In the field of mathematics, Shen Qi's name is everywhere.

Shen Qi expounded the BSD conjecture in "The History of Number Theory", which is inextricably linked with other problems, and the study of the BSD conjecture is actually a review of the history of modern number theory.

In the history of the development of modern number theory, 1995 is a key node.

In that year, Wiles proved Fermat's theorem by establishing a connection between elliptic curves and model theory.

It was also a year that had a significant impact on the BSD conjecture, which mathematicians were not 100% sure of its significance.

In the process of proving Fermat's theorem, Wiles easily proved the Taniyama-Shimura conjecture, and while he proved these two conjectures, he also made the mathematical significance of the BSD conjecture affirmed by the mathematical community.

So what is the mathematical significance of BSD?

What will be the effect of proving this conjecture?

The mathematical community, including Shen Qi, agrees that if the BSD conjecture is proved, then the finite theory of sand groups, which is one of the cores for understanding the arithmetic nature of mathematical objects, will also be proved.

In other words, the BSD conjecture, if proved, would give a definite answer to the question of the extent to which information in the algebraic number field can be glued together by information in all local domains, which has risen to the level of philosophy, which is known as the "partial wholeness principle".

Prove a mathematical problem and perfect a philosophical system.

This is the core meaning of the BSD conjecture.

Mathematics and philosophy are both cold subjects, and the CP of mathematics + philosophy is so cold that they have no friends.

There are very few scholars who have devoted themselves to studying the BSD conjecture, and they are lonely fireworks that bloom at a height of 10,000 feet.

So far, the closest BSD conjecture proof scheme to the truth comes from Gong Changwei and Skinner, as well as Bargava and Shankar.

The results of the four mathematicians' work that took more than a decade to translate into a paper are a staggering 6,098 pages that could fill the trunk of a car.

Four mathematicians, Gong Changwei, Skinner, Bargava, and Shankar, proved a conclusion: at least two-thirds of elliptic curves satisfy the BSD conjecture.

The results achieved by these four mathematicians on the BSD conjecture are equivalent to Chen Jingrun's proof of Goldbach's conjecture 1+2.

Gong Changwei, one of the four mathematicians, is Chinese, and he was Ouye's mentor when he was a graduate student at Columbia University.

Zhao Tian looked at the mathematical formula on the whiteboard and asked, "I have a question, Professor Shen analyzed the past and present lives of the BSD conjecture so thoroughly in "The History of Number Theory", why didn't he prove the BSD conjecture?"

The only person who can answer this question is Ou Ye, she said: "Because Professor Shen's level is limited. ”

"Hahaha!"

"Slightly. ”

“......”

After hearing Sister Ye's answer, the three students had different expressions.

Dare to say that Professor Shen's level is limited, and I am afraid that there is only Sister Ye Zi in the world.

The whole world is only allowed to beep you, and no one else is eligible.

This is also an alternative show of affection.

Since Professor Shen's level is limited, then the BSD conjecture should be left to the team with unlimited levels.

Ou Ye is good at analytic number theory, which is the hardest branch of number theory.

If algebraic number theory is compared to soft science fiction, analytic number theory is equivalent to hard science fiction written by Clark.

Ouye is probably Clark of number theorists.

Shen Qi was originally also a Clark, and he used a purely analytic number theory method to prove the Riemann conjecture, which can be described as invincible.

After the Riemann conjecture was completed, Shen Qi underwent some changes in his academic behavior, he became less hard, and he preferred a combination of software and hard when dealing with some academic problems, which is also the mainstream trend of the development of mathematics in the future, and the interdisciplinary disciplines are becoming more and more frequent and close.

The subtle changes in Shen Qi's academic thoughts more or less affected Ou Ye, after all, the two slept in the same bed.

Ou Ye realized that the pure number theory method could not solve the BSD conjecture, and he could not do it with the once invincible Shen Qilai.

Therefore, on the BSD conjecture, Euyeol chooses number theory + elliptic curve + ...... Combine the way and go with the flow.

If the mainstream research method of combining software and hardware is adopted, then Professor Shen, who has a limited level, still makes some indirect contributions to the BSD conjecture.

In the BSD conjecture, the larger r, the more rational points mathematicians want to see, and r is the rank of the curve, which is an important parameter in this problem.

Although mathematicians around the world have made remarkable progress in the study of elliptic curve theory in recent years, rank is still a mystery.

Even the basic question of how to calculate rank, or whether rank can be infinite, has not been solved.

Shen Qi wrote in "The History of Number Theory": "...... In order to better understand the BSD conjecture expounded in this chapter, I recommend that you read another book by me, "Before and After the Riemann Conjecture Proof". ”

Shen Qi's main purpose in writing this is to make the sales of "Before and After the Riemann Conjecture Proved" a little more.

Of course, if the reader understands the Riemann conjecture, it will also be helpful to interpret the BSD conjecture.

Readers only need to know a little about the Riemann zeta function to know that the Hasse-Weil function in the elliptic curve is actually the Euler product.

Shen Qi's real contribution to the BSD conjecture came from an unpublished paper manuscript.

In this manuscript, Shen Qi drew a picture casually.

Originally, he wanted to draw a flounder and tell Nofi a story by looking at the picture.

As a result, Shen Qi drew the fish into a coordinate system and curve.

This extremely ugly "fish", Ou Ye has seen it. Shen Qi tried to use the idea of group theory to explain the rank in the elliptic curve.

However, Shen Qi did not thoroughly explain the law of rank in the elliptic curve and the calculation principle, and there was no follow-up after he finished drawing "fish".

On the contrary, Ouye was deeply inspired, and she realized a new way of thinking from this "fish".

Ou Ye wrote on the whiteboard:

E（Q）≡Z^r×E（Q）f

E（Q）={（-d，0），（0，0），（d，0）......

Here E(Q) is actually a commutative group, i.e., the abelian group. Z is the set of infinite integers under addition.

The definition of the BSD conjecture is not difficult to understand, but the difficult part is to prove the derivation process.

The proof derivation of the BSD conjecture is a very complex and tedious task that requires a lot of reserve knowledge.

Number theory, group theory, elliptic curves, Riemann zeta functions, Euler products, Hasse-Wey functions, and even Gaussian conjectures in the second order domain...... The amount of knowledge required is too much.

Fortunately, Zhao Tian, Xiaoyun, and Zeng Han are the elites among the students, and their knowledge reserves are quite OK.

Scientific studies have shown that scumbags spend much more time studying than top students.

Zhao Tian, Xiaoyun, and Zeng Han spend more time studying than scumbags, they are super diligent scholars, so they are qualified to follow Sister Ye to overcome the BSD conjecture here.

The intelligent Xiaoyun quickly understood Ou Ye's strategic intentions: "So, we want to use the group theory as a breakthrough?"