I really just want to be a scholar

Chapter 920 My God, how did he do it!
Is mathematics aesthetic?

Yes, there is no doubt that all correct and perfect items will give people the enjoyment of beauty, especially for mathematicians. Whether a theory is perfect or not can be determined by whether it is "beautiful" or not.

Of course, this "aesthetic" is abstract and highly subjective.

Qin Ke has heard the story of Einstein since he was a child. Einstein was a person who persistently pursued the "beauty of theory".

Einstein was convinced that God must have constructed the world with simplicity and beauty, which made him have strict aesthetic requirements for a theory. He insisted that beauty is a guiding principle for exploring important results in theoretical physics, so whenever he If he feels that a theory is ugly, he will completely lose interest in it, or he will try to find ways to "make it beautiful."

From this perspective, Einstein is indeed a bit like Li Xiangxue's obsessive-compulsive disorder.For example, Einstein felt that the special theory of relativity and the Lorentz invariance in Maxwell's electromagnetism were not "beautiful" enough. In order to make them perfect, he established the general theory of relativity.

Of course Qin Ke is not so extreme, but he also agrees that the concept of "beauty" is common to all disciplines.

Now, he looked at the complex shapes drawn in his hands with satisfaction. Although due to his kindergarten-like painting skills, such complicated multi-curved shapes like overlapping petals did not look "perfect", Qin Ke showed some of the shapes, I really saw the "beauty", which is the beauty of numbers, and even more, the beauty of mathematics!
Finally finished!
The perfect blend of geometry and algebra!

"The Emperor of Algebraic Geometry" Grothendieck's unfinished perfect fusion and unity of geometry and algebra was realized under his pen!

This complex figure is a concrete embodiment of "new geometry".

Through "new geometry", any algebraic problem can be transformed into a geometric problem, and vice versa. In this transformation, partial differential equations and topology of mathematical analysis are the main bridges, and it runs through number theory, probability theory, group theory, etc. Theory, chaos theory, complex function, catastrophe theory, fuzzy mathematics and other key points of more than a dozen sub-disciplines.

Although the current "connection" is only connected through "bridges" and is not truly "inclusive", Qin Ke is confident that as long as he continues to study in depth along the "new geometry", one day he will be able to establish With "new geometry" as the core, it is a new framework theoretical system that includes all mathematical sub-disciplines, and is a true "programmatic unification" that can explain all mathematical problems!
And through this self-created "new geometry", Qin Ke wants to prove that the "Hodge Conjecture", one of the seven major problems of the millennium, is not difficult. The method used is even better than the S-level knowledge "Revealing the Hodge Conjecture" The proof method in " is much simpler!
Of course, for the current issue of detoxification of radioactive elements, Qin Ke is confident that through this "new geometry", he can solve the real obstacle to the problem of supersymmetric quantum field theory in four dimensions and above, and promote the development of M theory. further improvement!
After reading the graphics on the manuscript paper in his hand several times, Qin Ke felt a sense of accomplishment. He reached out and roughly tidied up the messy manuscript paper on the table, then wiped the sweat from his forehead and stood up.

Although his LV7 sports level gives him extremely strong physical and energy, entering the "Inspiration Amplification State" for a long time still consumes a lot of money. Qin Ke can't hide the sleepiness on his face, but it is still much better than before falling asleep directly from exhaustion. few.

The summer sun rises early. At this time, there is dawn outside, and the light shines in through the gaps in the curtains.

Looking at the time, it's already 6:15 in the morning. I guess Ning Qingyun has woken up, right?
Qin Ke wiped his sweat, opened the door and walked out of the study, and met Ning Qingyun who was looking for him.

Qin Ke pointed at the desk and showed a sleepy smile: "Honey, the 'New Geometry' is done. I want to sleep for a while, and I'll leave you to sort it out." He hugged him gently and was obviously attracted by him. Ning Qingyun was stunned by these words, then returned to the master bedroom, fell on the bed, and fell asleep in a blink of an eye.

Ning Qingyun did not go to the study immediately, but followed Qin Ke back to the master bedroom, wiped away the fine beads of sweat remaining on his forehead, covered him with the air-conditioned quilt, and closed the curtains to prevent the light from affecting Qin Ke's rest. Just walked out of the master bedroom.

Qin Xiaoke, who was wearing pajamas, happened to walk to the bathroom. She rubbed her eyes and yawned as she greeted Ning Qingyun: "Good morning, sister-in-law."

"Morning, Xiaoke."

06:30 is the fixed time for Qin Ke, Ning Qingyun, and Qin Xiaoke to practice the Eastern Secret Code. Qin Xiaoke is also used to getting up early, but she was still a little sleepy when she just woke up. She found that Ning Qingyun was missing someone, so she He asked: "Where is my brother? Still in the study?"

Ning Qingyun made a silent gesture, pointed to the master bedroom, and whispered: "He just went to bed, don't disturb him."

