Vol 3 Chapter 2113: Langlands Program [Third]

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The time returned to before twenty-seven hours.
Wang Qi walked out of his study with satisfaction and sighed.
"It's done." His heart was full of sufficiency after labor, but there was no "surprise".
This is the way of the Bulbaki school. For the Bulbaki school, there is only a matter of course, and there is no "unexpected comprehension".
Many earth mathematicians once described the way the Bulbaki school works-"their eyes only have their own destination, but they disdain the roadside scenery".
Of course, going all the way to your destination is not the wrong way of working.
However, for mathematicians, sometimes "roadside scenery" is more important than "destination". ;
In other words, the method discovered when studying a certain topic is more meaningful than the topic itself.
The most intuitive embodiment is Fermat's theorem, and Goldbach's conjecture.
Goldbach guessed it. Take Fermat's theorem for example. Fermat's theorem itself has triggered the birth of many mathematical tools. The Hilbert plan has the shadow of Fermat's theorem, and the ultimate answer to Fermat's theorem, the Gushan-Shimura conjecture, is part of the Langlands program.
Otherwise, who cares whether the equation x ^ n + y ^ n = z ^ n for x, y, and z has positive integer solutions when the integer n; 2?
Who cares if any even number greater than 2 can be written as the sum of two prime numbers?
Because of this, there are many mathematicians who hate the Bulbaki School very much and describe it as "uninteresting".
But it is undeniable that sometimes this kind of work is also very meaningful.
The accumulation of the nine-volume "Original Calculation" and the knowledge of the history of the earth are integrated at this moment.
Wang Qi completed the proof of the basic lemma.
The so-called basic lemma roughly means that it gives a formula about the relationship between the orbital integral on the reduced group on the local domain and the stable orbital integral on another group.
This may be a little more complicated.
After all, this is proof that it was only completed in the 21st century.
The development of mathematics to this extent is no longer understandable by mortals. If you want to use mathematics to explain this problem to you in "human words", he can only hopelessly express "it is impossible to explain this to you with your understanding ability".
In 2008, the Vietnamese mathematician Wu Baozhu completed the proof of the basic lemma in France.
The basic lemma is the preliminary proof of the Langlands program.
And what is the Langlands program?
It can be said to be an upgraded version of the Hilbert project, which is recognized by many mathematicians and the direction of the next era of mathematics.
The Langlands Program is a great attempt to unify mathematics.
In 1940, André Weil, one of the founding members of the Bulbaki School, was arrested and imprisoned in France.
In prison, Weil insisted on mathematical research. Once again, in his correspondence with his sister Simone Weil, a philosopher, he mentioned his views on the "megatrends" of mathematics. He explained this problem through an analogy between the two areas of most interest to him, number theory and geometry. He believes that these two categories are like two different languages.
This is precisely the idea of ​​the Langlands program.
In 1967, a young man who had just become a professor sent a letter to the Burbaki. In his letter he made a set of profound conjectures. These conjectures accurately predicted the possible connections between interdisciplinary fields of non-commutative harmonic analysis, automorphic form theory, and number theory in mathematics, and tried to unify them.
This professor is Robert Langlands.
We can think of different fields of modern mathematics as a language. In our eyes, some sentences in different languages ​​mean the same thing, but they read differently-this is the difference between "referred" and "signable" in modern linguistics.
People put these sentences together and keep accumulating them to form a translation standard. It can help mathematicians to complete translation work.
Different areas of mathematics are similar.
It is a magnificent and daunting conjecture that spans several major fields such as number theory, group theory, representation theory, and algebraic geometry in contemporary mathematics. Once fully proven, many central issues in these fields will be solved.
It is like the Hilbert plan, which can unify the entire mathematics and form a complete whole.
On the earth, the Langlands program is called "The Rosetta Stone of the Mathematics".
However, it is the difficulty of this "stone" that is sacred.
"I don't think there is an answer to this question." In his letter to Andre Weil, Langlands even wrote: "If you can read (my letter) as pure speculation, I will Thank you very much; if not-I believe you have a wastebasket at hand. "
Wang Qi couldn't even believe that he actually successfully completed the proof of the basic lemma.
This is simply a miracle.
"Great, me." He said so complacently.
He grabbed the 200-page proof process and was originally planning to leave.
But when he saw a large piece of yellow jade at the entrance of his study, he stopped.
"Well, I might have to preach later, I can prepare the teaching aids first."
