Enter the Immortal Cultivation

Time goes back to twenty-seven hours ago.

Wang Qi walked out of his study room with satisfaction and sighed.

"It's done." His heart was filled with a sense of contentment after labor, but there was no "surprise".

This is the Bourbaki way. For the Bourbaki school, there are only natural consequences, not "accidental realizations."

Many geomathematicians once described the working style of the Bourbaki school like this - "In their eyes, they only have their own destination, but they ignore the scenery on the roadside."

Of course, heading toward your destination is not the wrong way to work.

However, for mathematicians, sometimes the "roadside scenery" is more important than the "destination". ;

In other words, the method discovered when studying a certain topic is more meaningful than the topic itself.

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

Let’s not talk about Goldbach’s conjecture. Take Fermat's Last Theorem as an example. Fermat's Last Theorem itself triggered 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 part of the Langlands program.

Otherwise, who cares about whether the equation x^n + y^n = z^n about x, y, z has a positive integer solution when the integer n \u003e2?

Who cares whether 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 nine volumes of "Original Calculation" and the knowledge of earth history were integrated at this moment.

Wang Qi completed the proof of the basic lemma.

The so-called fundamental lemma roughly means that it gives a formula about the connection between the orbital integral on the reduction group in the local domain and the stable orbital integral on another group.

It might be a bit complicated to say this.

After all, this is proof that was only completed in the 21st century.

Mathematics has developed to this level and is no longer understandable to ordinary people. If you ask a mathematician to explain this problem to you in "human terms", he can only despair and say, "With your understanding, 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 the preliminary proof of Langlands' program.

And what is the Langlands Program?

It can be said to be an upgraded version of Hilbert's plan. It is recognized by many mathematicians as the direction of the next era in mathematics.

The Langlands Program was 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.

While in prison, Weil continued his mathematical research. Once again, in a correspondence with his sister Simone Weil, a philosopher, he mentioned his views on "major trends" in mathematics. He explained this problem through an analogy between number theory and geometry, the two fields in which he was most interested. He believes that these two categories are like two different languages.

This is exactly the idea behind the Langlands Programme.

In 1967, a young man who had just become a professor sent a letter to Bourbaki. In his letter, he proposed a set of far-reaching conjectures. These conjectures accurately predicted possible connections in mathematics between the interdisciplinary fields of noncommutative harmonic analysis, the theory of automorphic forms, and number theory, and attempted to unify them.

This professor is none other than Robert Langlands.

We can think of the different areas of modern mathematics as languages. Certain sentences in different languages ​​express the same meaning in our eyes, but they are read in different ways - 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 complete translation work.

Different areas of mathematics are similar.

It is a dauntingly grand conjecture that spans several major fields such as number theory, group theory, representation theory and algebraic geometry in contemporary mathematics. Once complete proofs are obtained, many central problems in these fields will be easily solved.

It is like Hilbert's plan, which can unify the entire mathematics to form a complete whole.

On Earth, the Langlands Program is known as the "Rosetta Stone of Mathematics."

However, what contrasts with the sacredness of this "stone tablet" is its difficulty.

"I think there is no answer to this question." Langlands even wrote in his letter to Andre Weil: "If you can read (my letter) as pure speculation, I will Thank you; if not - I'm sure you have a wastebasket handy."

Wang Qi couldn't even believe that he had actually successfully completed the proof of the basic lemma.

This is simply a miracle.

"Awesome, me." He said proudly.

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

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, so I can prepare the teaching aids first."

Wang Qi thought so and walked towards the largest piece of jade that he had specially left behind.

This piece of jade was as tall as a person, and he had finally pulled it out from the center of the mine.

"It's decided to be you." Wang Qi said so, and patted the jade. Suddenly, the stone rustled, and countless powders turned into dust and fell.

Finally, a regular tetrahedron was completed in a pile of dust.

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

Weil's original idea was the 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 difficult number theory problems, such as calculating the number of roots of an equation when the modulus is a prime number, which can be solved by harmonic analysis, specifically, by using automorphic functions.

This idea simply hits the essence of mathematical connection.

And the basic lemma is to declare to the world that this idea is feasible.

Langlands is not a member of the Bourbaki school. But the Langlands Program coincides with the ideas of the Bourbaki school.

It is just right for Wang Qi to throw out this program here.

He carved two more lines of words under "Number Theory".

One line of "Gavarro Group" [Gavarro Group]

One line of "Automorphic Function".

And on the second side, he also carved three words.

"Curves on the plane of finite fields".

"Gavarro Group".

"Automorphic function or automorphic layer".

Three words were also carved on the third side.

"Riemann surface".

"Basic group".

"Automorphic layer".

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

These are the three orbits of the Langlands Program.

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

It should be called...

"Foundation Program...?"

Wang Qi suddenly felt something in his heart.

In an instant, the wind and clouds changed color.

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

Countless creatures with magnetic sense suddenly cried out in pain.

Two Xiaoyao suddenly cried out: "Immortal Tribulation?"

This scale has already made them think of Immortal Tribulation.

However, there are not many Nirvana cultivators on this planet, how can there be Immortal Tribulation?

Unless...

"Wang Qi's clone has also made a huge breakthrough?"

Wang Qi's clone... No, it should be considered as "part" of the "whole", a physical body, right on this planet.

Wang Qi as a whole is like a huge immortal.

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

When an immortal faces a thunder tribulation, his fingers will naturally be attacked by some of the heavenly thunder.

In other words...

Wang Qi has made a huge breakthrough?

Wang Qi did not expect such a big change. He has completed the proof of the basic lemma, but at the moment of completion, he did not cause 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 "gradual change".

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

Since the Jindan stage, Wang Qi has been practicing the Wanfamen technique Xiangyu Tianwei Gong as the main method.

So...

This is a drastic change on the whole.

His attention is no longer on his own body.

This is a holistic change.

The mountain-like operators formed an unmatched wave, and the beast mechanism cluster was swept back and forth on the surface.

But this is only the surface.

The internal reconstruction is more complicated, and it is even difficult to describe it clearly in natural language.

A spiritual power vortex formed around him. The solar wind seemed to be enraged and roared at him. This was the rage of a star half an astronomical unit away. The storm of spiritual power swept high-energy particles towards Wang Qi.

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

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

This is the "heavenly tribulation" of the celestial demon level.

Fortunately, Wang Qi only broke through. His Yuanshen method was in operation, and this vast heavenly tribulation that was enough to destroy the planet was also absorbed by him and turned into his own power.

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

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

Wang Qi's physical body in a foreign land had completed an advancement along the Yuanshen method - from non-immortal to immortal.

Even according to the most stringent standards, he can call himself a free and easy monk.