Qin Xiaoke said in surprise: "Isn't it possible? My brother actually went back to sleep? The sun has risen from the west? Isn't he always very energetic?" He said with a sly smile: "It can't be the case. Did you do some morning exercise early in the morning?"

Ning Qingyun blushed and stretched out her slender little fingers to pinch Qin Xiaoke's cheek: "You girl, are you becoming more and more daring to talk nonsense?"

"Wow wow wow, sister-in-law, I was wrong, I don't dare anymore..."

In fact, it was Qin Xiaoke who was inexperienced. He had really experienced morning luck. How could Ning Qingyun look like this?
Of course, Ning Qingyun was not willing to really pinch the girl, so she put her hand away angrily: "Brother You just solved a math problem and fell asleep because he was too tired."

"Oh!" Qin Xiaoke suddenly remembered that something like this had happened before. Instead of worrying about his brother, he asked excitedly: "What kind of mathematical problem is it? Is it some new geometry that you have been discussing recently? "

"Yeah. It's this new geometry."

"Awesome, worthy of my sister-in-law's husband, my brother! Hehe, I still don't understand, which one is more powerful, this 'new geometry' or the Riemann Hypothesis, Goldbach's Hypothesis, etc."

Ning Qingyun could not hide the pride in her eyes. She thought for a while and said: "It's different. We can't directly compare it with these millennium conjectures. But if we must give an answer, I think that even if the Riemann Hypothesis, Brother Debach's conjecture, as well as the four millennium conjectures such as the NS equation and the Yang-Mills equation, combined, are not as great as the impact of this 'new geometry' on mathematics. Probably..."

She looked back at the master bedroom and whispered: "Probably, in the history of mathematics, there is no theory that can match this 'new geometry', including the Langlands Program!"

Ning Qingyun participated in Qin Ke's "new geometry" research almost from scratch, and his deep understanding of it was second only to Qin Ke.

The Langlands Program is nothing more than a series of conjectures revealing the connections between number theory, algebraic geometry, and group representation theory, and most of them have not been proven.

Qin Ke's "new geometry" is indeed a mathematical theory that is logically self-consistent, has been rigorously demonstrated in the process of establishment, and can be directly applied. It is based on a complete and strict axiomatic conceptual system. and expression methods, which closely connect the three major disciplines of algebraic geometry, topology, and mathematical analysis, unify them within the same theoretical framework, and can penetrate more than a dozen sub-disciplines such as number theory, probability theory, and group theory!

It can be said that the gap between the famous Langlands Program and "New Geometry" is equivalent to the gap between a sixth-grade primary school student and a university undergraduate majoring in mathematics!
……

In addition to Ning Qingyun and Qin Xiaoke, those who got up early in the morning were also older mathematicians, such as Faltings, Deligne, Wiles and Edward Witten.

When people reach a certain age, sleep time will naturally decrease, so when Ning Qingyun and Qin Xiaoke finished practicing the Eastern Secret Code, changed clothes and came down to the living room on the first floor to have breakfast, Faltings and several other senior group members The mathematicians, together with the neighbor Mr. Qiu who came for breakfast, were already sitting there drinking coffee and tasting the capital's breakfast, and of course discussing mathematics.Linden Strauss and Lao Tao, two middle-aged men in their 50s and [-]s who were not shown, were obviously still enjoying a good sleep in their respective rooms.

Seeing Ning Qingyun and Qin Xiaoke coming down from the second floor, everyone was not polite. They just said hello and continued the previous topic - As for Qin Ke's absence, everyone didn't pay much attention. After all, Qin Ke and Ning Qingyun is not inseparable. It is normal to come down early and late.

Mr. Qiu frowned and said: "The problem of high-dimensionalization of the Riemann-Roch theorem mentioned last night, I think Qin Ke's idea is right, but it is too difficult to really solve it, and the 'new geometry' has been stuck. I have been working on this problem for almost three days, and I still recommend skipping it. After all, this topic solves the problem of detoxification of radioactive elements, and the high-dimensional Riemann-Roch theorem should not be used."

Deligne put down his coffee cup and said with some reluctance: "The problem of high-dimensionalization of the Riemann-Roch theorem has been delayed for nearly half a century. I think if we can solve it in one go this time, it will be very important for the development of algebraic geometry. It is of great significance and the 'new geometry' can be more perfect. I also agree with Qin Ke's idea. Although it may take an extra month or two to solve it, I think it is worth it."

The Riemann-Roche theorem is an important tool in complex analysis and algebraic geometry that allows the calculation of the dimensions of a meromorphic function space with specified zeros and poles.The so-called high-dimensional problem of the Riemann-Roche theorem is simply to provide a general calculation formula for the global cross-section of the wire harness in high-dimensional situations, and it also has a certain relationship with number theory.

