The Science Fiction World of Xueba

"What's the situation? Did I hear it wrong? Why is there no Professor Pang Xuelin's name?"

"Aren't Professor Pang's academic achievements eligible for the Fields Medal?"

"If Professor Pang is not qualified, then the four winners are even less qualified."

"The International Mathematical Union must give a clear explanation. If I don't give an explanation, I will withdraw from the International Mathematical Union."

"Yes, we need a reasonable explanation..."

The whole hall was booed and booed everywhere.

Almost everyone disputes this result.

Seeing that the scene was about to get out of control, Pang Xuelin was thinking about whether to stand up and help restore the order of the scene, when he heard Robert Langlands say again: "Next, I will announce a winner of the Fields Special Award, That is Professor Pang Xuelin from Jiangcheng University."

The auditorium, which was supposed to be boiling, became quiet in an instant.

Everyone stared dumbfounded at Robert Langlands on the stage. No one expected that there would be a Fields Special Award.

Pang Xuelin looked at Robert Langlands dumbfounded. He felt that the old man did it on purpose.

At this time, Marcelo Viana, chairman of the organizing committee of the conference, did not seem to have thought that Robert Langlands deliberately late pronouncing Pang Xuelin's name would cause such a big disturbance.

He walked up to Robert Langlands, smiled and said, "I didn't expect everyone to love Professor Pang Xuelin so much, so let me first explain the origin of this Fields Special Award."

"During the selection of this Fields Medal, the judging committee originally planned to put Professor Pang Xuelin's name on the list of Fields Medal winners. But we found that this was not only unfair to Professor Pang Xuelin, but also to several other The Fields Medal winners are also unfair. After all, in terms of mathematical achievements alone, Professor Pang Xuelin’s achievements far exceed the level of ordinary Fields Medals. A single Fields Medal cannot fully present Professor Pang Xuelin Contributions to the mathematics community. So we decided to separate Professor Pang Xuelin's award from the ordinary Fields Medal and add a special Fields Award to Professor Pang Xuelin."

Marcelo Viana paused, and continued: "Moreover, starting from the next International Congress of Mathematicians, the Fields Special Award will be renamed the Pang Xuelin Award. The Pang Xuelin Award will be selected every four years, and each time a maximum of Awarded to a mathematician who has made significant original contributions to the field of mathematics.

Then there will be a void..."

After the words fell, the entire hall erupted again. This time, there were no boos, but thunderous applause and cheers instead.

No one questioned the decision of the International Mathematical Union, but felt that doing so was a fair evaluation of Professor Pang Xuelin's contribution.

And everyone knows that the Pang Xuelin Award will also replace the Fields Medal and become the number one award in the true sense of mathematics.

In the audience, Faltings said to Deligne: "The Pang Xuelin Award... I am afraid that in the future, it will be like Galois who created group theory, Mr. Chern who created differential geometry, and put forward Hilbert's twenty-three questions." The super geniuses such as David Hilbert and Pope Grothendieck in the field of algebraic geometry are likely to win the Pang Xuelin Award."

Deligne nodded and said, "I think it's not bad. It's our luck to be in the same era as such a genius."

At the same time, Ai Ai, who was sitting in the back row of the venue, said to Zuo Yiqiu with bright eyes, "Sister Zuo, Master is so handsome, and his prestige in the mathematics world is so high."

Zuo Yiqiu pursed his lips and smiled lightly, with an inexplicable gleam in his eyes, and he didn't know what was going on in his head.

Pang Xuelin had a faint smile on his face, and he didn't have any special feelings about the honor bestowed on him by the International Mathematical Union.

Travel through multiple sci-fi worlds, survive several near-deaths, and go back and forth for hundreds of years.

In Pang Xuelin's heart, there are more emotions about the past and expectations for the future. Pang Xuelin feels that it is his honor to be able to change the historical trend of an era and a world by himself.

The award ceremony continues.

Marcelo Sivina said: "Professor Langlands, you can continue."

Langlands nodded with a smile, feeling quite happy to have teased the many mathematicians attending the meeting just now.

Langlands said: "Okay, let's briefly review Pang Xuelin's resume. Professor Pang Xuelin was born in Jiangcheng in March 1997. He showed a strong mathematical talent when he was young. He graduated from elementary school in 2009 and was admitted to Jiangcheng Middle School. , won the gold medal in the International Mathematical Olympiad in 2013, entered Jiangcheng University in the same year, graduated in 2015, went to UCLA, and completed his doctoral studies in 2018, during which he did research on analytic number theory and additive combinations. Estimates of the sum product" and "Proof of the Andere-Oorte conjecture for polarized Abelian varieties."

