Into the Immortal Cultivation - Chapter 2101

[Chapter 114 Langlands Program [Third Edition]]

Time went back to twenty-seven hours ago.

Satisfied, Wang Qi walked out of his study and sighed deeply.

“It’s done.” His heart was full of a sense of sufficiency after labor, but there was no “surprise”.

This is the way of the Bourbaki school. For the Bourbaki school, there is only a matter of course, but no “accidental realization”.

Many earth mathematicians once described the way of the Bourbaki School of work as “they only have their own destination in their eyes, but they don’t care about the roadside scenery”.

Of course, going all the way to your destination is not the wrong way to work.

However, for mathematicians, sometimes, “roadside scenery” is more important than “destination”. ;

or, in other words, a method discovered while researching a topic is more meaningful than the topic itself.

The most intuitive manifestation is Fermat’s last theorem and Goldbach’s conjecture.

Goldbach’s conjecture. Take Fermat’s last theorem, which itself has led to the birth of many mathematical tools. Hilbert’s plan has the shadow of Fermat’s last theorem, and the ultimate answer to Fermat’s last theorem, the “Taniyama-Shimura” conjecture, is also part of the Langlands program.

Otherwise, who cares if there is a positive integer solution to the equation x^n+y^n=z^n for x, y, z when the integer n>2?

Who cares if any even number greater than 2 can be written as the sum of two prime numbers?

It is precisely because of this that many mathematicians hate the Bourbaki school and call it “boring”.

But it is undeniable that sometimes, this kind of work is also very meaningful.

The accumulation of the nine volumes of “Original Reckoning” and the knowledge of the history of the earth have been integrated at this moment.

Wang Qi completed the proof of the fundamental lemma.

The so-called fundamental lemma roughly means that it gives a formula about the connection between an orbital integral over a reduced group over a local field and a stable orbital integral over another group.

That might be a little more complicated.

After all, this is proof that it has only been accomplished in the twenty-first century.

Mathematics has developed to such a level that it is no longer comprehensible for mortals. Ask a mathematician to explain this problem to you in “human words”, and in the end he can only express in despair that “with your understanding ability, it is impossible to explain this to you clearly”.

In 2008, Vietnamese mathematician Wu Baozhu completed the proof of the fundamental lemma in France.

The Fundamental Lemma is a preliminary proof of the Langlands program.

And what is the Langlands Program?

It can be said to be an upgraded version of Hilbert’s plan, and it is recognized by many mathematicians as 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 Bourbaki School, was arrested and imprisoned in France.

In prison, Weil insisted on mathematical research. Once again, in a correspondence with his sister, Simone Weil, a philosopher, he mentioned his views on “big trends” in mathematics. He illustrates this problem through an analogy between number theory and geometry, two of his areas of greatest interest. He believes that these two categories are like two different languages.

This is exactly the idea of the Langlands Program.

In 1967, a young man who had just become a professor sent this Bourbaki a letter. In his letter he proposed a set of far-reaching conjectures. These conjectures precisely predict possible connections in mathematics between the interdisciplinary fields of non-commutative harmonic analysis, autonomic formal theory, and number theory, and attempt to unify them.

This professor is none other than Robert Langlands.

We can think of the different fields of modern mathematics as a language. Some sentences in different languages, in our eyes, express the same meaning, but the pronunciation is different. This is the difference between “signified” and “signifier” in modern linguistics.

People put these sentences together and accumulate them to form a translation standard. It can help mathematicians and complete translation work.

Different fields of mathematics are similar.

It is a grand and daunting conjecture, spanning several major fields in contemporary mathematics, such as number theory, group theory, representation theory, and algebraic geometry. Once fully proven, many of the central questions in these fields will be solved.

It is like Hilbert’s plan, which can unify the whole mathematics into a complete whole.

On Earth, the Langlands Program is called “the Rosetta Stone of mathematics”.

However, what contrasts with the sanctity of this “stele” is its difficulty.

“I don’t think there is an answer to this question,” Langlands even wrote in a letter to Andre Weil: “If you can read (my letter) as pure speculation, I would Thank you very much; if not, I believe you have a wastepaper basket at hand.”

Wang Qi couldn’t even believe that he actually successfully completed the proof of the fundamental lemma.

This is nothing short of a miracle.

“Amazing, me.” He said so contentedly.

He grabbed the 200-page proof process and was about to leave.

But when he saw a large piece of yellow jade at the door of his study, he stopped.

