After Qin Ke finished explaining, he stood there, waiting for everyone to ask questions or put forward new ideas.

This is also the unique communication method of their group. They usually think about things individually, and when they get together, they drink tea and coffee, have sparks of thinking in the form of chatting, and even brainstorm together.

Many new creativity and ideas are born through this easy and free communication method.

Although Mr. Qiu went to Qiuzhen Academy to handle matters today and was not here, Qin Ke, Ning Qingyun, Edward Witten, Tao Zhexuan, and Academician Tian Jianlan who were present were basically considered to be in Xia Dynasty.

He is the top mathematics master in the country. But yesterday, he was stuck on the optimal solution of the third set of partial differential equations. Except for Academician Tian Jianlan, the others have been thinking about it all day, and they have many new ideas.

Thinking of this, Lao Tao was the first to speak.

The entry point he chose was the three-dimensional hyperbolic manifold, because originally the third set of partial differential equations was derived from this special manifold. He calculated the complement of the hyperbolic knot under the hyperbolic metric.

A purely topological problem is transformed into a logarithmic function.

Although it failed to solve the problem raised by Qin Ke, it provided a new perspective.

Next, Ning Qingjun and Edward Witten presented their own thinking results from different directions of normalized tangent clusters, pseudo-effective cones and small remainder clusters, rationally connected clusters and Kato homology on KLT singularities.

It was Academician Tian Jianlan’s turn to speak last.

Academician Tian Jianlan thought for a long time before saying: "I don't know much about superstring theory, but just now Qin Ke used 'new geometry' to derive the third set of partial differential equations from the three-dimensional hyperbolic manifold.

Look, it is mentioned that for any non-negative number p, p-brane is indivisible. I can think that such p-brane can be regarded as one of the 'basic units of strings', and transform it into

What is the concept of ‘prime number’?”

Edward Witten praised: "Academician Tian's point of view is correct. In superstring theory, string is not the only basic unit. P-brane can indeed be called a 'basic unit', and its definition is somewhat similar to that of prime numbers.

Similarity.”

A prime number refers to a natural number that has no other factors other than 1 and itself among natural numbers greater than 1. It does have a certain similarity with p-brane in terms of "indivisible" and "indivisible".

Academician Tian Jianlan is an expert in number theory. Her way of thinking about problems is to find connections with number theory as much as possible, and approximately convert the problem into a number theory problem. At this time, she stepped forward to take the question from Qin Ke's hand.

Pen, wrote down a few strings of mathematical formulas, and said:

"I think the parameter issue that Qin Ke circled just now should be related to the existence of this p-brane. Can we set this changing p-brane as a number theory combination, by using Cochy-Darvin's Botter theorem?

,Introducing the definition and properties of Dyson e-transform..."

Academician Tian Jianlan's overall idea is to use Chen Jingrun's double linear sieve method, combined with Selberg's upper bound sieve method, to find the most suitable special prime number p, and substitute it into the formula derived from her custom gauge field and fiber bundle theory.

In the subroutine, parameter substitution is implemented.

"It's a pity that I can only think of this step. I failed to solve the problem you just raised. In the end, it seems that I have gone astray." After completing the replacement of parameters, Academician Tian Jianlan smiled self-deprecatingly and took the erasable pen.

Return it to Qin Ke.

After thanking Qin Ke, he looked at the dense calculations on the big whiteboard and fell into deep thought. After nearly five minutes, he erased all the calculations on it and wrote a line of words - "Normalize the local degree of freedom."

degree of freedom".

"I summarized everyone's ideas just now. Although the methods are different, the ideas are consistent and can be compared to the local degrees of freedom in the gauge degrees of freedom in gauge field theory. I also agree with this idea. What I just said

The parameter problem, in the final analysis, is to find the most suitable value in the parameter group with limited degrees of freedom that does not affect the overall situation, so that the optimal solution of our third group of partial differential equations is 6. In this case

, I have a new idea, we might as well transform it directly into a matrix problem, combining Lie groups and modular function theory..."

