## Béla Csákány - Obituary

BÉLA CSÁKÁNY (1932-2022)

Béla Csákány was born in Karcag, Hungary, on the 18th of September, 1932. He spent most of his childhood in Gyula, and graduated from high school there in 1950. He applied to the University of Debrecen to study chemistry and later to the University of Szeged to study law. Both applications were successful, yet he started his studies in 1951 as a mathematics and physics major at the University of Szeged. (In this year, the medical college split off as an independent university, and the remaining part was still called the University of Szeged until 1962, when it became Attila József University.) Béla Csákány graduated in 1955 as a mathematics and physics major with concentration in mathematics and physics education, and in 1957 he started to work as an assistant professor at the Department of Algebra and Number Theory of the Bolyai Institute of the University of Szeged. In 1958 he started a three-year stay at the Lomonosov State University in Moscow, studying under the supervision of the renowned algebraist A. G. Kurosh. After returning to Szeged, he received the degree “Candidate of Sciences” (CSc, higher than a PhD) in 1962, and was promoted to associate professor in 1964. In 1975 he received the degree “Doctor of Sciences” (DSc) in mathematics, and became a full professor in 1976. During the 1980’s and 1990’s he spent several months in Canada, Germany and the United States of America as a visiting researcher or visiting professor. Upon his retirement in 2002, he received the title Professor Emeritus from the University of Szeged.

Béla Csákány had an enviably wide range of knowledge in literature, philosophy and the sciences, he was well-informed, and had a broad vision. He often wove interesting facts from history or science into his mathematical lectures. He was an outstanding teacher. Generations of students were inspired by his lectures and his textbook (written in Hungarian) to study algebra. He introduced a large number of young people into mathematical research, and twelve students completed their PhDs under his supervision. More than half of the present members of the Department of Algebra and Number Theory are his “mathematical descendants”. He became the chair of the department in 1968, taking over the position from László Rédei, and led the department until 1993, except for a two-year interruption. Béla Csákány established a strong research group in general algebra in Szeged; by the mid 1980’s Szeged became an internationally recognized center of research in general algebra. This is partly also due to the series of algebra conferences in Szeged, initiated by Béla Csákány in 1971. Since then, there have been many more algebra conferences in Szeged, three of which were dedicated to his 70th, 75th, and 80th birthdays.

He also served in top leadership positions at Attila József University, Szeged: between 1969 and 1972 he was a vice rector, while between 1985 and 1990 he was the rector of the university. These years – around the fall of the communist regime – were quite eventful, and Béla Csákány has made significant contribu tions to starting the processes that later led to substantial structural changes within the university. In 1986 he invited the rectors of several major universities of Hungary (from Budapest, Pécs and Debrecen) to Szeged. This informal meeting may be considered as a precursor of the Hungarian Rectors’ Conference, founded in 1988. He was also among the founders of the Szeged Council for Higher Education – the first step towards the integration of all institutes of higher education in Szeged – which eventually culminated in (re)establishing the University of Szeged in 2000. Further developments during the period when he was the rector of the university include the establishment of a new dormitory and the Institute of Informatics. Béla Csákány was among the founding members of the Foundation for the Szeged Observatory, and provided substantial help in raising funds for building the observatory, which opened in 1992. (The telescope itself was already received in 1985 from a partner university in Odessa, but it could not be set up in Szeged due to the lack of a suitable building.)

Béla Csákány was also active in the broader scientific community in Hungary: he was a member of the János Bolyai Mathematical Society for 60 years, and served several terms as a member of the Committee for Scientific Degrees in Mathematics and the Mathematical Committee of the Hungarian Academy of Sciences. His scientific and public activities were recognized by numerous awards. Some of the most significant awards he received are the following: Tibor Szele Medal of the János Bolyai Mathematical Society (1981), Award of the Hungarian Academy of Sciences (1994), Albert Szent-Györgyi Award of the Ministry of Education (1996), Béla Szőkefalvi-Nagy Award of the Foundation for Szeged (2002), Pro Universitate Award of the University of Szeged (2002), József Eötvös Wreath of the Hungarian Academy of Sciences (2005), and the Béla Szőkefalvi-Nagy Medal of the Bolyai Institute (2006).

In research, his main field of interest was the theory of general algebraic systems. He obtained pioneering results on characterizing varieties of modules and related varieties (e.g., varieties of semimodules and varieties of affine modules) in a language-independent way, using only algebraic properties. One of the consequences of these theorems is his joint result with László Megyesi, stating that the variety of idempotent medial quasigroups is essentially the variety of affine $R$-modules for the ring \(R = \mathbb{Z}\)[x, 1/x, 1/(1 − x)]. In the mid 1960’s, he carried out a systematic investigation of “Abelian properties”, which were motivated by his work on module varieties, and preceded the birth of commutator theory for general algebras by about a decade. In 1970, he was one of three authors who independently published Mal’tsev conditions characterizing congruence regularity, and he also proved Mal’tsev or Mal’tsev-like characterizations for a number of other properties of varieties. In the late 1970’s he became interested in finite algebras and clones on finite sets. With his results on homogeneous algebras he initiated the study of the question: Under what symmmetry assumptions is it true that almost all finite symmetric algebras are functionally complete? His results in clone theory include a complete description of all minimal clones on a three-element set, a complete description of two of the three non-unary types of conservative minimal clones on arbitrary finite sets of size > 2, and completeness theorems for co-clones.

Later in his life he became interested in mathematical games (he was an excellent chess player from his youth), he has joint publications with his wife, Rozália Juhász, on this topic. He also created a new undergraduate course about discrete mathematical games, and wrote a textbook for the course. He taught and popularized mathematics outside of the university, too. He published several papers in the mathematics education journal *Polygon* of the Bolyai Institute, he gave presentations at popular math events at the university, and he was a member and lecturer of the Wesselényi Folk College at Zsombó for decades. Besides mathematics, he was also interested in the history of mathematics and in the history of Szeged, publishing articles in local journals. The history of the Bolyai Institute, which he wrote jointly with Antal Varga, is posted on the web site of the institute. His hobbies included collecting and making boomerangs, gardening, and hiking. His greatest hiking accomplishment is that he climbed Mount Kilimanjaro in 1996, at the age of 63!

With the passing of Béla Csákány, we lost a great scientist, teacher, and colleague. We will miss the serenity and wisdom manifesting in his comments. He was able to make interesting and valuable contributions to any discussion on any topic, sharing with us pieces of his extensive knowledge.