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

David Halker and Sophie looked at each other and said with a smile: "No, sure! If even the Hopf conjecture can't be solved, then I'd rather not graduate! ”

Sophie nodded solemnly.

Pang Xuelin couldn't help crying and laughing, his own students were very confident.

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 global Riemannian geometry.

It's been almost a hundred years, and no mathematician has ever proved it.

The simple formulation of this conjecture is that for a compact and boundless even-dimensional manifold M^2n, if it accommodates a Riemannian metric of the curvature of a non-regular section, then its Eulerian indicative number satisfies (?1)^nχ(M^2n)≥0...... (1) When the cross-section curvature is negative, the above equation is a strict inequality.

In the field of differential geometry and geometric topology, Hopf is of great significance.

Since Pang Xuelin proposed the theory of Ponzi geometry two years ago, some people believe that the solution of this conjecture will build a bridge between Ponzi geometry and differential geometry.

If Halque and Sophie can solve this conjecture, they will surely have a place on the list of four people for the next Fields Medal.

Pang Xuelin's eyes swept over Halke, Sophie and Ai Ai, his students are not weak in mathematics, and there are still four years before the next Fields Medal, if Halke and Sophie solve the Hopf conjecture in the next few years, Ai Ai will solve a heavyweight mathematical problem, the next Fields Medal will really have the possibility of being dominated by their own students.

"Master, why do you think of us like that?"

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

Pang Xuelin smiled and said, "It's nothing, if it's okay, you can go back and prepare well, if you have any questions, you can come to me directly." ”

"Oh!"

Everyone nodded and left.

After a while, Pang Xuelin raised his head, but found that Ai Ai was still standing in place, looking at him with a pair of beautiful eyes.

"Ai Ai, what's the matter?"

Ai Ai's delicate brows furrowed slightly, and she said, "Master, I don't know which topic to choose. ”

Pang Xuelin said with a smile: "You choose a field that interests you!" ”

Ai Ai hesitated for a moment and said, "I have an idea, but I'm worried that this project is too difficult, and if I can't do it, I may not be able to finish my ......."

"What subject?"

"Goldbach conjecture!"

"What?!"

"Goldbach conjecture! Master, am I too self-conscious?! ”

Ai Ai saw Pang Xuelin looking at him with a ghostly look, and at the same time, he was a little proud in his heart, but he was also a little worried that Pang Xuelin would laugh at him.

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

Goldbach guessed that he had wanted to solve it for a long time, but over the years, he had been going to the science fiction plane for decades, going around in circles, and his research was intermittent, and there was not much progress.

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

Therefore, since Ai Ai is interested in this conjecture, it is not impossible to leave it to her.

Pang Xuelin pondered for a moment and said, "Ai Ai, since you are interested in Gechai, then I won't stop you." But it's too difficult to guess, and if you can't prove it all the time, you can't keep dragging it out like this. Well, you only need to meet two conditions and I will allow you to graduate. ”

"What conditions, Master, you say!"

Ai Ai hurriedly said.

Although he has always been a student of Pang Xuelin, he can see his master from time to time, and Ai Ai also feels quite satisfied.

But after all, the love between teachers and students is still not very good, if he can graduate early, then he can pursue his master openly.

Pang Xuelin said: "Now to study the Goldbach conjecture, the best thing to do is the big sieve method, if you can go further on the basis of the existing big sieve method, or you can open up a new way to prove the Goldbach conjecture, then I agree with you to graduate!" ”

Ai Ai was slightly stunned, clenched her fists and smiled: "Master, I will definitely be able to meet the two conditions you said." ”

"Okay, then you don't have anything else to do, right?"

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

Looking at Ai Ai's back bouncing away, Pang Xuelin shook his head with a smile, then lowered his head and began to busy his work.

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

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

But this is only a prophecy after all, and Pang Xuelin does not dare to guarantee that it is 100% correct.

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

A few months ago, Pang Xuelin uploaded a preprint paper on the new theory of superconductivity on arXiv, which was later published in the inaugural issue of the journal Exploration.

In this paper, Pang Xuelin uses mathematical means to construct a new bridge between the strongly correlated materials such as heavy fermion compounds and the traditional condensed matter theory systems such as the BCS theory, so as to completely unify the two completely different superconductivity mechanisms.

This paper has caused a lot of repercussions in the physics community.

But it's also very controversial.

Proponents believe that Pang Xuelin's method is very ingenious, and the mathematical method he uses can make the mathematical model of strongly correlated superconducting materials and the superconducting model of traditional condensed matter theory equivalent after transformation, and then launch a programmatic superconducting theory, which will provide strong theoretical support for mankind to find new superconducting materials in the future.

The opposite side believes that although Pang Xuelin's theory is good, only some experimental data meet the conditions, and if you want to prove the accuracy of Pang Xuelin's theory, you must build a new superconducting material model on the basis of his theory, and manufacture it to prove that Pang Xuelin is correct.

And this is precisely the hardest point.

Because Pang Xuelin only gave a mathematical model, but did not give any predictions on the material 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 papers, and some of them have gained some results, but most of the new superconducting materials that conform to Pang Xuelin's theory require extreme physical conditions to achieve superconducting properties.

Finding a true room-temperature superconductor still seems to be a distant path.

Many people even believe that even if Pang Xuelin's theory is correct, it may be decades before it is verified.

Just like in 1964, the British physicist Higgs proposed the concept of the Higgs boson, and it was not until March 14, 2013, when CERN discovered the existence of the Higgs boson, that Higgs won the Nobel Prize in Physics that year.

Therefore, even if Pang Xuelin's theory is correct, it seems that winning the Nobel Prize in physics is a distant thing.