# Love for Equations Throughout Life

On December 17 in Tashkent, the Republican scientific conference on “Actual problems of differential equations and their applications” will begin at the Mirzo Ulugbek National University of Uzbekistan. The foreign scientists will take part in the event.

Our correspondent met with one of its organizers, the famous scientist, Doctor of Physical and Mathematical Sciences, Professor Bozor Islomov, and asked him to tell about the goals and tasks of this forum.

- The purpose of the scientific conference is to discuss the current state and prospects for the development of the main directions of the theory of partial differential equations and mathematical physics and its applications. The scientific program of the conference covers such areas as partial differential equations, mathematical physics, dynamical systems, function theory and functional analysis, mathematical modeling, and computational methods. - To what extent this forum is representative?

- Every year scientists of the CIS and other foreign countries take part in these conferences held in our republic. This year it will be attended by about 50 mathematicians from Russia, Kazakhstan, Tajikistan and Kyrgyzstan, as well as more than 140 scientists from our country.

- What can you say about the contribution of Uzbek scientists and mathematicians to the development of this science?

- Today, every educated person knows the name of Muhammad al-Khorezmi, immortalized in the term “algorithm”, and founded by him algebra. Before him, mathematics meant basically geometry with a certain dose of number theory.

The work of the scientist “The Short Book of Replenishment and Contradiction”, along with Euclid’s book “The Beginning” laid the foundation for the modern mathematics. It was rewritten many times in the original language and translated into Latin, as a result its name being reduced to the word “aljabra” “algebra”.

In his book Al-Khorezmi focused on two operations – “aljabr” and “almukabala”, which, unlike arithmetic, allow performing four arithmetic operations on expressions containing an unknown. That was really a great idea.

This is not coincidence, that I did an excursion into history. It is astonishing how Muhammad al-Khorezmi was perspicacious when he called of his treatise not the concept of the equation, namely the title of a pair of operations! In the future, more and more new types of algebras were introduced. It is pleasant to note that one of them - the topological Boolean algebras, that was developed by Uzbek mathematicians under Academician Tashmuhamed Sarymsakov in Tashkent. The monograph, written by him together with his colleagues, was republished in the USA in English translation, and then it was awarded the Abu Rayhan Beruni State Prize. And at present this whole direction of mathematics is intensively developing within the framework of the scientific school.

An important role in the cognition of nature plays the symmetry property, which is reflected in mathematical models. To express the most general concept of the symmetry of geometric objects, the Norwegian scientist Sophus Lee introduced the notion of a continuous group. Such objects turned out to be very difficult to investigate existing means at that time. Then the mathematicians turned to an idea on attracting a special algebra that is quite similar to Muhammad al-Khorezmi’s views. Thus, the notion of Lie algebra appeared. Later, other similar algebras were discovered, which made it necessary to study them in the most general form. At present, this task is being successfully developed by Uzbek mathematicians.

- Bozor Islamovich, and how did you come to mathematics?

“I was still raving about it at school, I could not fall asleep, if I couldn’t do a sum or an equation. And from the beginning of the student’s bench, I joined the research work. After listening to the special courses of Academician M. Salakhiddinov, I became interested in differential equations and equations of mathematical physics. Since 1979 I have been conducting scientific research related to the solution of boundary-value sums of a new type.

In 1981, a new stage of my scientific activity in the Institute of Mathematics of the Academy of Sciences of the Republic began. By that time I ‘was fond of and worked with great enthusiasm in a new direction- the study of boundary sums for partial differential equations of mixed type with two lines and different orders of degeneracy. This was the content of my candidate dissertation thesis, which I defended in 1986.

In 2000 I defended Ph.D. thesis on the topic “To the theory of a mixed-type equation with two lines and planes of degeneracy”, and in 2006 I was appointed professor.

- And can you translate somehow the title of the doctoral dissertation into a popular language?

- Yes I can, but it is not easy, it will take a long time. - Have you carried the love to the equations throughout your life?

“It’s love for science, love for mathematics”. I am always inspired by our great ancestors, who made an invaluable contribution to the development of science and world civilization. - How many researches did you publish?

- I did not specifically consider it, but not less than 170 - a monograph, teaching aids, scientific articles in national and international editions. - What does give you the greatest joy in your work now?

- First of all, these are my students, young mathematicians of our country. Among them there are many candidates of physical and mathematical sciences who work on doctoral and PhD theses. I am endlessly heartened by their work, enthusiasm, desire to make their contribution to science and to leave their mark. And I try to give them my experience and knowledge.