"What's the situation? Did I hear it wrong? How could there be no name of Professor Pang Xuelin? ”

"Isn't Professor Pang's academic achievements ineligible for a Fields Medal?"

"If Professor Pang is not qualified, then the four people who won the award are even less qualified."

"The International Mathematical Union must give a clear explanation, and if it does not give an explanation, I will withdraw from the International Mathematical Union."

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

The entire Great Hall was booed.

Almost everyone questioned the result.

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

The Great Hall, which would have been boiling, fell silent in an instant.

Everyone looked at Robert Langlands on the stage in amazement, and no one expected that there would be a Fields Special Award.

Pang Xuelin looked at Robert Langlands with a smile and a smile, and he felt that this old man was completely deliberate.

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

He walked up to Robert Langlands and said with a smile: "I didn't expect everyone to love Professor Pang Xuelin so much, so I will first explain the origin of this Fields Special Award." ”

"When this year's Fields Medal was selected, the jury originally planned to put Professor Pang Xuelin's name on the list of Fields Medal winners. But as a result, we found that this was unfair not only to Professor Pang Xuelin, but also to several other Fields Medal winners. After all, in terms of mathematical achievements alone, Professor Pang Xuelin's achievements far exceed the level of ordinary Fields Medals. The Fields Medal alone is not enough to fully present Professor Pang Xuelin's contributions to the mathematical community. Therefore, we decided to separate Professor Pang Xuelin's award from the ordinary Fields Medal, and add a Fields Special Medal to be awarded to Professor Pang Xuelin. ”

Marcelo Viana paused and continued: "And, starting with the next International Congress of Mathematicians, the Fields Special Prize will be renamed the Pang Xuelin Prize. The Pang Xuelin Prize is awarded every four years to a maximum of one mathematician who has made significant and original contributions to the field of mathematics. The principle of awarding this award is rather than indiscriminate, and if it does not meet the award criteria, there will be a vacancy......"

As the words fell, the entire Great Hall erupted again, this time no longer boos, but thunderous applause and cheers.

No one disputes the decision of the International Mathematical Union, but feels that it is a fair evaluation of Professor Pang Xuelin's contribution.

And everyone understands that the Pang Xuelin Prize will also replace the Fields Medal and become the first award in the real sense of the mathematics community.

Offstage, Faltins said to Deligne: "Pang Xuelin Award...... In the future, I am afraid that super geniuses such as Galois, who created group theory, Mr. Chern Shiingshen, who created differential geometry, David Hilbert, who proposed Hilbert's 23 questions, and Pope Grothendieck in the field of algebraic geometry, may be able to win the Pang Xuelin Prize. ”

Deligne nodded and said, "I think this is good, and it is not 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 on the side with his eyes shining: "Sister Zuo, Master is too handsome, and his prestige in the mathematical world is so high." ”

Zuo Yiqiu pursed his lips and chuckled, his eyes flashed with an inexplicable light, 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 this honor awarded to him by the International Mathematical Union.

Travel through multiple sci-fi worlds, and go through several near-deaths to survive, hundreds of years before and after.

Pang Xuelin's heart is more about the past and expectations for the future, to be able to change the historical trend of an era and a world with his own strength, Pang Xuelin feels that this is his honor.

The award ceremony continues.

Marcelo Sivina said, "Go on, Professor Langlands. ”

Langlands smiled and nodded, feeling quite happy that he had just teased the many mathematicians in attendance.

Langlands said: "Okay, let's take a cursory review of Pang Xuelin's resume. Professor Pang Xuelin was born in Jiangcheng in March 1997 and showed a strong talent for mathematics when he was a teenager. He graduated from primary 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 with a bachelor's degree in 2015, went to the University of California, Los Angeles, and completed his doctoral studies in 2018, during which he did research on analytic number theory and additive combinations. He has published "Sum Product Estimation of Rational Functions" and "Proof of the Andere-Oorte Conjecture of Polarized Abelian Clusters". ”

In 2019, Professor Pang Xuelin returned to China to teach at Jiangcheng University, and in October, he completed the proof of the BSD conjecture, and in early December, at the award ceremony held by the Clay Institute, he officially proposed the Ponzi geometry theory, opened up a new branch of mathematics, and used the theory to prove the ABC conjecture. Late December. He published "A Method for Solving Analytical Solutions of Nonlinear Partial Differential Equations with Extensive Significance", which greatly promoted the progress of physics, chemistry, biology and other disciplines through mathematical means. ”

In 2021, Professor Pang completed the proof of the twin prime conjecture and the Polygnac conjecture through the relevant theory of Ponzi geometry. In 2022, just over a month ago, Professor Pang and Professor Perelman collaborated to complete the proof of the Hodge conjecture......"

"It can be said that every achievement of Professor Pang Xuelin is worth a Fields Medal, but Professor Pang Xuelin's greatest contribution to the mathematical community lies in the ...... of the Ponzi geometry theory he proposed."

Mr. Langlands told Pang Xuelin's resume, and even roughly expounded the relevant ideas of Ponzi geometry.

