Pang Xuelin smiled and said, "This nesting doll is actually ......"

"Ahem......" Zuo Yiqiu, who was on the side, suddenly coughed dryly twice.

"Actually, I bought it myself, I saw that the nesting doll you gave me was very beautiful, so I went to buy another ......"

After speaking, Pang Xuelin winked at Zuo Yiqiu.

Zuo Yiqiu's fair face quickly flushed with a hint of redness, and even the roots of his ears were red.

Ai Ai didn't react at all, and wondered: "But didn't you go out yesterday?" ”

"I asked Professor Shinichi Mochizuki to buy it for me."

"Oh!"

Ai Ai faintly felt that her master was not telling the truth to herself, but she was not Pang Xuelin or anything, so she didn't want to ask much for a while.

She didn't suspect Zuo Yiqiu, Zuo Yiqiu's attitude towards Pang Xuelin on weekdays has always been businesslike, and basically didn't show anything special.

More importantly, she could feel that Zuo Yiqiu was a little contemptuous of her master's chaotic love life.

Bang bang bang –

At this time, there was another knock at the door, and the three of them followed the sound and saw a photojournalist and a female reporter in charge of the interview standing at the door.

"Professor Pang, I'm CCTV reporter Liu Xiaolin, is it convenient to be interviewed now?"

Pang Xuelin was slightly stunned, and then remembered that he won the award this time, and I am afraid that it will set off a lot of waves in the domestic media.

He smiled and said, "Okay, you guys come in." ”

At this time, Zuo Yiqiu said: "Okay, Ai Ai, Professor Pang still has something to do, let's not disturb him." ”

"Well, master, then let's go back to the room first."

Pang Xuelin said with a smile: "Go, go, go." ”

Ai Ai was the first to go out, and Zuo Yiqiu followed behind her.

When it was time to go out, Zuo Yiqiu couldn't help but glance back at Pang Xuelin, the two looked at each other, and saw that Pang Xuelin just looked at her with a light smile. Zuo Yiqiu hurriedly withdrew his gaze, but his heart couldn't help but beat violently.

Pang Xuelin shook his head with a smile, I really don't understand, one of these two girls is a little cute, the other looks a little cautious, but her skin is so thin, and I don't know how the two of them became best friends.

Then, Pang Xuelin turned his gaze to Liu Xiaolin and said: "Reporter Liu, it's half past twelve at noon, and there is a report meeting in the afternoon, and it will take about an hour to prepare, so I can only give you 10 minutes." ”

Liu Xiaolin said with a smile: "Professor Pang, ten minutes is okay, the time difference between St. Petersburg and China is five hours, and it is now half past five in the afternoon of the capital time. ”

"Okay, let's start now."

Pang Xuelin sat down on the sofa in the living room, and the photojournalist also pointed the camera at Pang Xuelin, and the interview officially began.

"Professor Pang, can you tell us how you felt when you won the award?"

Pang Xuelin laughed and said: "It's not a surprise to be able to win the award, the only thing that surprised me a little is that the International Mathematical Union will come up with a Fields Special Award, which makes me feel honored and happy." ”

Liu Xiaolin said: "Professor Pang, you are the first scientist in history to win both the Fields Medal and the Nobel Prize, which has won great honor for our country. ”

Pang Xuelin smiled and said: "There is a saying in the academic world that mathematics is the queen of science and the servant of science. Many problems in physics, chemistry and even biology can be solved mathematically, and they all have to follow the guidance of mathematics. This is why mathematics is the queen of science. But at the same time, mathematics is at the service of natural science, a tool we use to understand the objective world, so it is said to be a servant of science. For me, mathematics is fundamental and at the same time interested, so there is no such thing as balance, at least for me, when I work on problems in other fields, it does not affect my research in mathematics......"

"Professor Pang, after the news of your award came back to China, it caused a huge sensation on the Internet, and many young college students have taken you as an example and made you their spiritual mentor. Do you have anything to say to them? ”

Pang Xuelin pondered for a moment and said with a smile: "Thank you very much for your support, the future development of our country and the improvement of people's living standards all depend on the improvement of productivity." I hope that more and more young people will enter the field of scientific research, and at the same time, more people will be able to cope with the trivial things of life, and at the same time, they will have some time to look up at the sky above me......"

……

Next, Pang Xuelin answered a few more questions from Liu Xiaolin before ending this brief interview.

After Liu Xiaolin and the others left, Pang Xuelin did not directly start preparing for the afternoon report, but took out his mobile phone and looked at the reaction on the Internet.

Needless to say, the reports of the major media are basically cheers.

