National Institute of the Republic of Serbia

Slaviša Prešić (Kragujevac, 1933 - 2008) was a prominent Serbian mathematician, educator thinker and the professor at the Faculty of Mathematics of the University of Belgrade.

After completing the grammar school in Kragujevac, he started in 1952 the studies of mathematics at the Faculty of natural sciences and mathematics of the University of Belgrade. His complete academic and scientific career is associated with this Faculty. He graduated there in 1958 and immediately after graduation he became an assistant of Professor Dragoljub Marković who had great merits for introducing modern algebra at the Mathematical Department. Very soon Professor Marković allowed his young and talented assistant to read lectures on algebra. In meantime he earned there his doctorate in 1963 with the thesis "Contribution to the theory of algebraic structures" and soon he was elected for an associated professor. After Professor Marković's death in 1965, the Chair of Algebra was founded and Prešić became the head of the Chair continuing to be in charge of ever since that time. At the beginning of seventies Prešić introduced in undergraduate studies а course of mathematical logic, and since then the Chair carries the name "the Chair of Algebra and Logic". He became an associate professor in 1970 and a full professor in 1979. He stayed at the Faculty until his retirement in 2000.

He was also part-time member of Mathematical institute SASA participating in his activities and management. He was member of its Scientific Committee during the periods of 1966-1968, 1970, 1972-1991 and 1993-1997, also chairman of the Mathematics Colloquium from 13. 9. 1984 till 1.2. 1989. and chairman of the Seminar for Mathematical Logic from its inception untill 1977. Until 2004, he was in editorial board of the journal Publications de l'Institut Mathématique.

Professor Prešić was a suspicious person, not giving much attention to the authorities. He did not liked routine and straightforward, neither lengthy and complicated proofs. This distinctive features form the basis of Prešić's entire work: his research, his books, his public speeches, no matter where they were made - at scientific conferences, expert meetings or popular talks. In his scientific papers and books we often come across completely new ideas and original ways of solving mathematical problems. Mathematics, as well as other modern sciences, is characterized by а complicated and complex language. Even а good mathematician finds it difficult to adequately present results to the general public, as the main ideas often remain hidden under the heavy garment of technicalities and formalities. Prešić's language was clear and direct. His public speeches and discussions are remembered not only thanks to the picturesque and vital language with the help of which he immediately presents to the audience the essence of some mathematical problem or theory, but also thanks to his open criticism, а criticism without а compromise, of something that is not valid in mathematics. On such occasions the audience never remained indifferent. The discussion would become heated, with sharp remarks and plenty of enthusiasm. His opponents used to stay after the lecture "to see the matter through", and they often left with their opinion changed or at least less convinced that their point of view was right.

Another feature of Prešić's works is originality. His novelties had in several cases resulted in completely new methods and theories. An example of this kind is the reproductivity theory as one of the rare universal methods in solving general equations. Prešić showed how the reproductivity method is fruitful in the theory of functional equations, Boolean algebras and finite structures. His contributions are included into world famous monographs dealing with functional equations theory and Вoolean algebras (М. Kuczma, S. Rudeanu). Another example is the method of solving а system of equations in real unknowns, known as М-m calculus. Prešić developed this theory at the end of the eighties and at the beginning of the nineties of the XX century. The method is applicable to а wide class of equation systems, including all equations of the algebraic type and many classes of transcendental equations. In principle, the solving procedure is based on exhaustion method, and uses specific features of functions of bounded variation. The idea of the method consists in exhausting subsets of the domains which do not contain а solution, so that what is left over in the limit is the solutions of the system.

Prešić also successfully worked in the theory of polynomials, theory of quasigroups, universal algebras, theory of fixed points and field of artificial intelligence. The results of his research were cited by leading authorities in various mathematical disciplines, such as Р.М. Cohn in universal algebra, S. Rudeanu in Boolean algebra, and М. Kuczma in functional equations theory. In our country (and former Yugoslavia) а large number of mathematicians studied and developed Prešić's results in their research papers, books, MSc and PhD theses. We have every right to say that professor Prešić belongs to the narrow circle of our mathematicians who influenced considerably the development of modern mathematics in this country. Prešić also had other important activities in Serbian mathematics, particularly in mathematical logic. In the early sixties of the last century Profesor Prešić founded the Seminar of mathematical logic of the Mathematical Institute SASA. This is the oldest seminar of the Mathematical Institute and dozens of mathematicians from Serbia and the former Yugoslavia took part in its work. The chronicles of the Mathematical Institute say that among the guests at this seminar were the most prominent logicians and other mathematicians from the world: L. Henkin, Ј. Keisler, А.V. Arhangelski, М. Magidar, Т. Jech, К. Devlin, Van Benthem, S. Negrepantis, А. Dragalin, .... Within the limits of the seminar program numerous specialized courses were held, which embraced almost all disciplines of mathematical logic. Every MSc or PhD candidate that specialized in logic and algebra had to report his main results at the seminar before the formal defense of their thesis. About ten members of the seminar, the farmer students of professor S. Presic or students of his students, are now respectable professors at well-known universities in the USA, Canada and France. Let us also mention that at least 14 PhD theses and about 20 MSc theses were defended under professor S. Prešić's supervision.

Slaviša Prešić was also involved in various forms of social activities. For two years (1978-80) he was director of the Institute of Mathematics. In the period 1972-76 he was a member of the Educational Council of the Republic of Serbia and the President of the Commission for mathematics when he was the creator and one of the main active participants in the development of modern mathematics curricula for primary and secondary schools. For years he worked in the Mathematical Institute: he was President of the Council, a member of the Scientific Council, a project leader in the fields of mathematical logic, algebra and artificial intelligence. Finally, for years he was a member of the editorial board of the leading Serbian mathematical journal Publications de l'Institut Mathématique.

Prešić was the recipient of notable Humboldt scholarship (1971). Besides Germany, in the period 1970-2000 he also visited the following institutions and delivered there talks: the University of California at Berkeley, the Courant Institute in New York, New York University, Athens University and MGU in Moscow. Profesor Prešić published more than 50 scientific papers and about 20 books in mathematics or related to mathematics.

Source: А tribute to S. В. Prešić: Papers celebrating his 65th birthday, Aleksandar Krapež, ed., Beograd, Matematički institut SANU, 2001. (http://elibrary.matf.bg.ac.rs)

His bibliography is found here.

Authors: Mijajlović, Žarko