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

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

Everyone understands that Mr. Langlands is ridiculing Pang Xuelin for having too many fields of scattered research and failing to focus all his energy on mathematics.

Langlands also laughed and said, "Okay, the next step is the award ceremony, first of all, we have invited Professor Pang Xuelin to the stage." ”

Pang Xuelin was slightly stunned, and stood up with a smile.

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

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

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

Langlands smiled: "The old man would prefer to be able to see such a picture before he enters the ground." ”

There was another burst of laughter.

At this time, Langlands said, "Professor Pang, come on, come on, you stand by my side." ”

Pang Xuelin was slightly stunned, and wondered: "Didn't you give me an award next?" ”

Langlands said: "Who said that you were awarded an award, and you were asked to come up, it was for you to present awards to the Fields Medal winners." ”

Pang Xuelin couldn't help but be stunned.

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

Obviously, everyone recognized Pang Xuelin's award qualifications.

The Fields Medal winners also applauded.

Pang Xuelin smiled helplessly: "Okay, now we have Professor Jacob Lewis, Professor Occam Rodney, Professor Mark Mueller, and Professor Antonio Fraley come to the stage to accept the award." ”

Soon, to the applause of everyone, Jacob Lewis, Occam Rodney, Mark Mueller, Antonio Frally took the stage one after another.

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

The four winners delivered their acceptance speeches one after another.

It wasn't until all this was over that Pang Xuelin got his own Fields Special Award from Mr. Langlands.

Except for the gold medal, which was a lap bigger than the others, Pang Xuelin didn't feel anything special about this medal.

The prize money has increased to $50,000 compared to the $15,000 for others.

Subsequently, Pang Xuelin came to the stage and delivered his own acceptance speech.

The entire conference room hall fell silent, and thousands of people on the scene focused their eyes on Pang Xuelin.

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

There was another burst of laughter.

Pang continued, "Today is a special day for me, mathematics has been a part of my life since I was four years old. Whether it is studying, working, living, or studying mathematics, it is as natural as breathing. Professor Langlands has just said that I hope to see the day when algebra and geometry can be completely unified, and this is what I have been pursuing. ”

"For a long time, mathematicians have tried to bridge the gap between the two ancient disciplines of algebra and geometry, trying to construct some kind of grand unified theory. But to this day, this has been a dream of our mathematicians. But this dream is not out of reach. ”

"In ancient Greece, Aristotle said: We cannot prove geometric problems by arithmetic. He argues that geometry can help solve arithmetic problems. At the time, this view was not controversial, but it could not escape the test of history. Euclid, the father of geometry at about the same time as Aristotle, did not rely on numbers, but used as a graph to extend the axioms of logic to proofs. Numbers seem to stand in another time and space, and there is no way to find a way out of geometric skills. ”

This continued into the 17th century, when the Frenchman René Descartes combined algebraic techniques with Euclidean geometry to break the ice between numbers and geometry. Descartes introduced the concept of coordinate systems, that is, points, lines, and surfaces can be perfectly described by coordinate values, allowing geometricians to solve geometric problems using algebraic methods. ”

"It's like landing on the moon and finally being able to launch the rocket at the exact angle and position. But for pure mathematicians, there is still half the way to the end. For example, a circle can be accurately described by an algebraic equation, but a graph derived from the untraced points of the equation can never be fully pictured. Once the system of units of coordinates is changed (e.g. from 1 to π), as is often done by pure mathematicians, the equations still hold and the plots are confusing. ”

Fast forward to 1940, and another Frenchman, André Wey, was tormented by the chasm between numbers and geometry. A few months before the German occupation of France, Wey was detained in a prison outside Lyon, France, for refusing military service. It was this time in prison that gave him a lot of gains, and Wayy discovered the sporadic clues between algebra and geometry, which laid the foundation for us to find the Rosetta Stone that unified algebra and geometry. ”

This brings us to the Riemann conjecture, the well-known distribution of prime numbers. It has long been thought that there should be a geometric explanation for this conjecture. In the thirties of the last century, elliptic curves were already algebraically proven. We can translate the distribution of prime numbers into thinking about how many points there are on the curve. Wey's proof that the Riemann conjecture is equally applicable to solving more complex curves, and that the wall that has stood between the two disciplines since ancient Greek times finally cracked a gap, and Wey's proof established a good foundation for the discipline of algebraic geometry, overturning Aristotle's views in one fell swoop. ”

Until now, however, the Riemann conjecture has been confirmed on the first ten trillion primes, but there has not been a rigorous proof. In the post-war years, at the University of Chicago, where the environment was more comfortable, Wey tried to solve the prime puzzle, but never succeeded. The baton then passed to Alexander Grothendiek, who redefined algebraic geometry in the sixties. ”

