Great Country Academician

Sitting on the sofa, Xu Chuan was also reminded of some memories by Perelman's words.

The microelement construction method is a tool that solves the century-old problem of NS equations. It can also be called a brand-new 'discipline', as long as it is carried forward.

Of course, for Xu Chuan, what he misses even more is the inspiration, or state, triggered when creating this tool.

That wonderful feeling, even though it was four or five years ago, still made him miss it endlessly.

In the following time, he thought of many ways, but no matter what he did, he could not go back.

The closest thing is the study of topological states of matter in strongly correlated electronic systems.

That research provided complete theoretical support for how quantum computers control qubits and store information, but it is still far inferior to the state when studying NS equations.

Recovering from his memories, Xu Chuan looked into Perelman's brown-green eyes, smiled and said: "That was an inspiration I got in class. It was actually more physics-based." Some direction.”

Seeing him starting to tell the 'story', several scholars in the small living room turned their gazes over. Feeling these gazes, Xu Chuan continued with a smile:

"For the mathematical community, the NS equation is often used as a typical example to study nonlinear partial differential equations. The method of mathematical analysis is gained in the process of solving it, and we tend to pay more attention to this. Of course, whether the singularity on the vortex is Real existence is also the answer sought.”

"However, for the physics community, the existence or absence of a solution to the NS equation is the core of describing the motion behavior of fluids. That is, the fluid particles described by the NS equation are infinitesimal in space, but in fact they are infinitely large relative to the molecules. .”

"The core of solving this point lies in whether the divergent behavior of the fluid will eventually return to calmness from a physical perspective. Starting from the smallest microflow, we introduce it into the mathematical set concept to obtain the most core divergent microflow unit. Then we can topology and structure it, and its existence can be mathematically constructed."

Listening to Xu Chuan's words, Perelman fell into deep thought.

The answer he had been unable to find all this time made him feel unexpectedly 'simple' when it came from this person's mouth?

But he soon realized that this was not so-called 'simple', it was just that he looked at it from the perspective of the past.

In fact, to do this, I'm afraid it requires extremely profound knowledge in mathematics and physics. Only by fully understanding the Navier-Stokes equations from both aspects can there be a slight possibility to learn from both. In that narrow common connection, find a way to the other side.

Withdrawing his scattered thoughts, Perelman took a sip of the cold water in the cup, looked at Xu Chuan, and said, "So this is how it was born. Thank you for explaining my confusion."

After a slight pause, he seemed a little confused and said: "But compared to the perfection shown by that tool, I always feel that there seems to be something missing in your story."

Hearing this, Xu Chuan smiled and said, "That was probably the most wonderful short time in my life."

After briefly recalling the feeling, he continued with some nostalgia: "I don't know if you have experienced it, but for me at the time, it was like an 'epiphany' falling into a novel."

"The ideas in my mind were like trickling water. In that short period of time, mathematics was like my arm, and all the calculations were like the most tacit partners, following my footsteps as I pleased."

On the side, Tao Zhexuan frowned slightly and immediately added: "Are you saying that you completed the 'Micro Element Construction Method' in class?"

Xu Chuan nodded and said: "Yes, that short period of time brought about the 'micro-element construction method'. Even though I tried countless times in the following time, I could not enter that state again."

After a pause, he added: "Although it is a bit embarrassing to praise myself like this, but as Perelman said, it is perfect like a gift from the void."

Hearing this, Schultz didn't pay attention to the compliments at all. He just said with envy: "It's such an enviable experience. I didn't expect that there would be such a legendary story in the middle."

Although he didn't quite understand what Xu Chuan's "epiphany" felt like, he could understand it as an "outbreak of inspiration."

As a mathematician dedicated to achieving higher achievements in mathematics, he extremely hopes that he can have such an experience.

Not only Schultz, but also Terence Tao, Curtis, and even Perelman in the crowd all had a hint of envy in their eyes.

This sounds like a plot in a novel, but it has brought an exquisite tool to the entire mathematics world, and even a whole new discipline.

Withdrawing his eyes with a trace of imperceptible envy, Perelman said: "It is really an enviable and amazing experience, although I prefer to think that it is brought about by your profound attainments in mathematics and physics. inspiration.”

"But back to the topic, did you come here today with a math problem?"

For Perelman, the past is past, and even the most enviable things have long since become history. What he hopes and yearns for are only those mathematical problems that have not yet been solved.

Rather than listening to these "legendary" stories, he hoped that Xu Chuan came with mathematics.

Sitting opposite Perreman, Xu Chuan put down the water glass in his hand, nodded seriously, and said, "Of course."

As he spoke, he took out a portable notebook from his coat pocket and handed it over.

“Here are some things I’m thinking about in terms of topology and manifolds, and some questions that maybe you would think about differently?”

For Xu Chuan, the purpose of taking some risks to go abroad to participate in the International Congress of Mathematicians is to take a further step on the path of mathematics.

Going around in such a big circle to find the 'reclusive' Perelman, wouldn't it be a waste of time if we didn't exchange some mathematical ideas?

When it comes to mathematics, he is the same type of person as Perelman.

"Let me see"

Perelman reached out and took the notebook, quickly opened it and glanced at the ideas and calculations on it.

"Space-time manifold, dimensional space, gauge group, field theory. What on earth are you studying?"

After briefly browsing through the ideas and calculations in his portable notebook, Perelman showed a hint of surprise and surprise in his eyes.

The messy ideas and calculations on the portable notebook in his hand made it impossible for him to tell what this young man was trying to study, because there were too many things involved.

On the side, before Xu Chuan could answer, Tao Zhexuan asked curiously: "Can I take a look?"

The words were directed at Perelman, but his eyes were directed at Xu Chuan.

Although he was curious about what was written in the portable notebook, after all, this was an exchange between Xu Chuan and Perelman, so it would be better to ask them if they minded.

Xu Chuan nodded and said, "If he doesn't mind, I have no problem."

Hearing this, Perelman handed the portable notebook in his hand to Terence Tao, and then asked: "You haven't told me what exactly you are studying?"

Xu Chuan smiled and said: "If you are asking about recent research, it should be the mathematical unification of the three powerful forces of strong and weak electricity. Of course, the premise is that the proof of the Yang-Mills mass gap is correct, otherwise My time in the near future will probably be spent tinkering with it.”

"As for future research on the Riemann Hypothesis and the unification of algebra and geometry, it is a very good direction."

After a pause, he continued: "After all, I learned from Mr. Grothendieck, and completing this work is also what I should do."

Hearing this, Perelman muttered: "But there is no research related to the Riemann Hypothesis in your notebook."

Xu Chuan smiled and said: "Those are one of the reasons why I came to see you today."

"In terms of topology, you should be the person closest to the truth. I would like to ask, in mathematics, whether there is a one-way or two-way topological "tunnel" in a three-dimensional space!"

"Can topology allow such a configuration to exist mathematically and quantumly?"

PS: Second update, please vote for me.