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 firmly believed 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 aspect, 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 figures drawn in his hands with satisfaction. Although due to his kindergarten-like painting skills, such complex multi-curved figures like overlapping petals did not look "perfect", Qin Ke revealed some figures.

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 unfinished perfect integration and unity of geometry and algebra that Grothendieck, the "Emperor of Algebraic Geometry" had not completed, 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 such transformation, partial differential equations and topology of mathematical analysis are used as the main bridge, and it runs through number theory, probability theory, group theory, etc.

Theory, chaos theory, complex function, catastrophe theory, fuzzy mathematics and other more than ten sub-discipline key points.

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 can explain the true "programmatic unification" of 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 the 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 away 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 as he spoke 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 while saying hello to Ning Qingyun: "Good morning, sister-in-law."

"Morning, Xiaoke."

Six-thirty 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 was surprised and said: "No way? 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: "No way.

Did you do your 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 exercise. 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: "Your brother 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 mathematical problem is it? Is it some new geometry that you have been discussing recently?"

"

"Well. 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."

This chapter is not over yet, please click on the next page to continue reading! Ning Qingyun could not hide the pride in her eyes. She thought about it and said: "It's different. We can't directly compare it with these millennium conjectures. But we must give

If I have an answer, I think that even the four millennium conjectures, including the Riemann Hypothesis, Goldbach's Hypothesis, N-S Equation, and Yang-Mills Equation combined, are not as influential as this 'new geometry' on mathematics.

Big. 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 the conjectures have not been confirmed.

However, Qin Ke's "new geometry" is indeed logically self-consistent, a mathematical theory that has been rigorously demonstrated during the establishment process, can be directly applied, and 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 Beijing's breakfast, and of course discussing mathematics.

The two middle-aged men in their forties and fifties, Linden-Strauss and Lao Tao, who had not shown up, were obviously still enjoying a wonderful 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 care too much. 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 for now. 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 that 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-Roch theorem is an important tool in complex analysis and algebraic geometry. It can calculate the dimension of a meromorphic function space with specified zeros and poles. The so-called high-dimensional problem of the Riemann-Roch theorem is simply

To put it simply, we want to provide a general calculation formula for the global cross-section of the wire harness in high-dimensional situations, which 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, by the end of June at the latest, the "new geometry" must have a high degree of completion and be used to solve the problem of making radioactive elements harmless. Time is already very tight.

Edward Witten said: "Pierre, although it is somewhat regrettable to give up efforts to solve this problem, I think 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 theory, and used this 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. What Edward calls "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’s voice 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.

"

This chapter is not over yet, please click on the next page to continue reading! Even so, there was still some disappointment in his tone. He had also wanted to solve the problem of high-dimensionalization of the Riemann-Roche theorem, but it only took him nearly a year.

After failing to find a clue in the year, Qin Ke has proposed a solution, which is also Qin Ke's achievement. It is impossible for him and Deligne to abandon Qin Ke and other members and continue to move forward along this line of thinking. That would be equivalent to taking advantage of

Taking Qin Ke's research results was an unethical act that Faltings and Deligne could never tolerate, so they 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.
To be continued...