The current forum is part of a series of conferences organized in 2011 by Alexey Karapetyants, Director of the Regional Scientific and Educational Center of the Southern Federal University (Rostov-on-Don), Doctor of Physical and Mathematical Sciences, Professor. This year, such a conference is being held in Yerevan for the second time, since in the current difficult geopolitical conditions, the capital of Armenia is the neutral platform where scientists from different countries can meet. However, these conferences are organized not only in Armenia, the largest of them is held at the Southern Federal University.

Harmonic analysis is a branch of mathematical analysis that studies the properties of functions and other objects, representing them in some basic systems. Objects represented as waves are widely used for recording, encryption, and encoding and can be applied to specific developments. This is the basis of communication - transmission of video images, audio information, etc.

The importance of the conference is not limited to listening to reports and getting acquainted with the research results of colleagues. This is a great opportunity for a lively discussion of new ideas, an exchange of opinions and the establishment of scientific contacts - the implementation of joint projects, writing books, etc. According to tradition, workshops with a fairly limited number of participants interested in a particular problem are also held within the framework of these conferences. This is an opportunity to listen to lectures by reputable scientists and acquire new knowledge.  Such meetings are also used to support and promote scientific publications, some of the conference participants are associate editors of these journals. Issues related to publication activity, the problem of plagiarism, which is relevant all over the world, etc. are discussed.

 We asked some of the conference participants to share their impressions about the forum, the problems of modern science and plans for the future.

HELMUT MALONEK, Professor at the University of Aveiro (Portugal):

- I am German by origin, I was born and graduated from school in the GDR, then I was sent to study in the USSR under the student exchange program, graduated from the Mechanics and Mathematics Faculty of Yerevan State University and have been living and working in Portugal for many years. I know Armenia well, my student years were spent here, which I always remember with great warmth. At first, many things seemed unusual to me here, but I got to know this country, its nature, people with interest, I liked Armenia, I made many friends here, with whom I still maintain good relations. It was the time of the dawn of Armenian science. The level of training was high. I was taught by such famous mathematicians as Artashes Shaginyan and Mkhitar Jrbashyan.  I studied in the Russian-speaking sector, but Professor Jrbashian gave lectures on the theory of functions in Armenian. Russian was his book, which I studied and had no problems, and Professor Shaginyan knew German, so when I did not understand something in Russian, he explained it to me in German. In my third year, I was even offered to learn the Armenian language and study Armenian studies, but I decided to remain a mathematician. And here, in the journal of the Armenian Academy of Sciences, I published my first scientific article.

But I am glad to participate in the conference not only because it is taking place in Armenia. For me, as well as other participants, this is a great opportunity to get acquainted with the achievements of colleagues, exchange ideas, and establish contacts. Live communication between scientists is necessary, it gives excellent results. 

I know that Armenian science is going through a difficult period today, but the level of mathematics remains high. I cannot say how things are with other sciences, but I am always glad to come to Armenia. This is my second time here this year, and I hope to come here next year. Now many Armenian scientists are working in other countries, but I think they will return to their homeland and contribute to the development of science in your country. In general, it is not only Armenian science that is experiencing difficulties. Attitudes towards basic research have changed all over the world. Everyone wants to get a practical result quickly, but we must not forget that it is impossible to develop applied science without fundamental research.  And what is also very important - it is impossible to evaluate the effectiveness of a scientist by the number of publications.

Science is a special field that is disgusted by the haste and tension associated with the need to publish another article within a certain time frame. And new technologies are developing rapidly in all cases, today technical and technological development is taking place much faster than throughout the entire previous history of mankind. But you need to read a lot, think calmly and control the development of artificial intelligence. Whether he poses a threat to humanity is difficult to say. So far, artificial intelligence is not creative, it does not exceed human capabilities, however, it is possible that the time will come when it will be necessary to slow down technological progress, although this will certainly be a difficult task. 

The hero of one popular science story expressed a desire to be frozen for a hundred years with the expectation that he would be brought back to life when humanity made significant progress in its development. But he was woken up well ahead of schedule to give advice on how to stop progress. He advised to create funds and develop science within the framework of projects, which is associated with a lot of formalities, delays, and bias. This is what is happening in the world of science today, so unexpected manifestations of artificial intelligence do not pose a threat to humanity yet.

ILYA LIFLYAND, Professor at Bar-Ilan University (Israel):

- We met with the organizer of the conference, Professor Alexey Karapetyants, in 2005. Our rapprochement was also facilitated by the fact that I was acquainted with his father, the mathematician Nikolai Karapetyants, and his supervisor, Professor Samko. We are both engaged in harmonic analysis, and we managed to find those points of contact on which cooperation is possible. Now we are planning to write a book together. Alexey Karapetyants actively maintains contacts with both Armenian colleagues and scientists from other countries. I'm involved in some of these collaborations. At one time, one of my articles aroused interest in one of the directions in mathematics (Hausdorff operators), which is successfully developing today. It turned out that this is an opportunity to set and solve many different tasks, and therefore expand the boundaries of cooperation.  I managed to organize sections in this area three times within the framework of the conference "Operator Theory and Harmonic Analysis", which aroused the interest of many participants.

Last year I met with the director of the Institute of Mathematics, Professor Rafik Aramyan, and at the current conference I was interested in his report, and now we are planning cooperation. Live meetings of scientists are indispensable, they contribute to the establishment of new contacts, and therefore to the development of science. And Alexey Karapetyants understands this perfectly well - not only an excellent scientist, but also a very active person endowed with inexhaustible energy, who will always be able to organize a conference perfectly. It is not the first time that these forums have been held in Yerevan, it is a very correct decision. Armenia is one of the few places in the world where all the conditions for successful meetings of scientists, which have already become traditional, coincide. There is an atmosphere conducive to productive and pleasant communication, and the level of mathematics has been and remains high.  And if earlier these meetings began with acquaintance, now they begin with hugs, since most of the participants are well acquainted and have already become friends.

I also want to draw attention to one curious fact. Mathematics is not just an extremely interesting field of activity, it is somewhat close to writing detective novels. It's just that the symbols and the language are different. For example, in Michael Crichton's famous science fiction novel "Jurassic Park" there is a piece related to programming. And Arturo Perez-Reverte's detective novel "The Flemish Board" is tied to chess.

I would like to wish our Armenian colleagues success. There is scientific potential, but it is not being realized enough. We need to set ourselves serious tasks and fulfill them, publish more in reputable journals. It's real. You should not lower the bar of possibilities yourself.

Source: https://www.golosarmenii.am/article/208064/vstretilis-matematiki