Among a series of scholarly innovations, Grothendieck called a set of integers a spectrum, abbreviated as Spec(Z). The points on this non-drawable geometric entity are closely related to prime numbers. The Ponzi geometry that I later established myself was based on the Spec(Z) figure that Grothendieck was seeking. Ponzi geometry is completely different from any geometric object we are familiar with, such as a circular triangle in Euclidean geometry or a parabolic ellipse in a Cartesian coordinate system. In these planes, a point is just a point on the surface, but a point in Ponzi geometry is more like thinking in terms of the whole surface. It covers all possible situations of a face, such as drawing a triangle or ellipse on it, or even curling it up as if wrapped around a ball. ”

In addition to this, Robert Langlands, in his letter to André Wey, proposed that two branches of mathematics that are very far apart, number theory and harmonic analysis, may be related. The seeds of ideas contained in this program gave rise to the Langlands Program, which gave rise to a series of far-reaching mathematical conjectures that had the potential to unify the three core disciplines of mathematics: arithmetic, geometry, and mathematical analysis. Mathematical analysis is a very broad subject that includes calculus, which we learn in school. Hundreds of mathematicians around the world, including Schultz, are committed to perfecting the discipline. ”

The complete version of the Langlands program is not likely to be proved quickly, as the Riemann conjecture suggests, but this treasure trove of ideas contains many amazing discoveries: like Fermat's theorem, it took three hundred and fifty years to be proved by Professor Andrew Wiles in 1994, and this is only a special result of the Langlands conjecture. The most "

"In recent times, in addition to the latest core Ponzi geometry theory, the great unification of geometry and algebra has been followed by the p-incubation number, that is, the alternative representation of any given prime number p. To create a p-inward from an arbitrary positive integer, the integer is represented as a p-inward number, and then reverse. For example, if you want to represent the integer 20 as a decimal number, you can first write the binary expression 10100 of 20, and then write it in reverse order, which is 00101. Similarly, the 3 of 20 is 202 and the 4 is 011.

The characteristics of the number of p into the number will also be slightly different, the most obvious of which is the distance problem of the number: if the difference between two numbers is divisible by the power of p many times, then the distance between the two numbers is close, and the higher the power, the closer the distance. For example, the decimal numbers of 11 and 36 are close to each other because their difference is 52. But the 5 decimal numbers of 10 and 11 are far apart.

"For decades after the invention of the p-to-sum number, people just used it as a mathematical toy, and felt that it was of little practical use. It wasn't until the 20s that the German mathematician Helmut Hasset was fascinated by a booklet in a second-hand bookstore. He realized that p-in-the-numbers led to how to deal with the fact that prime numbers were not divisible by other numbers, and became a shortcut to solving complex proofs. ”

Since then, p-intro numbers have become a central part of the field of number theory. When Professor Wiles proved Fermat's theorem, he involved the concept of p-incubation in almost every step. ”

……

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

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, if you accidentally pull away." As for the academic aspects, let's wait until the afternoon presentation. Once again, I would like to thank the Fields Medal jury for giving me such a special award, and I am very grateful to all the family, lovers and friends who have stood behind me and supported me. Thank you all, I love you. ”

Subsequently, Pang Xuelin slowly stepped down from the stage and returned to his position to sit down amid warm applause from the audience.

Faltins on the side was curious: "Pang, can you show me your medal?" ”

"Absolutely."

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

Faltins looked at it for a while, handed the medal back to Pang Xuelin, and said, "Pang, at the afternoon report meeting, are you going to talk about the relevant propositions of Ponzi geometry?" ”

As soon as Faltins asked, the surrounding Robert Langlands, Pierre Deligne and others all cast their eyes on Pang Xuelin.

This year's International Congress of Mathematicians will last for nine days, with a total of more than 1,200 presentations.

Including the Filipino Prize winners, there are only about 20 scholars. With access to one hour of presentations, less than 50 scholars were given 45 minutes of formal presentations.

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

Everyone was curious about what Pang Xuelin would say at the report meeting.

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

"New ideas?"

Faltings' eyes lit up.

Not only Faltins, but Deligne also looked at Pang Xuelin curiously and said, "Pang, what new ideas?" ”

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

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

Subsequently, everyone left the venue one after another and went to the restaurant to eat.

Pang Xuelin and several winners, as well as Faltins, Deligne, Langlands, Yau Chengtong and other bigwigs, were invited by the organizing committee to have lunch in a small restaurant.

After eating, Pang Xuelin returned to his hotel room and prepared to take a rest.

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

Pang Xuelin was slightly stunned, got up to open the door, and saw Ai Ai and Zuo Yiqiu standing at the door.

"Why are you here?"

Pang Xuelin said curiously.

Ai Ai smiled, "Master, can you let me touch your Fields Special Medal medal?" Rub your luck. I don't want to get this medal, and one day I can get a regular Fields Medal, and I'll be satisfied. ”

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

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

Suddenly, her gaze swept over the upper compartment of the bookcase, and she was suddenly stunned, pointing to the two matryoshka dolls on it and said curiously: "Master, where did you get this matryoshka doll?" ”

Pang Xuelin was slightly stunned, and looked at Ai Ai's finger, the nesting doll that Ai Ai was referring to was the one that Zuo Yiqiu gave him.