Chapter 458: Modularity theorem Taniyama

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Chapter 458
After listening to Mr. Gil's account, Cheng Nuo finally understood the cause and effect of the matter.
The so-called "cleaning activity" of geometric conjectures, in a simple sense, is that the Cray Institute of Mathematics and nearly a hundred mathematicians from all over the world are expected to solve all mathematical conjectures in the field of geometry within three years.
The fuse of the incident was that a few months ago, Cheng Nuo announced the proof of the Jacobi conjecture.
Since the birth of geometry more than 300 BC, conjectures have been proposed, and conjectures have been proven.
Up to now, most of the conjectures in the geometric world have been solved seven or eighty-eight.
With the addition of front-end time, Jacobi conjectured that this hard bone was gnawed by Cheng Nuo, which inspired another round of conjecture in the geometric field.
This allowed the Cray Institute of Mathematics to see an opportunity to "catch it all in one go."
At present, the mathematical conjectures of the top five echelons in the field of geometry are no more than five fingers!
Therefore, the Cray Institute of Mathematics issued a convening order, inviting a total of 86 geometric mathematicians from all over the world to gather in the United States to discuss this "cleansing activity."
Cheng Nuo, as the prover of the Jacobi conjecture and one of the most popular mathematicians in front-end time, was naturally invited to participate in this "cleaning event."
Moreover, according to Mr. Gil's disclosure, Cheng Nuo will play an important role in this "cleansing activity", and it is definitely not just a pool of numbers in the past.
"That's it. Professor Cheng, I have brought you the invitation letter from the Cray Institute of Mathematics. This planned discussion will be held in a week. Please prepare in time." Mr. Gil took out an invitation from his pocket letter.
Cheng Nuo took the invitation letter, read it back and forth several times, and smiled, "Well, I know it."
Quite interesting!
To be honest, Cheng Nuo didn't expect that the guys at the Cray Institute of Mathematics would have ideas.
Arrange all geometric conjectures to be solved in the same time period. Once successful, the reputation of the Cray Institute of Mathematics can be like the seven conjectures with a reward of 1 million in the early 21st century, once again fame and fortune.
Moreover, in Cheng Nuo's view, the probability of their success at the Cray Institute of Mathematics is not small.
Eighty-six mathematicians in the field of geometry, even if some of them were just to make up the number of people in the past, there should be 30 mathematicians who have finally invested in this cleaning project.
This kind of power is comparable to the full geometric academic power of some small mathematics countries.
Moreover, the cleaning plan is not to solve all mathematical conjectures in the geometric world.
Those property insurances that do not even have a specific name, are fabricated without any theoretical basis, and have little academic value after being proven, will be discarded.
If you count them carefully, there will be less than ten.
The geometric world is not like the number theory world. In the field of number theory, top conjectures are everywhere, Riemann conjecture, Goldbach conjecture, twin prime conjecture...
Just picking up one of these can't be done by just finding a group of mathematicians in a few years.
In the field of geometry, the only conjecture in the first echelon is Hodge's conjecture!
Since the Crane Institute of Mathematics named Cheng Nuo to participate, Cheng Nuo couldn't escape it.
After a brief preparation, Cheng Nuo flew to Manchester, where the Cray Institute of Mathematics is located.
…………
The Cray Institute of Mathematics has a strong appeal in mathematics because of the seven major mathematical conjectures 20 years ago.
Soon, an international scientific research cooperation project named "gcpu" was led by the Cray Institute of Mathematics.
On the first day, the mathematicians finalized the list of this conjecture cleaning plan after discussion.
Eight mathematical conjectures including Hodge's conjecture, geometrical conjecture, and Shanguzhicun conjecture are included in the list.
The goal is determined, and the next step is to assign tasks.
The staff of the Cray Institute of Mathematics approached Cheng Nuo and conveyed their wishes.
There are two plans before Cheng Nuo.
One is to join the "Geometric Conjecture" certification team as the deputy team leader.
The other is to lead the proof of "Taniyama Shicun Conjecture" as the team leader.
Without any hesitation, Cheng Nuo chose the Gushan Zhicun Conjecture Proof Group.
Compared to being directed by others. Cheng Nuo still prefers to direct others.
The Cray Institute of Mathematics arranged it very quickly. In the morning, according to the wishes of the mathematicians, 38 mathematicians were divided into nine proof groups to prove the nine geometries including Hodge’s conjecture. Major conjectures in the field.
And Cheng Nuo is the controversial leader of the Sanguzhi Village Conjecture Proof Team.
Of the nine groups, Hodge conjecture proved that the group has the largest number of people, with a full eight people. Cheng Nuo and his group consisted of only three people, including Cheng Nuo.
Cheng Nuo's two professors, one from Belgium and one from Denmark.
The level of the two among all 38 mathematicians is the bottom one, otherwise they would not be willing to give a hand to a young man in his twenties.
Although many mathematicians criticized Cheng Nuo as the group leader, they did not include the two under Cheng Nuo.
The two professors were very honest, and did not follow Cheng Nuo's instructions based on their seniority, which made Cheng Nuo very satisfied.
When solving Jacobi’s conjecture, although Denton and Joanna two doctoral students used it relatively smoothly, their level is limited after all, and most of the content needs to be handled by Cheng Nuo alone.
But now it's different~EbookFREE.me~Professor-level bosses give him a hand, and Cheng Nuo only needs to solve the most core problems.
And he is just an associate professor.
Beautiful!
Cheng Nuoton felt refreshed.
I am afraid that this kind of treatment can only be enjoyed in such large-scale international scientific research cooperation projects.
Since the Cray Institute of Mathematics is willing to let him be the team leader when many people are not optimistic, Cheng Nuo will naturally complete the work they entrusted to him perfectly.
…………
November 28.
Cheng Nuo looked out the window blankly, his thoughts drifting in his mind.
The Gushan Zhicun conjecture was put forward by the island mathematician Gushan Zhicun at a mathematics seminar in 1984 and established a connection with Fermat's Last Theorem.
Today, Fermat's Last Theorem has been proven, but Gushan Zhicun's conjecture still stands.
The specific content of Gushan Zhicun’s conjecture is:
If p is a prime number and e is an elliptic curve in a field of q rational numbers, the equation defining e can be simplified modulo p; except for a finite number of p values, an elliptic curve in a finite field fp with np elements will be obtained. Then consider the following sequence
apnpp,
This is an important invariant of the elliptic curve e. From the Fourier transform, each modulus form also produces a sequence of numbers. An elliptic curve whose sequence is the same as that obtained from the modular form is called modular.
The Gushan Shimura conjecture is that: all elliptic curves on q are modular!
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