Chapter 456

Chapter 459

in a word, Gu shanzhicun conjecture means that the elliptic curves above the rational number field can be modeled.

The problem seems so simple that ordinary undergraduates can understand it.

But this conjecture has puzzled mathematicians all over the world for more than 50 years.

Even in the period when Gushan Zhicun conjecture was just put forward, the proof process can be described as difficult.

It was not until 1993 that wiles announced the proof of Fermat's theorem that the proof of Gushan's conjecture took a big step forward.

However, in recent years, as the number of mathematicians who devote their energy to the conjecture of Gushan village is becoming less and less, the road to explore the conjecture has become dark again.

In fact, every proof of a mathematical guess is like a long run.

Generation after generation, a mathematician, struggling to run, will continue to pass the baton in their hands.

Do not know the end point, do not know the direction, the people of the same trade constantly fall down, new running constantly join.

Now, the baton that Gushan village conjectures has been passed to Cheng Nuo's hand.

Around, there are not a few of them.

In front of us, we can't see any light.

Cheng Nuo can only follow the path of the predecessors, groping forward, looking for the light breaking the darkness, trying to rush to the end of the game.

…………

For the convenience of communication, Cheng and the other two professors in his group directly put their offices in an office in the clay Institute of mathematics.

The general direction of the proof work is controlled by Cheng Nuo.

Two mathematics professors from Denmark and Belgium filled in the details.

For the proof of Gushan Zhicun's conjecture, Cheng Nuo, like most of his predecessors, regards Fermat's theorem as his breakthrough.

In the language of mathematics, Fermat's theorem is a necessary and insufficient condition for Gushan Zhicun's conjecture.

In other words, after a certain deduction, the theorem of Gushan Zhicun can prove Fermat's theorem.

However, the existence of Fermat's theorem can not prove the correctness of Gushan Zhicun's conjecture.

In a certain sense, Fermat's theorem can only show that Gushan Zhicun's conjecture is true on the semi stable elliptic curve.

However, Fermat's theorem is still of great significance for the proof of Gushan Zhicun's conjecture.

Cheng Nuo also decided to start from this direction and try to prove the method.

A person in the office, has maintained a movement for more than an hour Cheng Nuo finally felt that he had caught the glimmer of inspiration, took the pen, and Shua Shua wrote down the inspiration on the draft paper.

According to Fermat theorem n = 4, the research object is defined as elliptic curve e: y ^ 2 = x ^ 3-x. let β be a prime number, and the number of solutions of this equation in finite field ft is β = 1, 3, 5 They are... "

“…… Next, we use the module group Γ (1): = SL2 (Ζ) to act on the complex upper half plane H = {Z ∈ C | im (z) > 0} by fractional linear transformation. "

“…… In the third step, suppose that E: y 2 = ax 3 + by 2 + CX + D is an elliptic curve over the rational number field Q, then we need to consider its "reduction" in the coefficient module prime number. In addition, isomorphic elliptic curves may give completely different "reductions": consider y 2 = 27 x 3 - 3 x and y 2 = x 3 - x, the former is not an elliptic curve on F3, the latter is an elliptic curve on F3. Therefore, it is concluded that ①: isomorphic elliptic curves should be regarded as equivalent! "

…………

Like Cheng Nuo and his team, the other seven certification teams started their research work under the leadership of their team leaders as soon as they got the task.

After all, they are not only racing against the three-year research cycle, but also competing with other groups.

The distribution of researchers is proportional to the difficulty of conjecture. The starting line was almost the same.

None of the mathematicians would like to be second to none.

Therefore, this cleaning activity has a trace of racing significance.

"Geometric conjecture" proving group.

As one of the famous mathematicians in the field of geometry, Professor Black was appointed to the position of group leader.

Like the "Gushan village conjecture" proof group, there are only three members in their group.

In terms of difficulty, the research difficulty of "geometric conjecture" and "Gushan village" conjecture is equivalent.

But the difference is that black's two mathematicians are better than Chennault's.

To put it simply, two of the three members of the black team have won the Veblen prize, while Cheng Nuo is the only one.

Therefore, from the beginning to the end, Blake did not regard the "Gushan village conjecture" research group next door as a face-to-face opponent.

However, this idea was completely changed in the regular progress report meeting held every three months by the clay Mathematics Institute for this cleaning activity.…………

It's January 2024.

The proof of Gushan Zhicun conjecture has been going on for three months.

For three months, Cheng Nuo refused almost all entertainment activities and devoted all his energy to the conjecture of Gushan village like an ascetic.

Although very tired, but the survival is very remarkable!

Today, it's the March routine progress report.

When Cheng Nuo came to the hall, most mathematicians were already in place.

The so-called regular progress report once a month is to make a brief overview of the subject research in this period, and to give a general plan for the future.

According to the difficulty of conjecture, Cheng Nuo is arranged in the third report.

The first Hodge conjecture is that the mathematician in his fifties seems to have been on it for more than ten minutes, but it can be summed up in four words: no clue!

Yes, Hodge's conjecture has not been solved for a hundred years, and it is one of the seven major mathematical conjectures. People have no expectation that they can sort out the clue in three months.

The second person to go up is Professor Black.

Compared with Hodge's conjecture, which proved that the group had no clue, but talked about a lot of hype, Professor Black's content was much more pragmatic.

After three months of research, they have a preliminary idea of the proof process of the "geometric" conjecture, and they are making steady progress. It is expected that the conjecture can be solved within a year.

In addition, Professor Black also gave a brief account of the specific reasoning content, which was unanimously recognized by all.

When he stepped down, Professor Blake was applauded.

Blake's mouth rose and sat back to his seat.

At this time, Cheng Nuo straightened his clothes, got up and went to the stage.

In an instant, Cheng Nuo attracted the attention of all the people.

Recently, although they work together in the clay Institute of mathematics, Cheng Nuo's research group has been isolated and it is difficult to hear anything about them.

In fact, they are also curious about the extent to which they can achieve in three months.

I just hope it's not Hodge's team that has no clue.

Cheng Nuo chuckled and went straight to the topic, "as we all know, there is a close relationship between Gushan Zhicun's conjecture and Fermat's theorem. For the patterning of self-discipline form, we can use Fermat's theorem to construct simple elliptic curve, and explain the relationship between polynomial mapping..."

“…… Then, for the curves in the complex field, we derive the simple isomorphism group Speaking of this, Cheng Nuo pauses for a moment, revealing a mysterious smile, "then, we found an interesting thing..."

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