It has been solved by Grothendieck in low-dimensional space, but it has stopped at Grothendieck. In the past few decades, countless mathematicians have charged at it, but they have not achieved breakthrough results.

As a student of Grothendieck, Deligne rarely saw the dawn of a solution to this high-dimensional problem, so he naturally wanted to conquer it with all his strength and give his Bourbaki school a glory worth showing off.

However, Mr. Qiu believes that this is a hard nut that is not important to "new geometry". Solving it is the icing on the cake. It is okay if it cannot be solved temporarily or postponed to the future.

According to the team's original goal, the "new geometry" must be completed to a high degree by the end of June at the latest and be used to solve the problem of detoxifying radioactive elements. Time is now very tight.

Edward Witten said: "Pierre, although it is somewhat regrettable to give up efforts to solve this problem at present, I think that next we should focus our energy on the connection between topological field theory and algebraic geometry." Well, for example, difficulties in homology theory, fiber bundle theory and K theory, which play a vital role in improving M theory."

Edward Witten has enough say on this issue. He is an absolute expert in topological field theory and algebraic geometry. He once cooperated with Seberg and proposed the Seberg-Witten theory, which successfully interpreted He discovered three- and four-dimensional supersymmetric quantum field theories, and used them to explain why the quarks in protons are tightly bound.

Nowadays, many theoretical predictions of quantum field theory are consistent with experimental results to an unprecedented extent. However, why quantum field theory can give surprisingly accurate predictions about the physical world is still a mystery. Edward said that "topological field theory and "The Correlation Problem between Algebraic Geometry" is to find the answer to this question.

When it comes to understanding this subject, Edward Witten is second only to Qin Ke.

Faltings, who had been silent, finally spoke: "As Edward said, although it is a pity, things have to be prioritized. It is more appropriate to delay solving the problem of high-dimensionalization of the Riemann-Roch theorem for another six months. "

Even so, there was still some unconcealable disappointment in his tone. He had also wanted to solve the problem of high-dimensionalization of the Riemann-Roch theorem, but it took him nearly a year to find a clue. Now Qin Ke proposed a solution. The idea is also the result of Qin Ke. It is impossible for him and Deligne to abandon Qin Ke and other members and continue to move forward along this idea. That is equivalent to taking Qin Ke’s research results. For Faltings and For Deligne, this was an immoral act that he could never tolerate, so he could only wait for Qin Ke to find time and everyone could solve it together.

"Well... I see that Qin Ke has solved the problem of high-dimensionalization of the Riemann-Roch theorem." Ning Qingyun interjected while peeling the egg shells for Qin Xiaoke.

The whole place suddenly fell silent, and even the sound of Ning Qingyun's peeling egg shells falling could be heard.

"There is also the connection between topological field theory and algebraic geometry that Edward mentioned just now. I saw that Qin Ke has also solved it. The general method is to construct a special function group whose genus is an arbitrary value and establish the corresponding elliptic curve. The system of equations realizes the homotopy-invariant loop integral, and ultimately promotes the convergence and unification of the gauge coupling constants..."

Her voice was as soft and pleasant as when she was eighteen or nineteen, full of the ethereal and sweet voice of a girl, but when it fell into the ears of Faltings, Deligne, Edward, Wiles and others, it was as shocking as thunder.

Ning Qingyun put the peeled eggs into Qin Xiaoke's bowl and took the soy milk brought by Qin Xiaoke. Then she raised her head and said with a playful, proud, arrogant, and smug smile:

"In the early hours of this morning, Qin Ke stayed up late to integrate all the results of our discussions over the past few days. On this basis, he solved all eleven unsolved problems, including the above two problems, in one fell swoop. It can be said,' The new geometry was born, perfectly born!"

The whole place fell silent again. Qin Xiaoke also secretly raised the corner of his mouth, took out his mobile phone, turned on the video function, and captured this unforgettable moment that is destined to be recorded in the history of mathematics.

She made the right decision, as the cell phone video captured the moment Wiles dropped the fork from his hand.

As if they were awakened by the crisp sound of the fork falling on the table, everyone shouted out in disbelief and disbelief almost at the same time:

"Oh my god, this..."

"Was it solved after staying up all night? Have all the 11 problems we listed been solved?"

"Where is Qin Ke? Where is Qin Ke? I'm curious now how he solved it!"

"Yes, yes, we can't wait! Oh my God, how did he do it!"

While exclaiming, everyone stood up excitedly.

Unless they are not excited, although "new geometry" does not yet equal the unification of mathematics, there is no doubt that the perfect birth of "new geometry" will push the unified theory of mathematics forward in a big way!It will have a huge impact on the world of mathematics!

Faltings looked up at the calendar, May 5th.

He knew that soon the entire mathematical community would remember this historic day.

　I worked overtime for a whole day yesterday, and I was tired and sleepy, so I really didn’t have time to update.I hope you can forgive me.Sending you today’s update.

　　
　
(End of this chapter)