National Institute of the Republic of Serbia

MILOŠ RADOJČIĆ

(1903 - 1975)

(1903 - 1975)

Miloš Radojčić is one of the most important Serbian mathematicians that were born in the first ten years of the 20th century. He was the first and only one to be distinguished from the famous mathematical authority, Mihaila Petrovića, having chosen one of the most difficult research topics in science. At the Department of mathematics of the University of Belgrade, he introduced three new courses and was the author of two books of the highest rang. Also, he was the first one to teach with highest mathematical precision, showing his students the true nature of mathematics. He wrote a book *General mathematics* with which he brought to focus the importance of the history of mathematics for the development of the mathematical thought. His contribution to that essential science was evident. He performed the role of a university professor with extreme dedication and conscientiousness.

Miloš was an intellectual person with a wide range of interests, broad culture, and creativity in many areas: philosophy, poetry, literature, drama and painting, the study of the Serbian folk literature, Njegoša and fresco painting, the study of exceptional characters from European poetry and philosophy. He was even interested in great world religions, Christianity and buddism. He was one of the greatest Serbian intellectuals at the first half of the 20th century.

He spent his life working as a professor at the Belgrade university until 1959, then he was a professor at the university of Kartum in Sudan until 1964, and finally he worked as an associate of the National center for scientific research in Paris (Centre national de la recherche scientifique). He was a corresponding member of the Serbian academy of science. While he was in Serbia he gave a major contribution to the development of the Department of theoretical mathematics at the Belgrade university. His teaching was conducted at the level of the highest mathematical precision. He cultivated the pureness and regularity of the Serbian language and he wrote with a style that could be considered exemplary.

He introduced the following subjects into the teaching of mathematics at the Belgrade university: synthetic geometry (Euclidean geometry and the geometry of Lobachevsky) and descriptive geometry. The scientific work of Miloš Radojčić went into two mathematical areas: the theory of analytic complex functions and the theory of relativity. The topic of his work in the first of these two areas is the multiform analytic functions and their Riemann's surfaces.

In the theory of analytic functions Radojčić proved that every analytic function (in whichever area of the Riemann's surface) can be approxFimated with algebric functions. Also, he generalized the famous statements of Weiersstras and Runge about the representation of analytic functions with polinomes and rational functions to the full extent. At the same time he generalized the famous Kosi integral formula, adapting it to domains on Riemann's surfaces. In the geometric theory of analytic functions he gave a general method for the splitting of whichever Riemann's surface into simple parts, wherever such splitting is possible, as the case is with the unlimited Riemann's surfaces. It gave him a basis for further work in general automorphic functions, as it did for the Japanese mathematician Shimizu (an example of that would be Radojčić's result that every meromorphic function is somewhat automorphic). Also, Radojčić studied the topologic properties of analytic functions in the proximity of essential singularities, including the problem of the type of Riemann's surfaces: a problem that was considered by a number of important mathematicians at the time.

Miloš Radojčić applied the geometric method of proving whenever he could. That is especially reflected with the problem of splitting of the unlimited Riemann's surface into simple parts. According to the competent opinion of the German mathematician E. Ulrich, Radojčić achieved the best results with that method. Radojčić also proved himself to be an excellent university professor: he had the intention to be the author of a book for every subject he used to teach. In such a way he created three exceptional books: two books for the students of mathematics and the history of anthic mathematics for the students of philosophy. He was a person whose moral virtues can be used as a model.

In the second area of his mathematical study, Miloš Radojčić worked on the axiomatic foundation of the special theory of relativity. However, he also had ideas about the way the general theory of relativity can be founded axiomatically. The summary of his finished work in this area can be found in the monography *Une construction axiomatique de la Theory de l'espace-temps de la Relativite restreinte*, Monographic t. CDLXII, Acad. Serb des Sc et des Arts, 1973. His approach to this problem is based on the principles of axiomatic foundation only known to Radojčić, which is essentially different from the approach of other scientists who were concerned with the foundation of the theory of relativity (for example S. Basri [B], A. Lihnerovich [Li] and P. J. Pimenov [P],

In the axiomatic foundation of the theory of relativity M. Radojčić did not include any completed structures, considering *it justified that the topic of a very fundamental and elementary importance such as the cinematics of the Theory of relativity, which includes the very basic Euclidean geometry, deserves an independent and, in the modern way, an elementary approach.* His principle is: the less assumptions, the more proving. Similarly, he disaggrees with the derivation that is analogous to the derivation of some known and appreciated constructions (such as [Rb]). His ideas in the choice of axioms was led by the tendency of the axioms to be, in their physical interpretation, as close to the observable facts as possible, or at least if the existence of the axioms could be imagined.