People's Daily Online: "Today, the opening ceremony of the 29th International Congress of Mathematicians was successfully held in St. Petersburg, Russia, and Professor Pang Xuelin won the Fields Special Prize, becoming the first Chinese mathematician in history to win the award. ”

Sina.com: "The Fields Special Award is tailored for Professor Pang Xuelin, and its status is much higher than that of the ordinary Fields Medal, and Professor Pang won the first throne in the contemporary mathematics field. ”

Observer: "Fields Special Prize?" Pang Xuelin Award? In any case, Professor Pang Xuelin has written his name in the history of mathematics. ”

Tencent News: "As both the winner and the presenter, the International Mathematical Union has tailored a new award for Professor Pang Xuelin, named after Professor Pang, who has won the respect and love of mathematicians around the world. ”

……

Compared with the major news media, the reports on social platforms are much more exaggerated.

In the hot search on Weibo, from the first to the fifth, they were once again occupied by Pang Xuelin alone, namely the Fields Special Award, the Pang Xuelin Award, the award ceremony almost overturned, Pang Xuelin won the Fields Special Award, Robert Langlands spoke highly of Professor Pang's achievements and so on.

At the same time, Pang Xuelin's personal Weibo has long been occupied by all kinds of sand sculpture netizens.

Among them, the one with the highest likes is like this.

"Professor Pang, can you take a picture of the Fields Medal medal and send it to us to see?"

"Haha, I watched the live broadcast of the award ceremony throughout the whole process, and I almost thought that Professor Pang's Fields Medal was cold. Fortunately, I insisted on watching, Professor Pang was awesome......"

"Professor Pang's acceptance speech is quite interesting, but unfortunately I didn't understand a word about the academic part."

"I don't know if you have noticed, at the beginning, Robert Langlands announced the list of winners, there was no name of Professor Pang Xuelin, and the entire conference hall was almost blown up, so you can imagine how high Professor Pang Xuelin's recognition is in the international mathematical community."

……

Pang Xuelin probably flipped through the comments on Weibo, thought about it, and then got up and found his Fields Special Gold Medal, took a photo on the front and back, and posted it on Weibo.

Then, Pang Xuelin ignored his personal Weibo, which had been completely boiling, and began to prepare for the report meeting in an hour.

If it were an ordinary person, the preparation time of such an ultra-high-level mathematics report would be as short as ten days and half a month, and as long as several months.

It's just that after the system transformation, Pang Xuelin's memory, thinking ability and neural reaction speed have been greatly improved.

Therefore, he does not need to make such meticulous preparations, he only needs to make an outline of what he wants to talk about.

An hour later, at 1:40 p.m., Pang Xuelin came out of the room and went to the venue of the report meeting.

By the time Pang Xuelin arrived, the entire lecture hall was packed with mathematicians from all over the world.

In the warm applause at the scene, Pang Xuelin walked on stage, and everyone focused on him.

Looking at the crowd in the audience, Pang Xuelin said: "Hello everyone! One hundred and twenty-two years ago, the German mathematician David Hilbert gave a famous speech at the International Congress of Mathematicians in Paris, in which he proposed Hilbert's 23 questions, which guided the development of mathematics throughout the 20th century, and some problems have not yet been solved, such as the famous Riemann conjecture, which have become the focus of our exhaustive attention. History teaches us that the development of science has continuity, and that every era has its own problems. These questions will provide a whole new direction for those who come after them. More than 100 years later, I think it's time for a formal review of some of the issues we face. The end of a great era not only prompts us to look back to the past, but also to adapt our minds to the unknown future. ”

"In mathematics, it's often more important to ask questions than to solve them. We are now faced with the question, what is the source of the problem in the discipline of mathematics? Of those branches of mathematics, the original oldest problems, which must have originated in experience, were put forward by the analysis of external phenomena, and it was in this way that the rules of integer arithmetic were discovered in the early days of human civilization. Just as today's children learn and do things empirically, the same is true of the first geometric problems, such as the two-fold cube problem, the circle squared problem, and so on. The same goes for the solutions of numerical equations, the calculus of curve theory, the Fourier series and the original problems of Wechsler theory, not to mention a large number of problems in chemistry, physics, astronomy, biology, etc. ”

"However, with the further development and refinement of the branches of mathematics. We began to come into contact with logical combinations, generalizations, specializations, and other methods, skillfully analyzing and synthesizing concepts, and asking fruitful questions. This gives rise to the problem of prime numbers, the problem of efficient solution of polynomial equations, the solution of discrete logarithms, the existence of one-way functions, and so on. ”

"As to the general requirements for the solution of a mathematical problem, I think it is first necessary for us to be able to prove the correctness of the problem by reasoning in finite steps based on finite premises, which are contained in the statement of the problem, and that there must be a precise definition of each problem. This requirement for logical deduction with the help of finite reasoning is, simply put, the requirement for the rigor of the proof process, which has become known in mathematics like a motto. On the other hand, it is only when such requirements are met that the ideological content of the question and its rich meaning can be fully reflected. A new problem, especially when it comes from the external world of experience, is like a young sapling, which only needs to be carefully transplanted to the existing old trunk according to the strict rules of horticulture, and it will grow vigorously and bear fruit. ”

"Therefore, today I will talk about some of the problems we will face in the development of mathematics with my shallow knowledge."

