# Blagoj Sazdov Popov

### Born: 17 January 1923 in Kochani, Serbia (now Northern Macedonia)

Died: 30 October 2014 in Skopje, Macedonia

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**Blagoj Popov**attended secondary school in Šhtip, which is about 25 km south west of Kochani. He graduated from the high school in Šhtip in 1940 and he went to Belgrade where he entered the Technical Department of the Electro-Engineering Division of the University to begin his study of mathematics. In April 1941, however, German troops invaded Yugoslavia and occupied the whole country. The University of Belgrade was closed so Popov, together with other Macedonian mathematics students who had been studying in Belgrade, went to Bulgaria where they entered the Department of Physics and Mathematics in Sofia University in 1942. By 1944 Macedonian military units were forming and becoming part of the People's Liberation Army of Macedonia. Popov left his studies in Belgrade and joined the new Macedonian army where he continued to serve until he was demobbed at the end of World War II. In November 1945 he returned to his studies in Belgrade where the university had been reopened by the new Communist government and he now studied as part of the Mathematics Group in the Philosophical Faculty. The University, having been a centre for democratic ideas between the two world wars, was put under strict political controls. Popov graduated from the University of Belgrade in June 1946. In 1946 and 1947, he continued studying in the Electro-technical Faculty in Belgrade.

In January 1948, Popov moved to the new Faculty of Philosophy in Skopje, as an assistant in mathematics. The University of Skopje was opened November 1946 with one faculty, namely the Faculty of Philosophy which consisted of two departments, the Department of History and Philology and the Department of Mathematics. Popov, at this stage, only had a first degree in mathematics from Belgrade so, in addition to his appointment as an assistant in the Department of Mathematics, he was also a Ph.D. student. His advisor was Dragoslav S Mitrinovič who had founded the Department of Mathematics in the University of Skopje. Let us say a little about Mitrinovič.

Dragoslav S Mitrinovič (1908-1995) was a Serbian who graduated with a Ph.D. from the University of Belgrade in 1933. His thesis was on differential equations. He worked as a secondary school teacher for over 10 years before going to Paris in 1946 He founded the Department of Mathematics at the newly created University of Skopje in 1946 and worked there until 1951 when he returned to the University of Belgrade [4]:-

It is clear that Popov was fortunate both in having Mitrinovič as his Ph.D. advisor and also in arriving at a new department which was put so rapidly on a firm footing by Mitrinovič. In 1949, after one year as an assistant, Popov was promoted to lecturer. Although he still had not submitted material for a doctoral thesis, Popov began publishing high quality papers in several languages. Those published in 1949-51 included:Mitrinovič started his university career in Skopje, Macedonia, as an Associate Professor at the Philosophical Faculty. It took him only five years(1946-1951)to found the Skopje School of Mathematics, including two mathematical journals. His persistent work[in Skopje]resulted in the foundation of a rich professional mathematical library there and in a wide exchange of scientific publications with foreign countries. Thanks to his scientific contribution he was elected a member of the Macedonian Academy of Sciences and Arts.

*Sur la condition d'intégrabilité de Karamata de l'équation de la balistique extérieure*Ⓣ (Serbian) (1949);

*Contribution à la géométrie du triangle*Ⓣ (Macedonian) (1949);

*Sur une condition d'intégrabilité de d'Alembert relative à l'équation différentielle de la balistique*Ⓣ (Macedonian) (1950);

*Sur une équation algébrique proposée par Pitoiset*Ⓣ (1951);

*Sur une équation algébrique*Ⓣ (Macedonian) (1951);

*On a property of the derivatives of orthogonal polynomials*(1951);

*Factorization of an operator*(Macedonian) (1951); and

*Remarque sur l'équation de Riccati*Ⓣ (Macedonian) (1951). In 1952 he submitted his thesis

*Formation des critériums de réductibilité des équations différentielles linéaires ayant des formes données à l'avance*Ⓣ (Macedonian) and he was awarded the degree in 1953. His 68-page thesis was published by the Faculty of Philosophy of the University of Skopje in a 1952 publication which, however, only appeared in print in 1954.

When Dragoslav Mitrinovič left the University of Skopje in 1951, Popov became head of the Department of Mathematics. Promoted to Assistant Professor in 1953 after the award of his doctorate, and then to associate professor in 1958, he became a full professor in 1963. He was dean of the Faculty of Natural Sciences and Mathematics in Skopje from 1958 to 1963 and again from 1985 to 1987, and Dean of the Faculty of Mathematics from 1976 to 1978. From 1967 to 1969 he was rector of the University of Skopje.

Popov was a member of the Macedonian Academy of Sciences and Arts since its formation, being one of the fourteen members elected on 18 August 1967 in the National Museum of Ohrid. In fact he was the only mathematician among these fourteen founding members. From 1976 to 1979 he was secretary of the Academy, from 1980 to 1983 he was vice president, and from 1985 to 1991 he was secretary of the Academy's Department of Natural and Mathematical and Technical Sciences.

