The Science Fiction World of Xueba

Pang Xuelin smiled slightly: "What? Not sure?"

David Harker and Sophie Heyman looked at each other and said with a smile: "No, sure! If I can't even solve Hopf's conjecture, then I'd rather not graduate!"

Sophie Heyman also nodded solemnly.

Pang Xuelin couldn't help crying and laughing, these students of his own had a lot of self-confidence.

The Hopf conjecture is one of several conjecture statements proposed by the German mathematician Hopf in differential geometry and topology in 1931, and it is also an open problem in the overall Riemannian geometry.

Almost a hundred years ago, no mathematician can prove it.

The simple expression of this conjecture is: for a compact and infinite even-dimensional manifold M^2n, if it accommodates a Riemann metric of non-positive section curvature, then its Euler characteristic satisfies (?1)^nχ (M^2n)≥0...(1), when the section curvature is negative, the above formula is a strict inequality.

In the field of differential geometry and geometric topology, Hopf has very important significance.

And since Pang Xuelin put forward Ponzi geometry theory two years ago, some people think that the solution of this conjecture will build a bridge between Ponzi geometry and differential geometry.

If Halke and Sophie can solve this conjecture, they will definitely have a place in the four-man list for the next Fields Medal.

Pang Xuelin glanced over Halke, Sophie, and Ai Ai. These students are not weak in mathematics. There are still four years before the next Fields Medal. If Hal If Ke and Sophie solve the Hopf conjecture in the past few years, and Ai Ai solves another heavyweight mathematical problem, the next Fields Medal may really be dominated by his own students.

"Master, why do you look at us like that?"

Ai Ai noticed the strangeness in Pang Xuelin's eyes.

Pang Xuelin smiled and said, "It's nothing. If there's nothing wrong, you can go back and prepare well. If you have any questions, you can contact me directly."

"oh!"

Everyone nodded and left.

After a while, Pang Xuelin raised his head, only to find that Ai Ai was still standing there pretty alive, with a pair of beautiful eyes looking at him without blinking.

"Ai Ai,

Is there a problem? "

Ai Ai frowned slightly and said, "Master, I don't know which topic to choose."

Pang Xuelin smiled and said, "Choose a field that interests you!"

Ai Ai hesitated for a moment, and said: "I have an idea, but I'm worried that this subject is too difficult. If I can't do it all the time, I might never be able to graduate..."

"What subject?"

"Goldbach Conjecture!"

"What?!"

"Goldbach's conjecture! Master, am I too overwhelmed?!"

Ai Ai saw Pang Xuelin looking at her with eyes that had seen a ghost, and at the same time she was a little proud, but at the same time worried that Pang Xuelin would laugh at herself.

Pang Xuelin shook his head and smiled, "How come? I didn't expect you to have such courage."

Goldbach guessed that he wanted to solve it a long time ago, but these years, he went to the sci-fi plane to stay for decades from time to time, going around, researching intermittently, and there has not been much progress.

Moreover, Goldbach's conjecture is only difficult. Even if it is solved, the significance in the mathematical world is far less than that of Riemann's conjecture.

Therefore, since Ai Ai is interested in this conjecture, it is not a bad idea to leave it to her.

Pang Xuelin pondered for a moment, then said: "Ai Ai, since you are interested in Brother Guess, then I won't stop you. But Brother Guess is too difficult, if you can't prove it, you can't keep procrastinating like this. How about it, You only need to meet two conditions, and I will allow you to graduate."

"What conditions, master, tell me!"

Ai Ai said quickly.

Although she has been a student of Pang Xuelin, Ai Ai also feels quite satisfied to see her master from time to time.

But the teacher-student relationship is not very pleasant after all. If I can graduate early, then I can pursue my master openly.

Pang Xuelin said: "The best way to study Goldbach's conjecture now is the large sieve method. If you can go further on the basis of the existing large sieve method, or you can open up a new way to prove Goldbach's conjecture , then I agree with your graduation!"

Ai Ai was taken aback for a moment, clenched his fists and said with a smile: "Master, I will definitely be able to meet the two conditions you mentioned."

"Okay, so you have nothing else to do?"

"It's okay, master, then I'll go first!"

Looking at Ai Ai's back bouncing away, Pang Xuelin smiled and shook his head, then lowered his head and started busy with his work.

Pang Xuelin is now writing a thesis on the theory of superconductivity.

Since successfully completing the construction of the superconducting theory a few months ago, although Pang Xuelin has sorted out the theoretical framework, he even predicted the existence of a room-temperature superconductor configuration in multi-walled carbon nanotubes through his own theory.

But this is just a prophecy after all, and Pang Xuelin can't guarantee that it is 100% correct.

It was not until Cao Yuan's team and Li Changqing's team successfully synthesized this material that Pang Xuelin began to write a paper on superconducting 128 materials.

A few months ago, Pang Xuelin uploaded a pre-printed paper on the new theory of superconductivity on arXiv, which was later published in the first issue of the "Exploration" magazine.

In this paper, Pang Xuelin built a new bridge between strongly correlated materials such as heavy fermion compounds and traditional condensed matter theory systems such as BCS theory through mathematical means, thus completely unifying the two completely different superconducting mechanisms.

This paper caused great repercussions in the physics community.

But there is also a lot of controversy.

Supporters believe that Pang Xuelin's method is very ingenious. The mathematical method he uses can make the mathematical model of strongly correlated superconducting materials equivalent to the superconducting model of traditional condensed matter theory after transformation, and then introduces a programmatic superconducting model. Conductivity theory will provide strong theoretical support for human beings to search for new superconducting materials in the future.

The opposing side believes that although Pang Xuelin's theory is good, only part of the experimental data meets the conditions at present, and to prove the accuracy of Pang Xuelin's theory, a new superconducting material model must be constructed on the basis of his theory, and the Only when it is produced can Pang Xuelin be proved correct.

And this is precisely the most difficult point.

Because Pang Xuelin only gave a mathematical model, but did not give any material predictions in the paper.

In the past few months, many physicists in the field of condensed matter have been looking for new superconducting materials based on Pang Xuelin's thesis, and some of them have gained some results. However, most of the new superconducting materials that conform to Pang Xuelin's theory require extreme physical conditions. achieve superconducting properties.

It seems that it is still an elusive path to find a real room temperature superconductor.

Many people even think that even if Pang Xuelin's theory is correct, it will be decades before it can be verified.

Just like the British physicist Higgs proposed the concept of the Higgs boson in 1964, it was not until March 14, 2013 that CERN discovered the existence of the Higgs boson that Higgs was granted the status The annual Nobel Prize in Physics.

Therefore, even if Pang Xuelin's theory is correct, winning the Nobel Prize in Physics seems out of reach.

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