Qin Ke's eyes shone with wisdom, and his whole person seemed to be shining with a different kind of brilliance. He wrote repeatedly: "∑t(n)q^n qn(1-q^n)*qΦ(q

^m)/η(z^ty)……”

He wrote faster and faster, and soon finished a series of derivation processes. When the whiteboard was finally filled, the final result was a set of extremely complex partial differential equations with the number "24" appearing 17 times.

"This is..." Edward Witten stood up almost in disbelief and lost his voice: "Ramanujan's magic number!"

The so-called "Ramanujan's magic number" refers to the "number" that appears in string theory and causes the magical cancellation of dimensions.

Ramanujan is a very magical master of mathematics. He is self-taught. "Mathematical intuition" accounts for a huge proportion in his mathematical theory. He has proposed a lot of incredible ideas without any argumentation process, but he was eventually accepted.

Proved to be correct mathematical theories, functions, and calculations. For example, the Ramanujan function and Ramanujan mathematical identity he proposed can be applied to string theory very accurately!

In string theory, there are a total of 26 dimensions, and the Ramanujan function can correspond to 24 kinds of physical vibrations of strings. Whenever a string performs its complex motion by decomposing and recombining in space and time, it can satisfy

Highly complex mathematical identities of Ramanujan.

No one can understand whether this is a coincidence or whether the truth of nature is the same, let alone what mathematical intuition Ramanujan based on when he wrote Ramanujan’s mathematical identity. However, string theory physicists all choose to

It is used as one of the basis to prove the rationality of string theory, and 24 is called "Ramanujan's magic number".

This chapter is not finished yet, please click the next page to continue reading the exciting content! Later, with the development of superstring theory, 24 dimensions were compressed by the 3-dimensional world to 8, so the critical number of superstring theory is 8+2, which is 10. Superstring

The theory is also known as the 10-dimensional theory.

To this day, whenever someone asks why superstring theory is 10-dimensional, the generalized Ramanujan function and Ramanujan’s magic number are always brought up as a basis for logical self-consistency, but no one can still

Answer "Why can strings vibrate in a self-consistent quantum form only when it is 10 dimensions?"

Now the derivation of Qin Ke's "transformation formula" is to perform a clever limited local free transformation on the third set of partial differential equations that originally had parameter problems, making it equivalent to the original formula.

What’s amazing is that in this new third set of partial differential equations, a large number of “24” appears, which seems to be somehow related to the generalized Ramanujan function and Ramanujan’s magic number!

Qin Ke turned the big whiteboard over and continued writing on the other blank side.

Edward Witten's breathing became a little faster, because he vaguely discovered that Qin Ke seemed to take this opportunity to reveal the mystery of the wonderful connection between "Ramanujan's magic number" and string theory, and this mystery

, it is very likely that it is essentially related to the 6-dimensional problem of "Calabi-Qiu space"!

Not only Edward Witten, but also Academician Lao Tao, Ning Qingjun, and Tian Jianlan all stared at Qin Ke's moving pen tip. They also valued Qin Ke's exquisite mathematical thinking in this transformation and derivation process.

and processing methods.

"Amazing... Is this guy possessed by Ramanujan?" Lao Tao murmured to himself, looking more and more excited. Qin Ke just sorted out the four people's suggestions at first, but as he continued

The derivation becomes more and more in-depth, and the creativity and super genius way of thinking reflected in it are simply amazing and astonishing!

Even though I have lived with Qin Ke for more than seven months, I have long been accustomed to Qin Ke's "super" performance, and even vaguely regarded him as the "God of Mathematics", but now I see Qin Ke's another super performance.

Lao Tao was still extremely shocked by his divine performance, especially his "mathematical intuition" that was like a divine help.

Because of this kind of wild imagination, he had only seen it in Ramanujan’s works!