Wang Qi thought so, and walked to the biggest piece of jade he left behind.
This piece of jade is tall enough to be pulled out of the center of the veins.
"It's up to you," Wang Qi said, patting the jade. Suddenly, the stone rustled, and countless powders fell into dust.
Finally, in a pile of dust, a regular tetrahedron was completed.
Wang Qi nodded, extended his hand, and engraved the word "number theory" on the first face of the tetrahedron.
Wei's initial vision was an analogy between geometry and number theory. Number theory and geometry have indeed played a huge role in the development of the Langlands program.
The core of the Langlands program lies in number theory. Langlands envisioned some of the more difficult number-theoretic problems, such as calculating the number of equation roots when the modulus is a prime number. Harmonic analysis can be used. Specifically, it is solved using a self-defense function.
This idea simply hits the essence of mathematics.
The basic lemma is to declare to the world that this idea is feasible.
Langlands is not a member of the Bulbaki School. But the Langlands program coincided with the ideas of the Bulbaki school.
Wang Qi throws out this program here, which is just right.
Under "Number Theory", he engraved another two lines of characters.
A line of "Garfield Group" [Gavaro Group]
A line of "self-defense function".
On the second side, he also carved three words.
"Curve on the plane of the finite field".
"Garden Group".
"Self-defense function or self-defense layer".
On the third side, three words are also engraved.
"Riemann surface".
"Basic group".
"Self-defense layer".
Except for the side facing the ground, the remaining three sides are inscribed.
These are exactly the three tracks of the Langlands program.
No, in this world, it is not called the Langlands program.
It should be called ...
"Building program ...?"
Wang Qi suddenly felt something.
In an instant, the situation changed.
The spiritual cycle of the whole planet is destroyed. The spiritual power of the entire planet is gathered where he is standing. He was like the third magnetic pole suddenly appearing on this planet.
Countless creatures with magnetic sensibility suddenly exclaimed in pain.
Two Xiaoyao suddenly exclaimed: "Fei Xian robbery?"
This scale has made them think of Fei Xian Jie.
However, there are not many monks in Nirvana period on this planet.
unless……
"Wang Qi's avatar also has a huge breakthrough?"
Wang Qi's doppelganger ... No, it should be regarded as a "part" of the "whole", a flesh, on this planet.
Wang Qi as a whole is like a huge fairy.
And his flesh in his hometown is like a fairy's finger.
When the fairy faced the Thunder Tribulation, his fingers would naturally be attacked by some Thunder.
In other words ...
Has Wang Qi made a huge breakthrough?
Wang Qi did not expect such a change. He has completed the proof of the basic lemma, but at the moment he completed it, he did not cause much change. He himself thought that this was the basic characteristic of the Bulbaki school, and all breakthroughs were realized in the form of "gradient".
At that moment, the part of Wang Qigong's body, which originated from the Ten Thousands of Falun Gong exercises and originated from mathematics, was instantly crushed and then reconstructed.
Since the formation of the Dandan period, Wang Qi happened to focus on the Ten Thousand Dharma Practitioners Xiangyu Tianwei Kungfu.
and so……
This is an earth-shaking change on the whole.
His attention is no longer above his own body.
This is a holistic change.
The mountain-like operators form an unparalleled wave, which is circulated back and forth in the beast organ cluster.
But this is just the surface.
The internal refactoring is more complicated and even difficult to describe clearly in natural language.
A vortex of spiritual force formed around him. The solar wind seemed to be irritated and snarled at him. This comes from the rage of stars beyond half an astronomical unit. A spiritual storm wrapped around high-energy particles and rushed to Wang Qi.
Generally speaking, the thin spiritual power of outer space will not cause the robbery when breaking through.
However, at this moment, Wang Qi's breakthrough was too significant, leading him to directly pull out a spiritual vacuum zone, which caused the sun's spiritual cycle to collapse and rebuild.
This is the "Sky Tribulation" at the level of celestial demon spirits.
Fortunately, Wang Qi is just a breakthrough. His primordial magical law is in operation, which is enough to exterminate the vast sky-tribulation of the planet, and he has absorbed it and turned it into his own strength.
He seemed to feel that he had made great progress again.
But when he came back to God, time had passed a long time.
Wang Qi's flesh in other countries has already completed a promotion along the primordial magic law-from non-eternal life to long-life promotion.
Even by the most demanding standards, he can claim to be a monk.
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