Pang Xuelin's words fell, and a buzzing sound couldn't help but sound at the scene.

Almost everyone looked at Pang Xuelin in shock.

No one expected Pang Xuelin to make such a speech at this report meeting.

Is he trying to emulate David Hilbert more than 100 years ago and point the way for the future development of mathematics?

There was a buzzing sound at the scene.

There was excitement on everyone's faces.

No one thinks that Pang Xuelin does not have this qualification.

In fact, although mathematics has advanced to the present day, the various branches are being refined step by step.

However, almost all advances in the field of mathematics are accompanied by the formulation and solution of problems.

From David Hilbert's 23 questions more than 100 years ago, to Robert Langlands's program more than 60 years ago, to the Clay Institute of Mathematics in the United States more than 20 years ago to put forward the seven conjectures of the millennium.

Each problem solution points out the direction for the development of mathematics and provides a new impetus.

Especially in recent years, with the emergence and rapid development of Ponzi geometric theory, BSD conjecture, ABC conjecture, Polygnac conjecture, Hodge conjecture and so on have been solved one after another, and the mathematical community needs a leader to stand up and point out the direction for future development.

As the creator of Ponzi geometry theory, Pang Xuelin is undoubtedly a suitable candidate.

Offstage.

Deligne said to Faltins, who was sitting beside him, "Faltins, I have a hunch. ”

"What hunch?"

"This young man may be far more successful than my teacher in the future,"

Faltins couldn't help but be taken aback.

Although the current mathematical community highly praises Pang Xuelin, they basically regard him as an equal to Grothendieck in the last century.

Even in Faltins' eyes, Pang Xuelin was a young version of Grothendieck.

"Pierre, why do you say that?"

Faltins wondered.

Deligne turned his head to look at Faltins and smiled: "I see enthusiasm and ambition in his eyes, he is only twenty-five years old now, at least twenty years old, can you imagine how much he can achieve in twenty years?" Even if he completely unified the two basic disciplines of algebra and geometry, it didn't surprise me. ”

Pang Xuelin ignored the noise from the audience, smiled slightly, and said: "I think that in the next 100 years, the following problems will be some of the problems that our mathematical community needs to solve urgently. First, the main conjecture of Iwasawa's theory. ”

In number theory, Iwasawa theory is the Galois modulus theory of ideal groups, which is a set of theories developed by Japanese mathematician Kenkichi Iwasawa in the late 1950s to study the arithmetic properties of Zp expansion in the number field (i.e., the finite expansion of Q), and the most common Zp expansion is the so-called circular Zp expansion. This type of domain was first studied by the German mathematician Kummer in order to prove Fermat's theorem. In fact, if the integer loop Z[C"] were the only decomposed ring, there would not have been so many difficulties in proving Fermat's theorem.

Circular Zp expansion is the expansion of the following circular domain:

K=Q(CP)C… CKn=Q(C； +1)••CXoo=Q(CP~)，

where the Galois group Gn of KJK is the projective limit of the cyclic group to any aZ/pnZ, aa(CP)=CpV is theorized by Galois, and the Galois group G of K/K is the projective limit of G", that is, p into the integer ring Zp.

……

The Iwasawa master conjecture (or master conjecture, i.e., the main conjecture of Iwasawa's theory) is to say: ch(A) = ch(s/C). It can be seen that A illustrates the ideal group of the number field, which is a purely algebraic object. Whereas, a rounding unit is essentially an analytical object. In fact, let ((P,s)=C(s).( 1-p~s) = ∑1/n^s, this function is called the V to C function, it is a continuous function, and its value at negative integers can be represented by the interpolation of a first polynomial.

The P-in-in function is an example of the P-in-I function, which embodies the analytic properties of the corresponding number field.

The work of Coates-Wiles and Coleman in the apparent reciprocal law shows that the above polynomial and ch(f/c) differ only by one fixed polynomial. So we know that the main conjecture is a conjecture about the deep connection between the algebraic properties and the analytic properties of the circular field.

Iwasawa Theory has been an important tool for the study of number theory since its inception. In 1972, Mazur established the Iwasawa theory of elliptic curves and proposed the master conjecture on imaginary quadratic domains. Later, many other forms of master conjecture were proposed, including the master conjecture on Motive. The study of Iwasawa theory on the p-in-Galois representation is very important for the p-in-BSD conjecture and the Serre conjecture.

