Chapter 105 Ye Fei completely defeated the descendants of two Fields Medal winners

Author: Big fish eats small fish

Chapter 105 Ye Fei completely defeated the descendants of two Fields Medal winners

Amata stood on the stage, looking at the dense crowd below.

He was a little excited, this was his stage, and here he was about to show his abilities to the world.

For the International Conference of Young Mathematicians, he showed great ability.

He has proved many conjectures and made significant contributions to BSD conjectures.

Today, he is going to come up with another conjecture, the Gaussian class conjecture.

He has been studying the Gaussian class conjecture for more than a year and finally proved it a month ago.

Compared with the conjectures he proved in the past, the Gaussian class conjecture is no easier than them.

In terms of importance, it is not weaker than them at all.

Gauss only proposed three conjectures in his life.

They are the Gaussian class conjecture, the Gaussian class conjecture in the imaginary quadratic field and the Gaussian class conjecture in the real quadratic field.

These three conjectures are combined into the Gaussian conjecture.

Gauss's conjecture was proposed in the mid-seventeenth century, about two hundred years ago.

For about two hundred years, people in the world have been studying Gauss's conjecture.

And so far it has not been proven.

Moreover, as the prince of mathematics, Gauss's conjectures were very high in terms of difficulty and importance.

And today he proved to the world the first conjecture of Gaussian conjecture, the Gaussian class conjecture.

As for the contest with Balazs, he didn't care.

In his opinion, there was no competition between them.

It's just an academic collision to prove the same issue.

And this kind of thing happens all the time in academia.

There are only so many conjectures, and many people will study them. It is very likely that many people will study the same conjecture.

Therefore, strictly speaking, it is not a competition between them.

Rather, inappropriate things happen at inappropriate times.

Totally accidental!

Amata said: "Suppose the positive integers d1 and d2 satisfy gcd(d1,d2)=1..."

As he spoke, he wrote a set of formulas on the whiteboard behind him.

At the same time, the content on the whiteboard is displayed on a large display screen hung on the wall.

This way everyone in the room can see it.

"good!"

Many people present nodded, including some academicians and fellows.

Their vision and wisdom are much higher than those of the young mathematicians present.

You can see Amata's proof idea at a glance.

Academician Wei said to a middle-aged white man with curly white hair next to him: "Amata used the generalized Ramanujan-Nagell equation and the Lucas/Lehmer sequence in the Gaussian class conjecture."

"Yeah!" Lyle, who was beside Academician Wei, said, "That's true. It's a very novel idea."

"His research can be used in cryptography."

Because Amata used ideal groups in his paper.

It is common sense in mathematics that ideal groups establish a quadratic domain cryptography system.

The smartest thing about Amata is to use the quadratic domain cryptography system to find the ideal subgroup of large prime order of the ideal class group in the quadratic domain, and to study the divisibility of class numbers.

Although this idea has been mentioned before, few people have applied it to Gaussian number conjecture as naturally as he did, which also made everyone's eyes light up.

Amata said: "Consider the Diophantine equation d1x^2+d2y^2=4p^z..."

"Equation (6.1) has at most one solution except for some known exceptions. These two theorems are proved."

"This is the Gaussian class conjecture."

"Bah bang bang..." Everyone burst into warm applause.

“As expected of Amata, wonderful!”

"Yeah, I don't know if Balazs will be able to give such a wonderful academic report in the future."

"Very good, very good, really a wonderful academic report."

"With such academic ability at this age, he will definitely be one of the top international mathematicians in the future."

"..."

Many people expressed emotion in their hearts.

There are also many people who envy Amata's mathematical talent.

There are also many people who envy that there are mathematician geniuses like Amata in England.

Among them were many mathematicians from the Xia Dynasty.

Academician Wei sighed with emotion: "What a genius in number theory. How come our Number Theory Association doesn't have such a genius!"

"Hey..." Academician Wei sighed helplessly: "Our country still has a long way to go in cultivating talents!"

Due to the large population, Xia State can only adopt exam-oriented education.

But exam-oriented education has a big drawback.

Good at taking exams, but not good at innovation and practical skills.

Many need inspiration, inspiration and innovation are the same thing.

A person who is good at taking exams but not good at innovation will not go far in mathematics.

Therefore, it is difficult to cultivate academic talents through examination-oriented education.

Unless this person is very talented.

Academician Wei gathered his mood, feeling sad and regretful, nothing could be changed.

Exam-oriented education is a national policy, and the national policy needs to serve the majority of people, not a small group of people.

He continued to read academic reports.

Next up is Amata answering questions from the audience.

After about half an hour, Amata's academic report ended.

Next is Balaz's academic report.

Everyone is very interested in the academic reports of both of them, and they all want to know who is stronger and who is weaker between the two of them on the same academic report topic.

Balazs walked onto the stage. He knew before attending the International Conference of Young Mathematicians that Amata's academic report was on the same theme as his.

He is not interested in competing with Amata.

Whether Amata is strong or weak, it has no effect on him.

There are always people in this world who are better than him. If he always thinks about competing with others, then his life will be very tiring.

Therefore, he only competes with himself.

Balazs said: "Suppose D is a positive integer without square factors, h(-D) is a Gaussian number, Q(-D) is a number..."

Academician Wei nodded in agreement: "Balaz's academic report is also very good, not inferior to Amata's at all."

"Lyle." Academician Wei looked at Lyle beside him and asked, "What do you think?"

"His point of view is also very novel." Lyle said: "He used the basic factors of the Lucas number."

"In the past, the basic prime factors of Lucas numbers were used to solve Diophantine equations. It was rarely used to prove the Gaussian number conjecture."

"And like Amata, he also used the basic prime factors of Lucas numbers to self-justify the Gaussian number conjecture."

"His views give us more ideas in proving the Gaussian conjecture."

"Yes!" Academician Wei nodded: "That's true."

"Hey..." He shook his head and sighed: "Amata and Balaz are both very good."

"To use our Xia country's idiom, their abilities are between equals, no distinction is made between high and low."

Lyle nodded and said: "That's true. If we look at the number theory research of the young generation around the world, these two are the best."

"Yes!" Academician Wei nodded.
To be continued...