We report with great sadness the passing away of Gyorgy Elekes, professor of the Department of Computer Science.

The mathematical talent of Elekes showed early. Between 1963 and 1967 he was a student of Károly Kõváry, the fine mathematics teacher of the renowed Fazekas Highschool, Budapest. In 1965 and 1967, he won third, and then first prize at the International Mathematical Olimpiade. He won second prize at the József Kürschák Memorial Contest in 1966.

Between 1967 and 1972 Elekes studied mathematics at the Roland Eötvös University. After graduation, he stayed at the university, earlier at the Analysis I Department (until 1980 as a Lecturer, then as an Assistant Professor), in 1983 he became one of the founding members of newly set up Department of Computer Science (until 1995 as an Assistant Professor, then till 2005 as an Associate Professor, after that as a Full Professor). He obtained the Dr. Rher. Nat. degree in 1978, the Candidate of Mathematical Sciences degree in 1994, and the Doctor of Mathematical Sciences title in 2001. He received a Szechenyi Fellowship between 1999-2002.

The in-depth study of his research contributions is a task of the future, here we give a short overview only.

Elekes started doing research in set theory. He solved a problem of Erdõs and Hajnal on partitions of infinite sets, which lead to the development (in part with Erdõs and Hajnal) of a new branch of combinatorial set theory. (Many of their results are still unpublished.)

Another important result is his theorem with György Hoffmann stating that there are almost-disjoint set systems with arbitrarily large chromatic number.

In all his life, Elekes was deeply interested in geometry, and from the 1970s, in the newly developed complexity theory. He proved a major result in the theory of geometric algorithms. With the application of an elegant new inequality, he proved that the volume of a convex body in general dimension can only be estimated with very large error in polynomial time. This paper initiated several branches of important research.

His interest in geometric algorithms motivated his teaching as well: he created the curriculum of this topic at the Eötvös University. He did, however, change his research profile in the 1980s, and became interested in combinatorial geometry—another topic invented by Erdõs. He discovered important connections to other branches of mathematics, in particualr number theory, and his research area became what is now known as additive combinatorics. He gained significant fame in this very active topic where several Fields Medalists and other leading researchers in number theory and combinatorics work. Elekes not only proved hard theorems, but succesfully discovered the algebraic structures hidden in the background of some combinatorial phenomena.

György Elekes was an outstanding teacher, who considered teaching his most noble task. His students loved him as teacher and as a person. He spent a lot of time writing and rewriting teaching resources, trying to find the best presentation of thoughts, examples, details.

During his fight with his illness, almost one year long, he closely followed the issues of the Institute, of teaching, and of research, and tried to participate in them. He worked on his papers as long as his strength allowed him.

He was good friend of many, and a good colleague of us all. We will sorely miss his knowledge and his deep devotion to teaching.

Department of Computer Science, Mathematical Institute

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