Tian Jianlan's eyes were also full of shock. The complicated and difficult mathematical calculations that were obviously unrelated were connected together in a natural way, which was extremely shocking and indescribable.

Even his teacher, Mr. Chen Jingrun, would be amazed when he saw this scene, right? Academician Tian Jianlan thought to himself, but a thought quickly emerged in his mind: Maybe, this is real mathematics, right?

——Unfettered, free to transform, like a Rubik's cube that changes in thousands of ways, but eventually turns into a regular and perfect cube!

Qin Ke's derivation process at this moment was like a Rubik's Cube expert resolving the Rubik's Cube with super-fast hand speed!

Ning Qingyun looked at Qin Ke with eyes full of admiration. The transformation essence of new geometry, Qin Ke's superhuman mathematical intuition and talent, and unparalleled profound knowledge were all displayed in his writing at this time.

!

Qin Ke's pen tip was writing faster and faster. Every time he finished writing a page, he would turn over the whiteboard, erase the content on it, and write again.

The smoothness of his pen tip is like a rushing river, and like the light cutting through the dark night. It seems that all the mathematical fog is defeated and dissipated in the face of such majestic momentum and indestructible light, revealing the truest truth!

Finally, Qin Ke's pen tip outlined the most perfect number "6".

This is the optimal solution to the third set of partial differential equations after transformation!

He turned back and showed a bright smile: "It's become the 'Calabi-Qiu space'. There is no secret in our eyes. Edward's M theory can be completed. At least in terms of dimensions, it will surpass all others in the world."

The theory of M!"

It was obvious that there were slight beads of sweat on Qin Ke's forehead, and his face was slightly pale due to excessive mental exertion. He was not as energetic as usual, but he stood there like a high mountain, a mountain that no one could surpass in the world of mathematics.

The great mountains!

There was silence in the guest room for a long time. Lao Tao was the first to come to his senses and clapped vigorously, while Ning Qingyun and Tian Jianlan couldn't help but follow suit.

A trace of regret flashed through Ning Qingyun's heart: It's a pity that Xiaoke is not here, otherwise it would be very exciting to record this scene with a brush.

Edward Witten's eyes sparkled with excitement. He kept clapping and looking at the last part of the equation written by Qin Ke over and over again.

He knew very well that an "unexplainable problem" that had troubled the string theory community for decades had finally received the most standard mathematical answer. This answer can also directly explain the generalized Ramanujan function, Ramanujan

The secret of the magic number!

Whether it is the world of mathematics or string theory, at this moment, a new page will be opened!

This Qin Kezhen... can no longer be described as a "genius", but can only be called a "god", the "god of mathematics"!

…

I don’t know if the system heard Edward’s call, or it was a coincidence. At this moment, Qin Ke’s ear heard the notification tone of the God of Learning to Save the World system.

"Ding! After testing, you have cracked the connection between Ramanujan's function, Ramanujan's magic number and the origin of nature with your unique and wonderful ideas, and established a logically self-consistent M theory'

The mathematical basis of dimensionality compression has brought a perfect end to the dimensionality problem of M theory, which has greatly promoted the improvement of M theory and human beings' understanding of the dimensions of the world. The 'scores make me progress' system evaluated the 'score' as 'S

Level', the 'Grades Make Me Improve' function is in effect, your academic points (mathematics) are 10,000! Academic points (physics) are 10,000!"

Along with the system's beep, Qin Ke's math upgrade progress bar and physics upgrade progress bar both moved forward.

Especially for mathematics, it was already close to the threshold for promotion. The difference was only about 7,000 academic points. This time, I gained 10,000 academic points and reached the finish line immediately.

"Ding! Your academic points (mathematics) have accumulated to 100,000, meeting the upgrade conditions!"

"Your mathematics level has been upgraded to: 'God of Mathematics Level'!"

Qin Ke was ecstatic, his mathematics level finally broke through to the long-awaited level of the God of Mathematics!
To be continued...