacobi conjecture in the mathematics world, it is unbelievable!

Cheng Nuo put his arms around the shoulders of the two of them, looked through the window, and looked into the distance, "Isn't the guess put there, it's just for people to conquer! And we want the conqueror, why can't we?"

"There is a saying in Huaguo that says, 'If you try, you may fail, but if you don't try, you will never succeed'! Believe me, we will definitely do it!"

"En!" The two nodded heavily, 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 blows, and the maple leaves flutter in the air.

In an office on the third floor.

Cheng Nuo turned the pen, leaned on the back of the chair and looked out the window, looking at the autumnal Cambridge University, his eyes were a little lost in thought.

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

boom boom boom

"Come in!"

The office door was pushed open.

Denton, wearing a peaked cap, put a stack of documents on Cheng Nuo's desk, his face was full of joy, "Cheng Nuo, I have shown our certification process to Director Ording."

"Oh?" Cheng Nuo turned the seat around, stroked his chin and said, "What did the director say?"

"The director took this document and looked at it for four days, but he didn't say anything when he returned it to me, but... he looked at me strangely!" Denton scratched his head and said.

Cheng Nuo smiled, "The director didn't say there was something wrong with our proof process?"

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

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

Cheng Nuo picked up the teacup and took a sip.

Compared with Denton's excitement, Cheng Nuo seemed much calmer.

In fact, as early as two months after the research started, when the derivation results of that time came out, Cheng Nuo knew that the direction of his proof was correct.

Getting this answer now is within my expectations.

Since Aldin said that there is no problem, it is probably not a big surprise. After all, Aldin has also been a review editor for the UK mathematics journal "Journal of the UK Mathematical Society".

Jacobi's conjecture... was really proved by himself!

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

Cheng Nuo seemed to feel a little swollen when the process happened naturally.

Jacobi conjecture?

It's just a small third-level conjecture.

The proof is out, what's there to show off?

It won't be too late to prove the Riemann conjecture.

"Has the hole been filled?" Cheng Nuo asked George with a smile.

George nodded, "I have sent the preprint of the paper to arXiv."

"That's good." Cheng Nuo tapped his forehead, "However, this paper must be submitted as soon as possible. Various universities have never stopped research on Jacobi's conjecture. It would be too uncomfortable if someone else preempted it. "

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

"Just vote for "Journal of Ying Country Mathematics Society"!" An old voice came. Director Aldin walked in without knocking on the door, "After all, I am one of the review editors of this journal, and writing a letter of recommendation will probably get your paper published as soon as possible."

"I didn't expect it, I really didn't expect it. I didn't expect much, but I didn't expect you to make it out of it." Ordin looked at Cheng Nuo with complicated eyes.

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