"Next, I would like to invite Mr. Junxin from China Shuimu University to give a keynote speech on this conference, everyone is welcome!"

After a round of warm applause, Junxin stood on the podium, unfolded his script, looked below and began to speak:

"Hello colleagues, ladies and gentlemen. I am very grateful to all my colleagues in the Academic Committee of the International Union of Crystallography for their support to me, to be honest, I still can't believe that you really dare to use me, a little-known hairy boy, to do such a big thing, for which I feel very honored and very frightened. ”

"Okay, without further ado, let's get down to business. Because I am a professional mathematician, and most of my research focuses on mathematics, the topic of my speech today is called mathematics and quasicrystals. ”

"Quasicrystals are, in my opinion, a joke of nature. In the 19th century, the study of crystals led to a complete enumeration of the species of discrete symmetric groups that could exist in Euclidean space. It has been shown that in three-dimensional Euclidean space, all discrete symmetry groups contain only 3, 4, or 6 rotations. After that, mathematician Roger? Penrose discovered the flat "Penrose brickwork method". The quasicrystalline array is a three-dimensional simulation of the two-dimensional Penrose brick patchwork method.

However, while nature has played a joke on chemical crystallography, it has also played a joke on mathematics, that is, the similarity of the behavior of quasicrystals and Riemann ζ function zeros. Mathematicians are fascinated by ζ zero point of the Riemann function because all the zero points fall in a straight line, and no one knows why. The well-known Riemann conjecture states that, with the exception of the mundane, the zero points of the Riemann ζ function are all in a straight line. For more than 100 years, proving the Riemann hypothesis has been a dream of young mathematicians. I am now bold in proposing: perhaps Riemannchai can be proved with pseudocrystals. Maybe it's a bit boring for mathematicians (including myself). However, I put this question before you and hope that you will think about it seriously. Physicist Leo as a young man? Dissatisfied with Moses' Ten Commandments, Zirat wrote a new Ten Commandments to replace them. Zirat's second commandment says: "Move and move towards worthy goals, regardless of whether they can be attained: action is a model and an example, not an end." Zirat put his theory into practice. He was the first physicist to imagine nuclear weapons and the first physicist to actively oppose their use. His second commandment applies here as well. The Dawn Conjecture proves to be a worthy goal, and we should not ask whether this goal can be achieved. I'm going to give you some hints that this goal can be achieved.

Until recently, there were two unsolved superproblems in the field of pure mathematics: the proof of Fermat's great theorem and the proof of the Riemann conjecture. The proof of Fermat's theorem is not only a technical feat, but also requires the discovery and exploration of new areas of mathematical thought, which is broader and more important than Fermat's theorem itself. Because of this, the proof of the Riemann conjecture will also lead to a deep understanding of many different fields of mathematics and even physics. Riemann ζ functions are similar to other ζ functions, which are ubiquitous in number theory, dynamical systems, geometry, function theory, and physics. ζ function is like a cross-junction point that leads to the paths of the parties. The proof of the Riemann conjecture will elucidate all these associations. Just like every serious student in the field of pure mathematics. I had some vague ideas about proving the Riemann hypothesis, and after the quasicrystals were discovered, my thoughts were no longer vague. I think it may be possible to prove the Riemann hypothesis by studying the alignment of crystals. On the other hand, a better understanding of the structure of quasicrystals may be used to prove the Riemann hypothesis. ”

"Not long ago, the Honorable Professor Watney proposed to modify the current crystal structure, and when asked for my opinion, in the spirit of a mathematician, I defined quasicrystals as follows: a quasicrystal is a distribution of discrete point groups, and their Fourier transform is the discrete point frequency. Or simply put, a quasicrystal is a pure point distribution with a spectrum of pure spots. This definition includes the exception of ordinary crystals, which are periodic distributions with periodic spectra. ”

"But obviously, as a mathematical definition, this was not adopted because Professor Watney told me that we can't tell the general public or senior students and college students in such complex language what quasicrystals are."

"A rough classification of alignment crystals, then according to the dimensional criterion, it is obvious that the simplest is the high-dimensional three-dimensional quasicrystals, because they are all deformations of the regular icosahedron; Roughly speaking, a unique type is associated with each regular polygon on a plane. The most complex is the one-dimensional quasicrystal, which is why I think it's related to the Riemannian function. ”

"If the Riemann conjecture is correct, then by definition, the zero point of the ζ function forms a one-dimensional pseudocrystal. They form a distribution of pointmasses in a straight line, and their Fourier variations are also a distribution of point masses, with the former having a point mass at the logarithm of each prime and the Fourier transform point mass at the logarithm of the power of each prime. ”

"Suppose we don't know if the Riemann conjecture is correct. Let's approach the problem from a different angle. We strive to obtain a full survey and classification of one-dimensional pseudocrystals. That is, we enumerate and classify all the point distributions that have a discrete point spectrum. Then, we discover the well-known quasicrystals related to the PV number, as well as other known and unknown pseudocrystalline worlds. Among the many other pseudocrystals, we look for a quasi-crystal that corresponds to the Riemann ζ function, and a pseudo-crystal that corresponds to each ζ function of other Riemannian ζ functions. Suppose we find a pseudocrystalline in the list of pseudocrystals with properties equivalent to the zero point of the Riemann ζ function. Then we proved the Riemann conjecture. ”

"Then, we defined all the quasicrystals and solved one of the most mathematically difficult problems to solve. Although, it may seem like just a delusion. Because defining the exact morphology of a one-dimensional quasi-crystal is no less difficult than solving a Fermat's theorem, if you want to find all one-dimensional quasicrystals, you need to do a good job of solving a problem that is no less difficult than solving Fermat's theorem. All in all, perhaps another distant problem. ”

"Is the relationship between mathematics and quasicrystals more than a matter of the Riemann conjecture? As for how much it has to do with mathematics, I'll briefly explain some of the connections between the two. ”

“…………”