“Well, I might have to give a sermon later. You can prepare teaching aids first.”

Wang Qi thought about it, and walked to the largest piece of jade that he had deliberately left behind.

This piece of jade is as tall as a person, and he finally pulled it out from the center of the ore vein.

“It’s up to you.” Wang Qi said so, and patted the jade. Suddenly, the stone rustled, and countless powders turned into dust and fell.

In the end, among the pile of dust, a regular regular tetrahedron was completed.

Wang Qi nodded, stretched out his hand, and engraved the word “number theory” on the first side of the regular tetrahedron.

Weil’s original idea was an analogy between geometry and number theory. Number theory and geometry did play a huge role in the development of the Langlands Program.

The heart of the Langlands program is number theory. Langlands imagined that some difficult number theory problems, such as calculating the number of roots of an equation when the modulus is a prime number, could be solved by using harmonic analysis, specifically, the use of automorphic functions.

This idea directly hits the essence of mathematical connection.

The fundamental lemma is to declare to the world that this idea is feasible.

Langlands was not a member of the Bourbaki school. However, the Langlands program coincides with the thinking of the Bourbaki 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 “Gavarian group” [Gavaro group] a

line of “autonomous function”.

On the second side, he also carved three words.

“Curves in the Plane of Finite Fields”.

“Garland Group”.

“Autonomous functions or autonomic layers”.

The third side is also engraved with three words.

“Riemann Surface”.

“Basic Group”.

“Self-defense layer”.

Except for the side facing the ground, the remaining three sides are engraved with characters.

These are exactly the three tracks of the Langlands Program.

No, in this world, it’s not called the Langlands Program.

It should be called…

“The Foundation Establishment Program…?”

Wang Qi suddenly felt something.

In an instant, the situation changed.

The spiritual power cycle of the entire planet has been destroyed. The spiritual power of the entire planet is converging towards where he is standing. He was like the third magnetic pole that suddenly appeared on the planet.

Countless magnetically sensitive creatures suddenly exclaimed in pain.

Two Xiaoyao suddenly exclaimed: “Flying Immortal Tribulation?”

This scale already reminded them of Feixian Tribulation.

However, there are not many monks in the Nirvana period on this planet, so how can there be flying immortals?

Unless…

“Wang Qi’s clone also has a huge breakthrough?”

Wang Qi’s clone… No, it should be regarded as a “part” of the “whole”, a physical body, on this planet.

As a whole, Wang Qi is like a giant immortal.

And his physical body in a foreign country is like the fingers of an immortal.

When immortals face thunder tribulation, their fingers will naturally be attacked by some thunder.

In other words…

Wang Qi has made a huge breakthrough?

Wang Qi did not expect such a change. He has already completed the proof of the fundamental lemma, but at the moment of completion, he has not caused much change. He himself thought that this was the basic characteristic of the Bourbaki school, and that all breakthroughs were achieved in the form of “gradients”.

At that moment, the part of Wang Qi Gong’s body that originated from Wanfamen Gongfa and mathematics was instantly shattered and then reconstructed.

And since the stage of forming an elixir, Wang Qi happened to be a master of the Wanfamen Gongfa Xiangyu Tianwei Gong.

So…

it’s a sea change overall.

His attention was no longer on his own body.

This is a holistic change.

The mountain-like operator formed an unrivaled wave, and the beast organ cluster was swiped back and forth on the surface.

But this is only superficial.

The internal refactoring is more complicated and even difficult to describe clearly in natural language.

A spiritual vortex formed around him. The solar wind growled at him as if provoked. This is the fury of a star half an AU away. The storm of spiritual power rushed to Wang Qi with high-energy particles.

Generally speaking, the thin spiritual power in outer space will not cause doom when breaking through.

However, at this moment, Wang Qi’s breakthrough was too significant, causing him to directly draw out a spiritual power vacuum, causing the sun’s spiritual power cycle to collapse and rebuild.

This is the “celestial robbery” of the celestial demon spirit level.

Fortunately, Wang Qi was just a breakthrough. His Primordial Spirit Law was operating, and the vast catastrophe that was enough to wipe out the planet was also absorbed by him and turned into his own power.

In the daze, he seemed to feel that he had made great progress again.

But when he came back to his senses, a long time had passed.

Wang Qi’s physical body in a foreign country has completed a promotion from non-longevity to longevity along the Yuanshen method.

Even by the most demanding standards, he could call himself a free-spirited monk.

[End of this Chapter]