universal data

Chapter 455 Taniyama Shimura Conjecture
458 chapter

After listening to Mr. Jill's narration, 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 Clay Institute of Mathematics unites nearly a hundred mathematicians from all over the world, and it is estimated that within three years, all mathematical conjectures in the field of geometry will be solved.

The fuse of the matter was Cheng Nuo's paper announcing the proof of Jacobi's conjecture a few months ago.

Since the birth of geometry in more than 300 BC, conjectures have been put forward and conjectures have been proved.

Up to now, most of the conjectures in the geometry world have been solved in sevens and eighties.

In addition to the front-end time, Jacobi's conjecture was cracked by Cheng Nuo, which triggered another wave of conjectures in the field of geometry.

This allowed the Clay Mathematics Institute to see an opportunity to “catch them all”.

At present, the mathematical conjectures of the top five echelons in the field of geometry are already less than five fingers!

Therefore, the Clay 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 "cleaning activity".

As the prover of the Jacobi conjecture and one of the most popular mathematicians in the front-end world, Cheng Nuo was naturally invited to participate in this "cleaning event."

Moreover, according to Mr. Jill's disclosure, Cheng Nuo will take an important position in this "cleaning operation", not just gathering the number of people in the past.

"That's it. Professor Cheng, I have brought you the invitation letter from the Clay Institute of Mathematics. The planned discussion meeting will be held in a week. Please prepare in time." Mr. Jill took out an invitation from his pocket letter.

Cheng Nuo took the invitation letter, read it back and forth several times, and said with a smile, "Well, I understand."

Very interesting!

To be honest, Cheng Nuo didn't expect that the guys at the Clay Institute of Mathematics were quite thoughtful.

Arrange all the geometric conjectures to be solved in the same time period. Once successful, the reputation of the Clay Mathematics Institute will be the same as the seven major conjectures with a 21 million bounty at the beginning of the 100st century. Once again, both fame and fortune will be achieved.

Moreover, in Cheng Nuo's view, the possibility of Clay Mathematics Institute's success is not small.

There are 86 mathematicians in the field of geometry, even if some of them are just to make up the number in the past, there should be [-] mathematicians who finally invested in this cleaning plan.

This kind of power is comparable to all the geometric academic power of some small mathematics countries.

Moreover, the purge program is not intended to solve all the mathematical conjectures that exist in geometry.

Those property insurances that do not even have a specific name, have no theoretical basis to be fabricated, and are proven to have little academic value will be discarded.

If you count carefully, there are less than ten.

The geometry 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...

Any one of these cannot be solved safely by just finding a group of mathematicians in a few years.

In the field of geometry, the only conjecture that ranks in the first echelon is Hodge's conjecture!
Since Clay Mathematics Institute nominated Cheng Nuo to participate, Cheng Nuo couldn't shirk it.

After a brief preparation, Cheng Nuo flew to Manchester, where the Clay Institute of Mathematics is located.

…………

The Clay Institute of Mathematics has a strong appeal in the mathematics community because of the seven mathematical conjectures 20 years ago.

Soon, an international scientific research cooperation project called "GCPU" was led and sponsored by the Clay Institute of Mathematics.

On the first day, after discussions among digital mathematicians, the list of conjecture cleaning plans was finalized.

Eight mathematical conjectures including the Hodge conjecture, the geometric conjecture, and the Yamakoshimura conjecture were included in the list.

After the goal is determined, the next step is to assign tasks.

The staff of the Clay Institute of Mathematics approached Cheng Nuo and conveyed their wishes.

Cheng Nuo had two options in front of him.

One is to join the "Geometric Conjecture" proof team and serve as the deputy team leader.

The other is to lead the proof of the "Taniyama Shimura Conjecture" as the team leader.

Without any hesitation, Cheng Nuo chose the Gushan Shimura conjecture proof team.

than being directed by others.Cheng Nuo still prefers to direct others.

The Clay Institute of Mathematics made arrangements very quickly. In one morning, according to the wishes of the mathematicians, 38 mathematicians were divided into nine proof groups to prove nine major geometric fields including Hodge's conjecture. guess.

Cheng Nuo, on the other hand, was the leader of the Yamagushimura conjecture proof team who was quite controversial.

There are nine groups, and Hodge conjectures that the number of groups is the largest, with a total of eight people.Cheng Nuo and his team consisted of only three people including Cheng Nuo.

The two professors under Cheng Nuo, one is from Belgium and the other is from Denmark.

The two are at the bottom of all 38 mathematicians, otherwise they would not be willing to help a young man in his 20s.

Although many mathematicians complained about Cheng Nuo being the team leader, these two under Cheng Nuo were not among them.

Both professors were very honest, and they did not rely on their seniority to push Cheng Nuo's orders, which made Cheng Nuo very satisfied.

When solving the Jacobi conjecture, although the two doctoral students Denton and Joya were relatively easy to use, their abilities were limited after all, and most of the content still needed to be solved by Cheng Nuo alone.

But it's different now.

The professor-level boss will help him, and Cheng Nuo only needs to solve the most core problems.

And he was just an associate professor.

Beautiful!

Cheng Norton 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 Clay Institute of Mathematics is willing to let him be the team leader when many people are not optimistic about it, Cheng Nuo will naturally complete the work they assigned him perfectly.

…………

11 month 28 day.

Cheng Nuo looked out the window in a daze, his thoughts wandering in his mind.

The Taniyama Shimura conjecture was proposed by the island country mathematician Taniyama Shimura in a mathematics seminar in 1984, and established a connection with Fermat's last theorem.

Today, Fermat's Last Theorem has been proven, but Taniyama Shimura's conjecture still stands.

The specific content of Taniyama Shimura's conjecture is:
If p is a prime number and E is an elliptic curve over a Q (the field of rational numbers), the equation defining E modulo p can be simplified; except for a finite number of p values, an elliptic curve over a finite field Fp with np elements is obtained .Then consider the following sequence
ap = np p,

This is an important invariant of the elliptic curve E.From the Fourier transform, each modular form also produces a sequence.An elliptic curve whose sequence is the same as that obtained from the modular form is called modular.

Taniyama Shimura's conjecture said: All elliptic curves on Q are modular!
(End of this chapter)