Chapter 317

In his famous speech at the Second World Congress of mathematicians held in Paris on August 8, 1900, David Hilbert put forward 23 mathematical problems.

In the past hundred years, Hilbert problem has inspired the wisdom of mathematicians and guided the direction of mathematics. Its influence and promotion on the development of mathematics is enormous and immeasurable.

Since the beginning of the 21st century, the Scientific Advisory Committee of Cray Institute of mathematics has selected seven "Millennium award questions".

Although Cray Institute of mathematics does not have the unique appeal in mathematics as Hilbert did more than 100 years ago. It is estimated that even if the "seven Millennium prize questions" are put forward, it is estimated that not many mathematicians in the world are keen to solve them, but They have money!

The board of directors of the Cray Institute of mathematics decided to set up a $7 million grand prize fund. Each solution to the "Millennium prize problem" will receive a $1 million award.

Those top mathematicians may not care about this small amount of money, but there are a few mathematicians who are rich and regard money as dirt.

So Countless mathematicians regard these seven Millennium mathematical problems as their lifelong goals. However, it has been 20 years since the issue of the Millennium prize was proposed. However, the only problem that has been solved is the Poincare conjecture. The rest, however, is rather slow.

Seven centuries ago, it's still unclear whether the grand prize will be solved in the next half of the century.

……

The seven Millennium prize problems are: NP complete problem, Hodge conjecture, Poincare conjecture, Riemann hypothesis, Yang mills existence and quality gap, Navier stoke equation and BSD conjecture.

Obviously, the BSD conjecture mentioned by Professor Fang is naturally listed here.

Facing Professor Fang's inquiry, Cheng Nuo nodded.

As such a famous problem of seven Millennium awards in mathematics, Cheng Nuo has no reason to be unclear.

"Yes, the BSD conjecture, the full name of which is the Borch and Swinnerton Daya conjecture."

The conjecture is: let e be an elliptic curve defined on an algebraic number field K, e (k) be a set of rational points on e, and E (k) is known to be a finitely generated Abelian group. Note that l (s, e) is the Hasse Weill function of E. It is conjectured that the rank of E (k) is exactly equal to the order of the zero point of L (E, s) at S = 1. And the first nonzero coefficient of the Taylor expansion of the latter can be accurately expressed by the algebraic properties of the curve

BSD conjecture is a complex conjecture, which can't be compared with Goldbach's conjecture.

But in the eyes of a mathematician like Cheng Nuo, he still understands it very well.

In short, the BSD conjecture describes the relationship between the arithmetical and analytic properties of Abelian clusters. However, for thousands of years, no one has turned this conjecture into a practical theorem.

"Professor, what is this Cheng Nuo doubts.

Professor Fang chuckled. "What if I told you that I was participating in the proof of this conjecture?"

"Why What? " Cheng Nuo opens his mouth in surprise.

Professor Fang pressed his hands down and said with a smile, "don't be too surprised. It's a wonderful thing to prove the seven conjectures. If we can really prove the Millennium problem, it will be a great achievement. "

"What's more, what I'm doing now is not to prove the generalized BSD conjecture, but to prove the weak BSD conjecture when the analytic rank is 1."

"Weak BSD conjecture with analytic rank 1?" Cheng Nuo is light.

"Yes." Professor Fang nodded and opened his mouth to explain, "the generalized BSD conjecture is that given an Abelian cluster on a global field, we guess its The free part volume, the period of all elements and the sand group have exact equation relations. The first half of it refers to the weak BSD conjecture

"As early as four years ago, there were two mathematicians in Yingguo and degau who proved the weak BSD conjecture when the analytic rank is 0, and the exact BSD conjecture holds except 2."

"It was only two years ago that I started to study this conjecture. The current progress Alas Speaking of this, Professor Fang raised the draft paper in his hand and gave a wry smile, "the Millennium problem is worthy of being called the Millennium problem. Although it is only a weak conjecture of the general conjecture, in two years' time, there is only one useful thing I can get. I'm afraid I haven't even finished one percent of the way to prove the whole BSD conjecture. "

With that, Professor Fang handed the draft paper to Cheng Nuo.

Cheng Nuo hesitated for a moment and didn't take it. "Professor, this is your two years' hard work. Let me see Isn't it appropriate? "

Take Professor Cheng Nuo's paper and look at it. Besides, the last thing I called you in was related to this BSD conjecture. "

"I want you to be my assistant in solving the weak BSD conjecture in the case of rank 1 and jointly attack the weak BSD conjecture!"When Cheng Nuo just took over Professor Fang's several drafts, the thunder like news rang in his ear.

Me? BSD conjecture?

Cheng Nuo's head is a little dizzy now.

It was a bit of a surprise.

To tell you the truth, Cheng Nuo also tried to solve the world's mathematical problems by using the power before he got the power. He found that his hardware equipment was not enough.

A rookie who has not graduated from a novice village has the delusion to challenge the last World boss. Even if he holds a sword of 999, he has no strength to fight back. So since then, Cheng has rarely thought about challenging the world's mathematical problems. Instead, he keeps reading and accumulating.

Originally, according to the plan, Cheng Nuo was going to try again when he graduated from the undergraduate program and went to graduate school or master's degree. But unexpectedly, Professor Fang invited himself to join the work of proving the weak BSD conjecture.

Before Cheng Nuo is to make ordinary small mathematical problems, this suddenly came on a millennium mathematical problem.

If the pace is too big, will you pull the egg?

"Classmate Cheng Nuo, classmate Cheng Nuo?"

Until Professor Fang called several times in Cheng Nuo's ear, Cheng Nuo's thoughts returned to reality.

"Oh, Professor," you said Cheng Nuo came back to God.

Professor Fang's mouth was filled with a faint smile, "classmate Cheng Nuo, how do you feel about my proposal?"

Cheng Nuo pondered for a few seconds, and finally nodded, "dry!"

"Yes." Professor Fang was also very happy, "take these drafts back and have a look, and then we will talk about the follow-up."

"The proof of the world's problems is not overnight, so you don't have to rush as hard as you did in your last project. Step by step. "

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