In 1983, Mazur and Wiles proved the Iwasawa Lord conjecture using profound algebraic geometry. Using Kolivarkin's Euler system, Rubin proves the master conjecture on the imaginary quadratic domain and gives a new proof of the master conjecture in the circle domain.

Other forms of master conjecture are still hot topics in the study of number theory and arithmetic algebraic geometry. ”

……

"THE SECOND QUESTION, HOPF'S CONJECTURE."

"One of the core problems of global differential geometry is the study of the relationship between local and global invariants, the relationship between curvature and topology.

Let's look at the surface S, which has a measure on it, and also the Gauss curvature K, if the surface is compact and boundless, the Gauss curvature K can be integrated on the entire surface. A surface does not necessarily have only one measure, but can have another measure, after changing the measure, the corresponding Gauss curvature K will also change, but the integral value has nothing to do with the measurement of the surface, but only related to the Euler infraction x(*5) of the surface.

This is the profound meaning of the Gauss-Bonnet formula.

For the high-dimensional Riemannian manifold M, the Gauss curvature can be generalized as the cross-sectional curvature, which is determined by the Riemannian curvature tensor, and the integrand is a very complex algebraic formula composed of the curvature tensor, called the Gauss-Bonnet integrand, which is integral to the entire manifold and should be determined by the Euler schematic number of the manifold. Its connotation proved to be obtained by Chern, which was later called the Gauss_Bonnet-Chen formula.

For a compact and boundless even-dimensional manifold M2", if it accommodates a Riemann metric of the curvature of a non-regular section, then its Euler indicative number satisfies

(-l)nX(M2n)0(1) (when the cross-section curvature is negative, the above equation is a strict inequality).

This is known as the Hopf conjecture.

So far, the Hopf conjecture has only been tested under some additional conditions, such as the cross-sectional curvature sandwiched between two negative constants: Bourguignon-KarcherPl, Donnelly-Xavier, and Jost-Xin.

Borel confirms the conjecture for non-compact rank-1 symmetric spaces.

If the manifold has a KShler metric, the conjecture has been confirmed by Gromov in the case of curvature of a negative section and by Jost-Zuc and Cao-Xavier in the case of curvature of a non-positive section. ”

……

"The third question, Kaplansky's sixth conjecture."

Kaplansky's sixth conjecture is one of the ten conjectures about Hopff's algebra proposed by Kaplansky in 1975, and it is also one of the cutting-edge problems in the field of Hopf's algebra and even algebra. Hopff algebra originated in the forties of the twentieth century, and is mainly an algebraic system established by Hopf's axiomatic study of the topological properties of Lie groups.

In the sixties of the twentieth century, Hochschild-Momostow developed and enriched Hopf's theory of this algebraic system and laid the basic framework of Hopf's algebraic theory in the application of Lie group and subsequent research.

In the eighties of the twentieth century, with the rise of the quantum group theory established by mathematicians such as Drinfeld and Jimbo, it was discovered that quantum groups were a special class of Hopf algebras. Quantum group theory is closely related to many other fields of mathematics, such as low-dimensional topology, representation theory and noncommutative geometry, as well as the theory of exact solvable models of statistical mechanics, two-dimensional conformal field theory, and quantum theory of angular momentum.

The rise of quantum group theory has also promoted the rapid development of Hopf's algebra theory, and many wonderful research results have been achieved around Kapplansky's ten conjectures, which have led to the solution or partial solution of some of these conjectures.

Kaplansky's sixth conjecture assumes that H is a finite-dimensional semi-mono Hopf algebra on an algebraic closed field, then the dimension of any irreducible representation of H is divisible by the dimension of H.

This conjecture is closely related to the classification of finite-dimensional semi-mono Hopf algebras, which has attracted the interest of many algebraists.

In 1993, Zhu used the feature label theory to study Kaplansky's sixth and eighth conjectures, and obtained partial results.

He proved that if char(4)=0, H is semi-singular and R(H) is in the center of the dual algebra of H, where R(H) is the child algebra of JI* formed by the irreducible characteristic of H, then Kaplan's sixth conjecture holds.

Nichols and Richmond (1996) demonstrated that if H is congruent and has a 2-dimensional single comodus, then H is even-dimensional.

In 1998, Etingof and Gelaki demonstrated that W: if ugly is a semi-monolithic Hopf algebra and D{H) is a Drinfelddouble of H, then the irreducible dimension of D(H) is divisible by the dimension of H.

From this they show that if H is a semi-monolithic semi-monolithic Hopf algebra of pseudo-trigonograms, then the irreducible dimension of H is divisible. ”