"In 2019, Professor Pang Xuelin returned to China to teach at Jiangcheng University. In October, he completed the proof of the BSD conjecture. In early December, at the award ceremony held by the Clay Institute, he formally proposed Ponzi's geometry theory, opening up a new branch of mathematics. And use this theory to prove the ABC conjecture. In late December. Published "A Method for Solving Analytical Solutions of Nonlinear Partial Differential Equations with Broad Significance", which greatly promoted the progress of physics, chemistry, biogeography and other disciplines through mathematical means."

"In 2021, Professor Pang completed the proof of the twin prime number conjecture and the Polignac conjecture through the relevant theories of Ponzi geometry. In 2022, just over a month ago, Professor Pang and Professor Perelman cooperated to complete the The proof work of Hodge's conjecture..."

"It can be said that every achievement of Professor Pang Xuelin is worth a Fields Medal. However, Professor Pang Xuelin's greatest contribution to the field of mathematics lies in his proposed Ponzi geometry theory..."

Mr. Langlands talked about Pang Xuelin's resume, and even briefly explained the related ideas of Ponzi's geometry.

Finally, he said: "The emergence of Ponzi geometry has shown us the dawn of the complete unification of the two basic mathematical disciplines, algebra and geometry. I also hope that Professor Pang Xuelin can devote more energy to the development of mathematics. Riemann's conjecture, Goldbach's conjecture, P/NP problem, existence and smoothness of N-S equation solutions, Yang-Mills gauge field existence and mass interval assumption, etc. There are still many difficult problems waiting for you to solve... ..."

After Langlands' words fell, the scene couldn't help but burst into laughter.

Everyone understands that Mr. Langlands is teasing Pang Xuelin. There are too many scattered research fields, and he has not been able to devote all his energy to mathematics.

Langlands also laughed and said, "Okay, next is the awards ceremony. First of all, we invite Professor Pang Xuelin to come on stage."

Pang Xuelin was taken aback for a moment, then stood up with a smile.

Afterwards, amidst the applause of everyone present, he walked slowly onto the podium and came to Langlands.

The host on the side quickly handed the microphone to Pang Xuelin.

Pang Xuelin said with a smile: "Thank you for your encouragement, old man. But please rest assured, old man, I have not relaxed my research on mathematics. I hope that one day, we can truly see the emergence of a grand unified theory of algebra and geometry."

Langlands said with a smile: "The old man hopes to see such a picture before he is buried."

There was another burst of laughter at the scene.

At this time, Langlands said: "Professor Pang, come here, you stand beside me."

Pang Xuelin was taken aback for a moment, and asked doubtfully, "Wouldn't you be giving me an award next?"

Langlands said: "Whoever said that it was for you to present the award, you were asked to come up to present awards to the Fields Medal winners."

Pang Xuelin couldn't help being taken aback.

On the contrary, there was a burst of cheers and applause at the scene.

Obviously, everyone recognized Pang Xuelin's qualifications for the award.

The winners of the Fields Medal also applauded.

Pang Xuelin smiled helplessly: "Okay, then we invite Professor Jacob Lewis, Professor Occam Rodney, Professor Mark Muller, and Professor Antonio Flatley to come to the stage to accept the award."

Soon, in the applause of all, Jacob Lewis, Occam Rodney, Mark Muller, Antonio Frari took the stage one after another.

Pang Xuelin received Fields Medals and certificates from the on-site staff and awarded them to the four winners one by one.

The four winners delivered acceptance speeches one after another.

After all this was over, Pang Xuelin received his own Fields Special Award from Mr. Langlands.

Pang Xuelin didn't feel that there was anything special about this medal except that the gold medal was a circle larger than the others.

But the bonus, compared to the 15,000 Canadian dollars for others, directly increased to 50,000 Canadian dollars.

Afterwards, Pang Xuelin came to the podium and delivered his acceptance speech.

The entire meeting room fell silent, and thousands of people at the scene focused their attention on Pang Xuelin.

Pang Xuelin said: "Thank you, thank you for the kindness of the Fields Medal Committee. To be honest, although I thought I would win the award, I didn't expect to win it in this way."

There was another burst of laughter at the scene.

Pang Xuelin continued: "Today is a special day for me. Since I was four years old, mathematics has become a part of my life. Whether it is study, work or life, studying mathematics is as natural as breathing. Just now, Professor Langlands once said that he hopes to see the complete unity of algebra and geometry one day, which is also the goal I have been pursuing.”

