universal data

Chapter 477 Found something incredible

480 chapter

Cheng Nuo tentatively named his newly derived theorem "Elliptic Abelian Group Theorem".

With the elliptic Albert group theorem, the proof work of the BSD conjecture can continue.

"Brother, I will trouble you next."

"Well. Give me a week, oh no, four days, and I'll give you the result."

The appearance of the elliptical Albert group gave Zhang Wei a real hope of overcoming the BSD conjecture.

He has decided to turn down his other job and put all his energy on the BSD conjecture.

After all, once the BSD conjecture is proven, the benefits he can get will be thousands of times higher than his other projects.

…………

The proof work of the BSD conjecture is proceeding in an orderly manner.

Cheng Nuo and Zhang Wei, brothers and sisters, apart from the daily work of advising graduate students, devoted all their remaining energy to this.

Soak in the office every day, there is no need to even go out.

This kind of workaholic attitude, invisibly, has brought vague pressure to many professors in Tsinghua University.

On one side, Cheng Nuo and Zhang Wei, two brothers, were so busy that they even trotted to the cafeteria for dinner.

On the other side, these professors were sitting leisurely in the office drinking tea and chatting happily.

In an instant, the judgment will be judged!
Therefore, in just a few days, many professors suddenly became active when working on projects.

The long-lost hard work reappeared in them.

While the school's scientific research atmosphere was slowly changing under the influence of Cheng Nuo, Cheng Nuo and Zhang Wei were having a heated discussion in the office.

If we calculate it carefully, it has been nearly four months since the BSD conjecture proof project started.

During these four months, Cheng Nuo and Zhang Wei finally solved the first piece of the puzzle that BSD conjectured.

Prove the ultimate goal of the BSD conjecture, progress 1/3.

The two poorest puzzle pieces are Abelian groups and Modal groups.

According to the framework, the next piece of the puzzle that needs to be solved is the modal group.

The Modal group, in the BSD conjecture, is a finitely generated commutative group, which, like elliptic curves, also exists on the overall field.

What the two are discussing now is what is the cutting direction for the next stage.

Zhang Wei believes that the study should be conducted from the modular theorem of the Modal group. The reason is that mathematicians of all generations have conducted in-depth research on this part of the BSD conjecture.

Cheng Nuo had a different view.

Cheng Nuo did not deny the views of the mathematicians who conducted research on the BSD conjecture in the past, but he did not agree with them either.

Since there is no real proof, it means that the previous reasoning scheme may not be correct.

Instead of following the old path of the predecessors, it is better to find another way and walk out of a broad road of our own.

Compared with the modulus theorem, Cheng Nuo thinks that the problem of congruent numbers is a better way to start.

The final result of the debate was that Cheng Nuo convinced Zhang Wei.

In the next few months, I will work hard to understand the second piece of the puzzle.

…………

In midsummer, an ordinary morning.

On the plastic running track of Tsinghua North Playground, Cheng Nuo was jogging at a constant speed wearing headphones.

"Professor, good morning!"

A voice sounded, and then a figure appeared in Cheng Nuo's sight.

This person was none other than Cheng Nuo's student who liked to flatter him, Zhang Minghua.

Thinking of the impression this student had brought to him for more than half a year, Cheng Nuo could only describe it as speechless.

"Yeah." Cheng Nuo nodded as a greeting.

Zhang Minghua didn't look like he was leaving, and while running side by side with Cheng Nuo, he said with an expression of admiration, "Professor, I didn't expect you to be so busy with work and take time out to exercise, no wonder you became the youngest winner of the Veblen Prize." .To a teacher like you, I should be a role model for my generation!"

"Uh..." Cheng Nuo was a little embarrassed by being licked, and smiled, "I heard from Fan Yi that your graduation thesis is about to be completed, which is pretty good!"

"No, no, it's still far from you, professor! A graduation thesis is extremely difficult in our eyes, but in your eyes, it's just a matter of using your brain. This trivial matter is not worth it in front of you. Mention."

"Then after you finish writing your dissertation, are you going to study in another country, or stay and do a project with me?"

"Of course I will stay with you, professor." Zhang Minghua replied without hesitation, "In my opinion, none of the foreign mathematicians is better than you, and in my eyes, you are the biggest boss in the world of mathematics. , I don’t need to go abroad, just stay by your side!”

Looking at Zhang Minghua's upright and dignified look, Cheng Nuo was a little uncertain. Was Zhang Minghua licking those words, or did they really come from his heart?
"Show me the graduation thesis after you finish writing it. If you can't even pass my test, I won't let you participate in the graduation defense." Cheng Nuo said lightly, "Just to remind you, I'm very strict!"

"Professor, you don't know, I just like strict teachers!" Zhang Minghua showed a row of neat and white teeth, "The stricter you treat students, the more you show your attitude towards students! Professor, you are an admirable teacher, I am honored I can be your student!"

Cheng Nuo: "..."

Being licked was a bit unbearable, Cheng Nuo lowered his head and ran around twice without saying a word. After returning to the apartment to take a shower, he went straight to the office of the research institute.

When Cheng Nuo arrived, Senior Brother Zhang Wei had just arrived.

"Senior brother, good morning!"

"morning!"

"That's right. Cheng Nuo, I've compiled the summation of the square factors you want into a file. Come on, let's see if there is any problem."

Cheng Nuo flipped through it briefly, "Senior Brother Zhang, you did a good job. Below that, there is the problem of constructing rational points on an infinite-order curve. Leave it to me."

"Cheng Nuo, this..." Zhang Wei hesitated.

The problem of constructing rational points on infinite curves mentioned by Cheng Nuo is the most critical part of the second puzzle, and it is also the most difficult part.

Cheng Nuo saw Zhang Wei's worry and shrugged easily, "Senior brother, just leave it to me. I already have some ideas. If I deduce it in practice, it shouldn't be a problem."

"Then, please Cheng Nuo."

…………

Cheng Nuo took a pen and calculated on the draft paper.

The research object is the representation of the rational points obtained when the congruent number of the Modal commutative group intersects with the infinite order curve.

This was a rather complicated question. Fortunately, Cheng Nuo had some inspiration.

These inspirations came to Cheng Nuo when he was running in the playground these mornings.

So he has the habit of going to the playground twice every morning.

"Assuming that D has no square factors, simple elementary considerations show that D is a congruence number equivalent to the elliptic curve E_D: y^2=x^3-D^2x has a rational point of y \neq 0. It can be proved that this The point does not belong to T, so D is a congruence number and is equivalent to r_D>0. Determine all congruence numbers D such that r_D>0, and then..., and in this way, you can determine that this rational point is..."

"Oh, no, wait!"

Suddenly, Cheng Nuo's pen stopped and his eyes narrowed.

The corner of his mouth curled up, and he muttered to himself, "I seem to have discovered something extraordinary."

(End of this chapter)