Several research visits abroad by Popov should be mentioned. In 1955-1956 he visited Paris and in 1963-1964 he visited Hamburg. In the summer of 1970 he visited West Virginia University in Morgantown in the United States and a report of this visit appeared in the

*Raleigh Register*which we present [5]:-

Popov retired in 1987 at the age of sixty-four. The mathematical conference "85 Years of Professor Blagoj Popov's Life", held in his honour, was organized by the Institute of Mathematics and Institute of Informatics of the Faculty of Natural Sciences and Mathematics of Saints Cyril and Methodius University of Skopje, Republic of Macedonia. The conference took place 4-7 September 2008, at Saints Cyril and Methodius University Congress Centre, Ohrid, on the shores of the Ohrid lake. There were about 60 participants from Macedonia and countries such as Austria, Bulgaria, Croatia, France, Netherlands, Romania, Serbia, Turkey, and the United States. Virginia Kiryakova writes in a publication arising from this conference about Popov's importance to Macedonian mathematics [3]:-Dr Blagoj S Popov, head of the department of Mathematics at the University of Skopje in Yugoslavia, is visiting West Virginia University this summer. His visit is being sponsored by the American Academy of Arts and Sciences and the Yugoslav Council of Academies under an exchange program between the two countries. During his visit, which will end July20, Dr Popov will do research on special mathematical functions. "At the moment I am interested in the problem of linearization of the product of orthogonal functions and the summation of certain series," Dr Popov said. "It will be of interest to me to become acquainted with methods of present research(in America)and an exchange of ideas." Dr Popov is the author of35publications on special functions and differential equations and has published a textbook on calculus. He received his doctorate from the University of Skopje and has taught there since. He did postdoctoral work at the University of Paris and the University of Hamburg. Dr Popov will give a seminar talk on his research at a time to be announced, according to Professor Henry W Gould of the West Virginia University Department of Mathematics who is acting as host for the National Academy of Sciences.

Virginia Kiryakova also writes about Popov's importance to Bulgarian mathematics [3]:-The Macedonian mathematicians faithfully recognize Professor Blagoj Popov as a founder, together with Professor Dragoslav Mitrinovič(his Ph.D. adviser), of Mathematical Analysis in Macedonia. His research interests and numerous publications(more than70)are in the areas such as functions of complex variables and algebraic calculus, and, in particular, in the field of differential equations and special functions related to them. He had the chance to specialize and develop himself as a scientist, and to play his pioneering role in Macedonia at the time when this field became particularly important for the applications of mathematics to Engineering and Physics; the time of the first electrotechniques(related to systems of linear differential equations), rocket techniques(differential equation with variable mass), nuclear energy problems(special functions and differential equations of mathematical physics), control theory, etc. Nowadays, looking back at the list of his publications, it appears that there is no kind of differential equation or special function that has not been studied by him! He had investigated: the equation of ballistics, the hypergeometric, Riccati, Legendre, confluent hypergeometric, Bessel, Weber, Hermite, Darboux, Whittaker, and Laplace differential equations; orthogonal polynomials, Legendre, Gegenbauer, Jacobi, Hermite, Laguerre, Bernoulli, Bessel, and Chebyshev polynomials, the associate spherical Legendre functions, the ultraspherical polynomials, the generalized Legendre and q-Appell polynomials.

Popov received other honours such as on the occasion of the 40th anniversary of the Macedonian Academy of Sciences and Arts in November 2007, he was decorated with the Order of Merit of the Republic of Macedonia for his "rich scientific and research work."For the Bulgarian mathematical audience, it is a great honour that Academician Blagoj Popov had been introduced to mathematical sciences during his studies in Sofia University, by our classical mathematicians, then being his lecturers in the Department of Physics and Mathematics. In the post-war years which saw the establishment and development of a new era for mathematical sciences in Balkan countries, Academician Blagoj Popov was in close collaboration with our older Bulgarian teachers and colleagues, both officially in the context of the Balkan Mathematical Union as well as on the basis of personal friendship. After a period of inactivity for the Balkan Mathematical Union, lasting more than a decade, after the political and structural changes since1989the Mathematical Societies of the Balkan countries decided to revive the activities of the Balkan Mathematical Union and to establish a new organization, called "Mathematical Society of South-Eastern Europe." In September2003in the Bulgarian winter resort Borovets, the first Congress of the Mathematical Society of South-Eastern Europe was held. At this Congress, Academician Blagoj Popov was honoured with the title of Foreign Fellow of the Union of Bulgarian Mathematicians, and during the Ohrid conference, on the occasion of his85th anniversary, I had the pleasure to hand him another Bulgarian distinction, namely an Honorary Medal with a ribbon of the Union of Bulgarian Mathematicians, for his essential contribution to the development and collaboration between the mathematical societies of the countries in South-Eastern Europe.

Following Popov's death on 30 October 2014, a joint commemorative session of the Macedonian Academy of Sciences and Arts and the Faculty of Natural Sciences and Mathematics of the Saints Cyril and Methodius University of Skopje was be held on Tuesday 4 November 2014 followed by his burial in the City Cemetery "Butel", the largest cemetery in Skopje.

**Article by:** *J J O'Connor* and *E F Robertson*

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