"For a long time, mathematicians have tried to build a bridge between the two ancient disciplines of algebra and geometry, and wanted to build some kind of grand unified theory. But until now, this has always been just a dream of our mathematicians. But this The dream is not out of reach."

"In the ancient Greek era, Aristotle once said: We cannot prove geometry problems through arithmetic. He thought that geometry can help solve arithmetic problems is nonsense. At that time, this view was not controversial, but it cannot escape history. The test of wind and frost. Euclid, the father of geometry at almost the same time as Aristotle, did not rely on numbers, but used diagrams to expand logical axioms into proofs. Numbers seem to stand in another time and space, geometry There is no way out of skill.”

"This situation lasted until the 17th century, until the Frenchman René Descartes combined algebraic skills with Euclidean geometry, breaking the ice between numbers and geometry. Descartes introduced the concept of the coordinate system, that is, points, lines , Surfaces can be perfectly described by coordinate values, allowing geometers to use algebraic methods to solve geometric problems."

"It's like landing on the moon. We can finally launch the rocket at the exact angle and position. But for pure mathematicians, it's still halfway to the end. For example, a circle can be accurately expressed by algebraic equations. description, but the graph obtained by plotting the solution points of the equation will never be complete. Once the unit system of coordinates is changed (for example, from 1 to π), as pure mathematicians often do, the equation still holds, and the plot makes People are helpless."

"Fast forward to 1940 and another Frenchman, André Weil, was tormented by the gap between numbers and geometry. A few months before the German occupation of France, Weil was interned outside Lyon, France for conscientious objection It was this time in the prison that made him very fruitful. Weil discovered the sporadic clues between algebra and geometry, which laid the foundation for us to find the Rosetta Stone of the unity of algebra and geometry. Base."

"This involves the Riemann conjecture, a well-known prime number distribution problem. People have long believed that this conjecture should have a corresponding geometric explanation. In the 1930s, elliptic curves have been algebraically proved. We can use the prime number Distribution, transformed into thinking about how many points there are on the curve. Weil proved that the Riemann conjecture is also applicable to solving more complex curves. Gap, Weil's proof has established a good foundation for the subject of algebraic geometry, overthrowing Aristotle's point of view in one fell swoop."

"However, until now, although the Riemann conjecture has been confirmed on the first ten trillion prime numbers, there is still no strict proof. In the post-war years, in a more comfortable environment at the University of Chicago, Weil is still trying to solve The prime number puzzle, but it never worked out. The baton then passed to Alexander Grothendieck, who redefined algebraic geometry in the 1960s."

"Among a series of academic innovations, Grothendieck called a set of integers a spectrum, abbreviated as Spec(Z). The points on this undrawable geometric entity are closely related to prime numbers. Then I myself established the Ponzi geometry is based on the Spec (Z) figure sought by Grothendieck. Ponzi geometry is completely different from any geometric object we are familiar with, such as the circular triangle of Euclidean geometry, or the parabola in the Cartesian coordinate system Ellipse. On these planes, a point is just a point on the surface, but a point in Ponzi geometry is more like thinking from the perspective of the entire surface. It covers all possible situations of a surface, such as drawing a Triangle or ellipse, or even curl it up, as if wrapped around a ball."

"Besides, Robert Langlands, in his letter to André Weil, suggested that two very different branches of mathematics, number theory and harmonic analysis, might be related. This program contains The seeds of thought sprouted into the Langlands program, which produced a series of far-reaching mathematical conjectures. This program may unify the three core disciplines in mathematics: arithmetic, geometry and mathematical analysis. Mathematical analysis is a scope Its breadth of disciplines includes calculus, which we learn in school. Hundreds of mathematicians around the world, including Schultz, have worked to perfect this discipline."

"The complete version of the Langlands program is not like the Riemann conjecture, which may be proved soon, but this treasure house of ideas contains many amazing discoveries: just like Fermat's last theorem, three hundred years after it was proposed Fifty years, it was proved by Professor Andrew Wiles in 1994, and this is just a special result of the Langlands conjecture. Most”

"Recently, in addition to the latest core Ponzi geometry theory, the unification of geometry and algebra research is the p-adic number, which is the alternative representation of any given prime number p. Create a p from an arbitrary positive integer To enter a number, it is necessary to express this integer as a p-ary number, and then express it in reverse. For example, to express the integer 20 as a binary number, you first write the binary expression of 20 10100, and then reverse the order Write, it is 00101. Similarly, the 3-adic number of 20 is 202, and the 4-adic number is 011.

"The characteristics of p-adic numbers will also be slightly different, the most obvious of which is the distance between numbers: if the difference between two numbers can be divisible by multiple powers of p, then the distance between the two numbers will be close, and the higher the power , the closer the distance. For example, the 5-adic numbers of 11 and 36 are very close, because their difference is 52. But the 5-adic numbers of 10 and 11 are far apart.

"In the decades after the p-adic number was invented, people just regarded it as a mathematical toy and felt that it had no practical use. Until the 1920s, the German mathematician Helmut Hassey found it in a second-hand bookstore. After seeing it in this booklet, he was fascinated by it. He realized that the p-adic number guides how to deal with the property that prime numbers are not divisible by other numbers, and it becomes a shortcut to solve complex proofs.”

"Since then, p-adic numbers have gradually become a core part of the field of number theory. When Professor Wiles proved Fermat's last theorem, almost every step involved the concept of p-adic numbers."

...

Time passed by every minute and every second, and the entire hall of the conference room was quietly heard, and everyone listened quietly to Pang Xuelin's explanation.

It wasn't until the host reminded Pang Xuelin of the time that Pang Xuelin came back to his senses, and said with a smile: "Okay, I've gotten away with it accidentally. Regarding the academic content, let's wait until the afternoon report. Here, I would like to thank the Fields Medal jury once again for giving me such a special award, and I am also very grateful to those relatives, lovers and friends who have always stood behind me and supported me. Thank you everyone, I love you.”

Afterwards, Pang Xuelin stepped off the stage slowly amidst warm applause from the audience, and returned to his seat to sit down.

Faltings on the side asked curiously: "Pang, can you show me your medal?"

"No problem at all."

Pang Xuelin smiled and handed the Fields Special Award medal to Faltins.

Faltings flipped through it for a while, returned the medal to Pang Xuelin, and said, "Pang, for the afternoon report, are you going to talk about the relevant propositions of Ponzi geometry?"

When Faltings asked, Robert Langlands, Pierre Deligne and others around him cast their eyes on Pang Xuelin.

This International Congress of Mathematicians will last for nine days, and a total of more than 1,200 lectures will be held under normal circumstances.

Including the Philippine Prize winners, there are only about 20 scholars. One-hour lecture time can be obtained, and less than 50 scholars can obtain 45 minutes of formal lecture time.

But this time the conference made an exception for Pang Xuelin, and the whole afternoon would belong to Pang Xuelin.

Everyone is curious about what Pang Xuelin will say at the report.

Pang Xuelin shook his head with a smile, and said: "I originally planned to give a speech on Ponzi geometry at this report meeting, but just now, Professor Langlands mentioned the unification of algebra and geometry, which gave me some ideas. new ideas..."

"new idea?"

Faltings' eyes lit up.

Not only Faltings, Deligne also looked at Pang Xuelin curiously: "Pang, what new idea?"

Pang Xuelin shook his head with a smile, and said: "It's hard to say now, it's just a very preliminary idea, and you will know it in the afternoon."

At this time, Marcelo Sivina, chairman of the organizing committee of the conference, came to the stage to announce that the morning press conference was officially over.

Afterwards, everyone left the venue one after another and went to the restaurant for dinner.

The organizing committee of the competition prepared an exquisite buffet lunch for the participating mathematicians from all over the world. Xuelin Pang and several winners, as well as big names such as Faltins, Deligne, Langlands, and Qiu Chengtong, were invited by the organizing committee. Head to a small restaurant for lunch.

After eating, Pang Xuelin returned to the hotel room, ready to take a rest.

He had just sat down at the desk in the hotel when there was a knock on the door.

Pang Xuelin was slightly taken aback, got up and opened the door, and saw Ai Ai and Zuo Yiqiu standing in the doorway.

"Why are you here?"

Pang Xuelin asked curiously.

Ai Ai smiled and said: "Master, can you let me touch your Medal of Fields Special Award? It's just luck. I don't want to get this medal, one day I can get ordinary Fields I will be satisfied with the medal."

Pang Xuelin pointed to the medal on the bookcase beside him and said, "Touch it."

Ai Ai picked up the medal and looked around with a smile, and even took out her mobile phone to take a few photos.

Suddenly, her gaze swept across the upper shelf of the bookcase, she was taken aback for a moment, pointed to the two matryoshka dolls on it and asked curiously: "Master, where did you get this doll?"

Pang Xuelin was slightly taken aback, and followed Ai Ai's fingers to look over, the matryoshka that Ai Ai was pointing at was the one Zuo Yiqiu gave him.

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